Gang Tao's Adaptive Control Books

[1] Adaptive Control of Systems with Actuator and Sensor Nonlinearities

[2] Adaptive Control of Nonsmooth Dynamic Systems

[3] Control of Sandwich Nonlinear Systems

[4] Adaptive Control Design and Analysis

[5] Adaptive Control of Systems with Actuator Failures

[6] Advances in Control Systems Theory and Applications

[7] F. Y. Chen, G. Tao and B. Jiang, Adaptive Control, Science Press, Beijing, 2015.

[8] R. Y. Qi, G. Tao and B. Jiang, Fuzzy System Identification and Adaptive Control, Springer, 2019.

[9] D. Deb, J. O. Burkholder and G. Tao, Adaptive Compensation of Nonlinear Actuators for Flight Control Applications, Springer, 2022.

Aaptive Control of Systems with Actuator and Sensor Nonlinearities

Gang Tao and Petar Kokotovic

(published by John Wiley & Sons, 1996; ISBN 0-471-15654-X; TJ217.T36 1996)


Errata: errata.pdf


Imperfections of system components, especially those of actuators and sensors, are among the factors that severely limit the performance of feedback control loops, the vital parts of industrial automation, consumer electronics, and defense and transportation systems. Most often, a critical imperfection is a nonlinearity which is poorly known, increases with wear and tear, and varies from component to component. Components without such imperfections are costly to manufacture, and their maintenance usually requires specialized personnel.

It is appealing to think of more intelligent approaches to increase the accuracy achievable with imperfect, but sturdy and inexpensive components. Can the control system, after a period of learning or adaptation, recognize the imperfection and compensate for its harmful effects? With such adaptive controllers, the component specifications could be greatly relaxed, their cost reduced, and their reliability increased.

This book points to a direction in which this goal can be achieved for some of the most common component imperfections: dead-zone, backlash, and hysteresis. These ``hard'' nonlinearities are ubiquitous in a wide variety of components: mechanical, hydraulic, pneumatic, magnetic, piezoelectric, etc. They often serve as aggregate representations of more complex microscopic phenomena: friction, viscosity, elasticity, etc. While the ``hard'' nonlinearities have all but disappeared from the academic texts, they have become more common in engineering practice, because feedback controls have entered many new areas of applications. In particular, control systems have contributed to recent dramatic increases in fuel efficiency, drivability, and safety of passenger cars. Such successful applications show that it is more rational to improve performance with control algorithms than with more expensive mechanical components. The adaptive inverse methodology presented in this book is aimed in this direction.

The nonlinearities in this book are approximated by piecewise linear characteristics. A difficulty with such characteristics is that they have break-points, so that they are not differentiable. Existing adaptive control techniques are not applicable to such nonlinearities. However, a major advantage of the piecewise linear characteristics is that they admit linear parametrization with unknown break-point and slope parameters. This property is crucial for effective design and implementation of robust adaptive control, one of the main subjects of this book. The unifying theme of the book is its adaptive inverse approach. Not only are the nonlinear characteristics linear in their parameters, but so are their inverses, which, in the case of dead-zone and backlash, are discontinuous. While the inverses of the actuator nonlinearities are explicit, those of the sensors have a more complicated implicit form. The essence of the adaptive inverse approach is that, upon an adaptation transient, the inverse cancels the effects of the unknown nonlinear characteristic. In this way a significant improvement of accuracy and performance is achieved with inexpensive components. In other words, the adaptation in the controller has ``removed'' the imperfection of the component.

All the results in this book are new and have evolved from the recent journal papers of the authors. The style of presentation is aimed at an audience of practicing engineers and graduate students in electrical, mechanical, chemical, aeronautical, and computer engineering departments, as well as those pursuing interdisciplinary studies such as biomedical engineering. The assumed background is a standard course in control theory, while the required knowledge of model reference adaptive control is concisely presented in Appendix A.

Our interest in the problem of adaptive compensation of ``hard'' nonlinearities was ignited by Jim Winkelman and Doug Rhode, our colleagues at Ford Motor Company. Several years ago, they presented to us and Darrel Recker (then a Ph.D. student, now a researcher at Ford) a problem with a hydraulic valve dead-zone in an automotive suspension system. The dead-zone's purpose was to prevent the leakage and maintain the height when the car was parked and the engine was turned off. However, when the suspension was active, the effect of the dead-zone was harmful. In his Ph.D. thesis, Darrel Recker addressed the problem of using adaptation to remove the harmful effects of the dead-zone. His successful algorithms and experiments have encouraged us to pursue a broader investigation in this direction. We acknowledge with gratitude the pioneering contributions of Darrel Recker and his cooperation in this project. We also greatly benefited from the experience of Doug Rhode and Jim Winkelman. For our understanding of hydraulic components we are indebted to Vladimir Kokotovic, also at Ford. For many years we have been inspired and helped by Petros Ioannou, University of Southern California, without whose vast knowledge of robust adaptive control a project like this would not have been possible. With their patience and understanding our wives, Lanlin and Anna, generously contributed to the writing of this book.

Our research summarized in this book was not only initiated, but also financially supported by, the Ford Motor Company. It was also supported by the National Science Foundation grant ECS-9203491 and RIA ECS-9307545 and by the Air Force Office of Scientific Research grant F-49620-92-J-0495.

Gang Tao
Charlottesville, Virginia

Petar Kokotovic
Santa Barbara, California


Chapter 1 shows the evolution of the new adaptive inverse approach.

Chapter 2 explains the importance and relevance of the control problem with nonsmooth nonlinearities.

The key component of the proposed approach, the inverse, is introduced in Chapter 3, for an actuator nonlinearity.

Control designs with a fixed inverse, exact or detuned, continuous-time or discrete-time or hybrid, are developed in Chapter 4 for systems with actuator nonlinearities.

Like neither an exact inverse which needs the nonlinearity knowledge nor a detuned inverse which results in a compensation error, an adaptive inverse, introduced in Chapter 5, is able to adaptively cancel the effects of an unknown nonlinearity.

With such an adaptive inverse, adaptive inverse controllers are designed in Chapter 6 in continuous time and in Chapter 7 in discrete time, for systems with actuator nonlinearities.

A sensor nonlinearity is more difficult to deal with, as indicated in Chapter 8, where a more sophisticated inverse design is also presented to achieve the desired output matching.

Chapter 9 develops adaptive inverse control designs for systems with sensor nonlinearities.

With partial system knowledge, the order of an adaptive control design can be reduced and the performance can be improved, as shown in Chapter 10.

As a further development of the adaptive inverse approach, Chapter 11 has the desired inverse control designs for a class of sandwich nonlinear systems, those with both actuator and sensor nonlinearities.

Appendix A summarizes the model reference adaptive control theory in a unified and compact form for both the continuous-time and discrete-time designs with new proofs of the desired stability and tracking properties.

The closed-loop signal boundedness with an adaptive inverse controller is proved in Appendix B for the continuous-time case, in Appendix C for the discrete-time case, and in Appendix D for sensor nonlinearity cases.

Bibliography has the most important references, in particular, the complete collection of the recent results, in the related research areas.

Finally, Index helps locating many new concept items used throughout the book.

Adaptive Control of Nonsmooth Dynamic Systems

Gang Tao and Frank F. Lewis, Eds.

(published by Springer, 2001; ISBN 1-85233-384-7; TJ217.A319 2001)


Nonsmooth nonlinearities such as backlash, dead-zone, component failure, friction, hysteresis, saturation and time delays are common in industrial control systems. Such nonlinearities are usually poorly known and may vary with time, and they often limit system performance. Control of systems with nonsmooth nonlinearities is an important area of control systems research. A desirable control design approach for such systems should be able to accommodate system uncertainties. Adaptive methods for the control of systems with unknown nonsmooth nonlinearities are particularly attractive in many applications because adaptive control designs are able to provide adaptation mechanisms to adjust controller parameters in the presence of parametric, structural and environmental uncertainties. Most adaptive or nonlinear control techniques reported in the literature are for linear systems or for some classes of systems with smooth nonlinearities, but not for nonsmooth nonlinearities. The need for effective control methods to deal with nonsmooth nonlinear systems has motivated growing research activities in adaptive control of systems with such common practical nonsmooth nonlinearities. Recently, there have been many encouraging new results on adaptive control problems with backlash, dead-zone, failures, friction, hysteresis, saturation, and time delays. This book, entitled Adaptive Control of Nonsmooth Dynamic Systems , is aimed at reflecting the state of the art in designing, analyzing and implementing adaptive control methods which are able to accommodate uncertain nonsmooth nonlinearities in industrial control systems.

Backlash, dead-zone, component failure, friction, hysteresis, saturation, and time delays are the most common nonsmooth nonlinearities in industrial control systems. Backlash, a dynamic (with memory) characteristic, exists in mechanical couplings such as gear trains, and always limits the accuracy of servo-mechanisms. Dead-zone is a static input-output relationship which for a range of input values gives no output; it also limits system performance. Dead-zone characteristics are often present in amplifiers, motors, hydraulic valves and even in biomedical actuation systems. Failures of different types in actuators, sensors and other components of a control system can cause major system performance deterioration. Friction exists wherever there is motion or tendency for motion between two physical components. Friction can cause a steady-state error or a limit cycle near the reference position and stick-slip phenomenon at low speed in the conventional linear control of positioning systems.

Hysteresis, another dynamic characteristic, exists in electromagnetic and piezoelectric actuators which are used for micromotion control and high-accuracy positioning. Saturation is always a potential problem for actuators of control systems---all actuators do saturate at some level. Actuator saturation affects the transient performance and even leads to system instability. Time delays are also important factors to deal with in order to improve control system performance such as for teleoperations and in real-time computer control systems.

Although backlash, dead-zone, failure, friction, hysteresis, saturation, and time delay characteristics are different, they are all nonsmooth in nature. Therefore, most existing adaptive control methods are not applicable. Unfortunately these nonlinearities can severely limit the performance of feedback systems if not compensated properly. Moreover, adaptive control of dynamic systems with each of these nonsmooth characteristics is a control problem that needs a systematic treatment. It makes the control problem even more challenging when there are more than one nonlinear characteristic present in the control system.

In this book it will be shown how nonsmooth nonlinear industrial characteristics can be adaptively compensated and how desired system performance is achieved in the presence of such nonlinearities. The book has 16 chapters on issues including system modeling, control design, analysis of stability and robustness, simulation and implementation:

Chapter One:
New Models and Identification Methods for Backlash and Gear Play, by M. Nordin, P. Bodin and P.-O. Gutman

Chapter Two:
Adaptive Dead Zone Inverses for Possibly Nonlinear Control Systems, by E.-W. Bai

Chapter Three:
Deadzone Compensation in Motion Control Systems Using Augmented Multilayer Neural Networks, by R. R. Selmic and F. L. Lewis

Chapter Four:
On-line Fault Detection, Diagnosis, Isolation and Accommodation of Dynamical Systems with Actuator Failures, by M. A. Demetriou and M. M. Polycarpou

Chapter Five:
Adaptive Control of Systems with Actuator Failures, by G. Tao and S. M. Joshi

Chapter Six:
Multi-mode System Identification, by E. I. Verriest

Chapter Seven:
On Feedback Control of Processes with ``Hard'' Nonlinearities, by B. Friedland

Chapter Eight:
Adaptive Friction Compensation for Servo Mechanisms, by J. Wang, S. S. Ge and T. H. Lee

Chapter Nine:
Relaxed Controls and a Class of Active Material Actuator Models, by A. Kurdila

Chapter Ten:
Robust Adaptive Control of Nonlinear Systems with Dynamic Backlash-like Hysteresis, by C.-Y. Su, M. Oya and X.-K. Chen

Chapter Eleven:
Adaptive Control of a Class of Time-delay Systems in the Presence of Saturation, by A. M. Annaswamy, S. Evesque, S.-I. Niculescu and A. P. Dowling

Chapter Twelve:
Adaptive Control for Systems with Input Constraints: A Survey, by J.-W. John Cheng and Y.-M. Wang

Chapter Thirteen:
Robust Adaptive Control of Input Rate Constrained Discrete Time Systems, by G. Feng

Chapter Fourteen:
Adaptive Control of Linear Systems with Poles in the Closed Left Half Plane with Constrained Inputs, by D. A. Suarez-Cerda and R. Lozano

Chapter Fifteen:
Adaptive Control with Input Saturation Constraints, by C.-S. Zhang

Chapter Sixteen:
Adaptive Control of Linear Systems with Unknown Time Delay, by C.-Y. Wen, Y.-C. Soh and Y. Zhang

The authors of the chapters in this book are experts in their areas of interest and their chapters present new solutions to important issues in adaptive control of industrial systems with nonsmooth nonlinearities such as backlash, dead-zone, failure, friction, hysteresis, saturation, and time delay. These solutions result from recent work in these areas and are believed to be attractive to people from both academia and industry. Adaptive control of nonsmooth dynamical systems is theoretically challenging and practically important. This book is the first book on adaptive control of such systems, addressing all these nonsmooth nonlinear characteristics: backlash, dead-zone, failure, friction, hysteresis, saturation and time delays. Such a book is also aimed at motivating more research activities in the important field of adaptive control of nonsmooth nonlinear industrial systems.

Recent advances in adaptive control of nonsmooth dynamic systems have shown that those practical nonsmooth nonlinear characteristics such as backlash, dead-zone, component failure, friction, hysteresis, saturation and time delays can be adaptively compensated when their parameters are uncertain, as is common in real-life control systems. Rigorous designs have been given for selecting desirable controller structures to meet the control objectives and for deriving suitable algorithms to tune the controller parameters for control of systems with uncertainties in dynamics and nonsmooth nonlinearities. There have been increasing interest and activities in these areas of research, as evidenced by recent conference invited sessions and journal special issues on related topics. It is clear that this is a promising direction of research and there have been many encouraging results. Given the practical importance and theoretical significance of such research, it is time to summarize, unify, and develop advanced techniques for adaptive control of nonsmooth dynamic systems.

Since this book is about some important and new areas of adaptive control research, its contents are intended for people from both academia and industry, including professors, researchers, graduate students who will use this book for research and advanced study, and engineers who are concerned with the fast and precision control of motion systems with imperfections (such as backlash, dead-zone, component failure, friction, hysteresis, saturation and time delays) in mechanical connections, hydraulic servovalves, piezoelectric translators, and electric servomotors, and biomedical actuators systems. The book can be useful for people from aeronautical, biomedical, civil, chemical, electrical, industrial, mechanical and systems engineering, who are working on aircraft flight control, automobile control, high performance robots, materials growth process control, precision motor control, radar and weapons system pointing platforms, VLSI assembly. The adaptive system theory developed in this book is also of interest to people who work on communication systems, signal processing, real-time computer system modeling and control, biosystem modeling and control.

The first editor would like to gratefully acknowledge the partial support from National Science Foundation under grant ECS-9619363 and National Aeronautics and Space Administration under grant NCC-1342 to this project. He would also like to thank his graduate student Xidong Tang for his editorial assistance on this project. The second editor acknowledges the vital support of the Army Research Office under grant DAAD19-99-1-0137.

Gang Tao
Charlottesville, Virginia

Frank L. Lewis
Fort Worth, Texas

Control of Sandwich Nonlinear Systems

Avinash Taware and Gang Tao

(published by Springer, 2003; ISBN 3-540-44115-8; TA 342.T43)


The control problem: control of sandwich nonlinear dynamic systems is addressed in this monograph. Of interest are sandwiched nonsmooth nonlinearities such as dead-zone, hysteresis and backlash between dynamic blocks. Some continuous-time control designs are proposed. A framework for hybrid control is developed to design control schemes for different cases of the control problem with required modifications. Friction compensation is addressed for systems with sandwiched friction along with sandwiched dynamics. The problem of control of sandwich nonlinear systems with uncertain actuator failures is introduced, and an adaptive control solution scheme is developed for this problem. An optimal and nonlinear control solution is proposed for control of multi-body, multi-input and multi-output nonlinear systems with joint backlash, flexibility and damping.

The proposed hybrid control framework employs an inner-loop discrete-time feedback design and an outer-loop continuous-time feedback design, combined with a nonlinearity inverse to cancel the nonlinearity effect, for improving output tracking. The first control design using this framework is a nominal one with an exact nonlinearity inverse, which establishes a basic solution to the stated control problem. The second design is an adaptive one which employs an adaptive inverse to cancel the unknown sandwiched nonlinearity effect for improving output tracking. The third one is also an adaptive one using the framework with a neural network based inverse compensator. The adaptive inverse is updated from an adaptive law. The neural network based nonlinearity compensator consists of two neural networks, one used as an estimator of the sandwiched nonlinearity function and the other for the compensation itself. The compensator neural network has neurons that can approximate jump functions such as a dead-zone inverse. The weights of the two neural networks are tuned using a modified gradient algorithm. For an adaptive inverse or neural network based inverse, a control error equation is derived based on which a desirable tracking error equation is obtained for an adaptive update or tuning law design. Stability and tracking performance of the closed-loop control system are analyzed. Simulations are used to illustrate the effectiveness of the proposed hybrid control designs.

Friction compensation is addressed for a benchmark sandwich system having sandwiched friction between linear dynamic blocks as illustrated by a two-body system with load friction plus joint flexibility and damping. Several non-adaptive and adaptive compensation designs are analyzed, based on a Model Reference Adaptive Control (MRAC) scheme that uses static state feedback for control and dynamic output feedback for parameter adaptation to achieve output tracking. When applied to the benchmark system, necessary and sufficient output matching conditions are derived for friction compensation. Approximate linear parametrizations of nonlinear friction are developed for adaptive friction compensator designs. The control problem for a sandwich nonlinear system with friction sandwiched in between linear and nonlinear dynamics is also addressed. Whenever load velocity is nonzero, adaptive linearizing control is designed for such an unknown system with unknown friction. This linearizing control has a contributing adaptive term that compensates for the estimated friction. In the case the load velocity is zero, a maximum-magnitude controller is employed to overcome static friction effects. The proposed adaptive friction compensation control schemes promise to bring considerable improvements to the system performance.

Adaptive tracking control of sandwich nonlinear systems with actuator failures is formulated and several suitable control designs are developed, including an adaptive state feedback control scheme to achieve state tracking, and an adaptive output feedback controller for output tracking for linear time-invariant plants with input actuator nonlinearities and failures. Conditions and controller structures for achieving plant-model state or output matching in the presence of actuator failures and nonlinearities are presented. Adaptive laws are designed for updating the controller parameters when both the plant parameters, actuator nonlinearities and actuator failure parameters are unknown. Adaptive inverse compensation is employed for the unknown actuator nonlinearities. The effectiveness of the proposed adaptive designs is illustrated with simulation results.

An optimal and nonlinear solution scheme is proposed for control of multi-body, multi-input and multi-output nonlinear systems with joint backlash, flexibility and damping, represented by a gun turret-barrel model which consists of two subsystems: two motors driving two loads (turret and barrel) coupled by nonlinear dynamics. The key feature of such systems is that the backlash is between two dynamic blocks. Optimal control schemes are employed for backlash compensation and nonlinear feedback control laws are used for control of nonlinear dynamics. When one load is in contact phase and the other load is in backlash phase, a feedback linearization design decouples the multivariable nonlinear dynamics so that backlash compensation and tracking control can be both achieved. Nonlinear zero dynamics systems caused by joint damping are bounded-input, bounded state stable so that feedback linearization control designs ensure that all closed-loop signals are bounded and asymptotic tracking is achievable.

We wish to gratefully acknowledge the valuable help rendered by institutions and individuals in our conducting the research presented in this book.

This research was supported in part by the National Science Foundation under grant ECS-9619363, by Techno Sciences Inc. under a US Army subcontract grant, and by NASA Langley Research Center under grant NCC-1342. We would like to thank their financial support that made this research possible. We are also thankful to University of Virginia for a pleasant and supportive environment to do our research.

We would like to express our gratitude to Professor Petar Kokotovic for his encouragement, help and support to this research. We are grateful to Dr. Carole Teolis at Techno-Sciences Inc. for her collaboration and help in conducting this research. We would like to thank Professors Petros Ioannou and Frank Lewis for their interest and comments to this work. We would also like to thank Professors Zongli Lin, Steve Wilson and Jim Aylor for their help to our research. We should mention that the research results on adaptive actuator failure compensation by Shuhao Chen and Xidong Tang, with the valuable help of Dr. Suresh Joshi of NASA Langley Research Center, contributed to the framework used in Chapter 9 of this book for actuator failure compensation schemes for systems with actuator nonlinearities. We would like to recognize the contribution of Xiaoli Ma and Yi Ling to the work reported in Chapter 10 on control of nonlinear systems with joint backlash, flexibility and damping (for which Dr. Kenan Ezal's work also inspired our results), and the contribution of Nilesh Pradhan to the proposed friction compensation designs in Chapters 7 and 8. We would also like to express our appreciation for the helpful comments from anonymous reviewers on this book and our related journal and conference papers which laid down the foundation for this manuscript.

Finally, we would like to thank our families for their love and support without which this project would have never been possibly completed.

Avinash Taware
Schenectady, New York

Gang Tao
Charlottesville, Virginia

Adaptive Control Design and Analysis

Gang Tao

(published by John Wiley & Sons, 2003; ISBN 0-471-27452-6; TJ217.T34 2003)


Additional Notes: notes.pdf

Errata: errata.pdf


Adaptive control is becoming popular in many fields of engineering and science as concepts of adaptive systems are becoming more attractive in developing advanced applications. Adaptive control theory is a mature branch of control theories, and there is a vast amount of literature on design and analysis of various adaptive control systems using rigorous methods based on different performance criteria. Adaptive control faces many important challenges, especially in nontraditional applications, such as real-time systems, which do not have precise classical models admissible to existing control designs, or a physiological system with an artificial heart, whose unknown parameters may change at a heart beat rate which is also a controlled variable. To meet the fast growth of adaptive control applications and theory development, a systematic and unified understanding of adaptive control theory is thus needed.

In an effort to introduce such an adaptive control theory, this book presents and analyzes some common and effective adaptive control design approaches, including model reference adaptive control, adaptive pole placement control, and adaptive backstepping control. The book addresses both continuous-time and discrete-time adaptive control designs and their analysis; deals with both single-input, single-output and multi-input, multi-output systems; and employs both state feedback and output feedback. Design and analysis of various adaptive control systems are presented in a systematic and unified framework. The book is a collection of lectures on system modeling and stability, adaptive control formulation and design, stability and robustness analysis, and adaptive system illustration and comparison, aimed at reflecting the state of the art in adaptive control as well as at presenting its fundamentals. It is a comprehensive book which can be used as either an academic textbook or technical reference for graduate students, researchers, engineers, and interested undergraduate students in the fields of engineering, computer science, applied mathematics and others, who have prerequisites in linear systems and feedback control at the undergraduate level.

In this self-contained book, basic concepts and fundamental principles of adaptive control design and analysis are covered in 10 chapters. As a graduate textbook, it is suitable for a one-semester course: lectures plus reading may cover most of the book without missing essential material. To help in understanding the topics, at the end of each chapter, there are problems related to that chapter's materials as well as technical discussions beyond the covered topics. A separate manual containing solutions to most of these problems is also available. At the end of most chapters, there are also some advanced topics for further study in adaptive control.

Chapter 1 compares different areas of control theory, introduces some basic concepts of adaptive control, and presents some simple adaptive control systems, including direct and indirect adaptive control systems in both continuous and discrete time, as well as an adaptive backstepping control design for a nonlinear system in continuous time.

Chapter 2 presents some fundamentals of dynamic system theory, including system models, system characterizations, signal measures, system stability theory (including Lyapunov stability and input--output operator stability), signal convergence lemmas, and operator norms. In particular, it gives a thorough study of the Lyapunov direct method for stability analysis, some time-varying feedback operator stability properties, several important inequalities for system analysis, some detailed input--output L^p stability results, various analytical L^p signal convergence results, some simplified analytical tools for discrete-time system stability, and multivariable operator norms. These results, whose proofs are given in detail and are easy to understand, clarify several important signal and system properties for adaptive control.

Chapter 3 addresses adaptive parameter estimation for a general linear model illustrated by a parametrized linear time-invariant system in either continuous or discrete time. Detailed design and analysis of a normalized gradient algorithm and a normalized least-squares algorithm in either continuous or discrete time are given, including structure, stability, robustness, and convergence of the algorithms. A collection of commonly used robust adaptive laws are presented which ensure robust stability of the adaptive schemes in the presence of modeling errors. An L^{1+alpha} (alpha >= 1) theory is developed for adaptive parameter estimation for a linear model, revealing some important inherent robustness properties of adaptive parameter estimation algorithms.

Chapter 4 develops two types of state feedback adaptive control schemes: for state tracking and for output tracking (and its discrete-time version). For both continuous- and discrete-time systems, adaptive state feedback for output tracking control, based on a simple controller structure under standard model reference adaptive control assumptions, is used as an introduction to adaptive control of general linear systems. Adaptive disturbance rejection under different conditions is addressed in detail; in particular, adaptive output rejection of unmatched input disturbance is developed based on a derived property of linear systems. Another development is a derived parametrization of state feedback using a full- or reduced-order state observer, leading to the commonly used parametrized controller structures with output feedback.

Chapter 5 deals with continuous-time model reference adaptive control using output feedback for output tracking. The key components of model reference adaptive control theory---a priori plant knowledge, controller structure, plant--model matching, adaptive laws, stability, robustness, and robust adaptation---are addressed in a comprehensive formulation and, in particular, stability and robustness analysis is given in a simplified framework. The plant--model matching equation for a standard model reference controller structure is studied in a tutorial formula. Design and analysis of model reference adaptive control schemes are given for plants with relative degree 1 or larger, using a Lyapunov or gradient method based on a standard quadratic or nonquadratic cost function. For the relative degree 1 case, an L^{1+alpha} (0 < alpha < 1) adaptive control design is proposed for reducing output tracking errors. An L^{1+alpha} (alpha > = 1) theory is developed for adaptive control with inherent robustness with respect to certain modeling errors. Robust adaptive control is formulated and solved in a compact framework. Assumptions on plant unmodeled dynamics are clarified, and robust adaptive laws are analyzed. Closed-loop signal boundedness and mean tracking error properties are proved. To develop adaptive control schemes without using the sign of the high frequency gain of the controlled plant, a modified controller parametrization leads to a framework of adaptive control using a Nussbaum gain for stable parameter adaptation and closed-loop stability and asymptotic output tracking.

Chapter 6 develops a model reference adaptive control theory for discrete-time linear time-invariant plants. A unique plant--model matching equation is derived, with unique controller parameters specified to ensure exact output tracking after a finite number of steps. A stable adaptive control scheme is designed and analyzed which ensures closed-loop signal boundedness and asymptotic output tracking. It is shown that the model reference adaptive control system is robust with respect to L^2 modeling errors and with modification is also robust with respect to L^{1+alpha} (alpha > 1) modeling errors. Thus an L^{1 + alpha} (alpha > = 1) robustness theory is developed for discrete-time adaptive control. Robust adaptive laws are derived for discrete-time adaptive control in the presence of bounded disturbances.

Chapter 7 presents two typical designs (and their analysis) of indirect adaptive control schemes: indirect model reference adaptive control and indirect adaptive pole placement control in both continuous and discrete time. Examples are used to illustrate the design procedures and analysis methods. For indirect model reference adaptive control in continuous or discrete time, a concise closed-loop error model is derived based on which the proof of signal boundedness and asymptotic output tracking is formed in a feedback and small-gain setting similar to that for the direct model reference adaptive control scheme of Chapters 5 and 6. For indirect adaptive pole placement control, a singularity problem is addressed, and closed-loop stability and output tracking are analyzed in a unified framework for both continuous and discrete time. As a comparison, a direct adaptive pole placement control scheme is presented and discussed for its potential to avoid the singularity problem.

Chapter 8 conducts a comparison study of several adaptive control schemes applied to a benchmark two-body system with joint flexibility and damping, including direct state feedback, direct output feedback, indirect output feedback, direct--indirect state feedback, and backstepping state feedback designs, with detailed design and analysis for the last two designs. With different complexity, they all ensure closed-loop signal boundedness and asymptotic output tracking. The design and analysis of the direct--indirect adaptive control scheme demonstrate some typical time-varying operations on signals in time-varying systems.

Chapter 9 first gives the design and analysis of adaptive state feedback state tracking control for multi-input systems. A multivariable state feedback adaptive control scheme is derived using LDU decomposition of a plant gain matrix. Multivariable adaptive control is applied to system identification. This chapter then develops a unified theory for robust model reference adaptive control of linear time-invariant multi-input, multi-output systems in both continuous and discrete time. Key issues such as a priori plant knowledge, plant and controller parametrizations, design of adaptive laws, stability, robustness, and performance are clarified and solved. In particular, an error model for a coupled tracking error equation is derived, a robust adaptive law for unmodeled dynamics is designed, a complete stability and robustness analysis for a general multivariable case is given, and a unified multivariable adaptive control theory is established in a form applicable in both continuous and discrete time. The chapter presents some recent results in reducing a priori plant knowledge for multivariable model reference adaptive control using LDU parametrizations of the high frequency gain matrix of the controlled plant. Model reference adaptive control designs for multivariable systems with input or output time delays are also derived. Different adaptive control schemes, including a variable structure design, a backstepping design, and a pole placement control design for multivariable systems, are presented. Finally, robust adaptive control theory is applied to adaptive control of robot manipulator systems in the presence of parameter variations and unmodeled dynamics.

Chapter 10 presents a general adaptive inverse approach for control of plants with uncertain nonsmooth actuator nonlinearities such as dead-zone, backlash, hysteresis, and other piecewise-linear characteristics which are common in control systems and often limit system performance. An adaptive inverse is employed for cancelling the effect of an actuator nonlinearity with unknown parameters, and a linear or nonlinear feedback control law is used for controlling a linear or smooth nonlinear dynamics following the actuator nonlinearity. This chapter gives an overview of various state feedback and output feedback control designs for linear, nonlinear, single-input and single-output, and multi-input and multi-output plants as well as open problems in this area of major theoretical and practical relevance. A key problem is to develop linearly parametrized error models suitable for developing adaptive laws to update the inverse and feedback controller parameters, which is solved for various considered cases. The chapter shows that control systems with commonly used linear or nonlinear feedback controllers such as a model reference, PID, pole placement, feedback linearization, or backstepping can be combined with an adaptive inverse to handle actuator nonlinearities.

The book is focused on adaptive control of deterministic systems with uncertain parameters, dynamics and disturbances. It can also be useful for understanding the adaptive control algorithms for stochastic systems (see references for ``Stochastic Systems'' in Section 1.4 for such algorithms). The material presented has been used and refined in a graduate course on adaptive control which I have taught for the past ten years at the University of Virginia to engineering, computer science, and applied mathematics students. Comments and modifications to the book can be found at

If used as a reference, this book can be followed in its chapter sequence for both continuous- and discrete-time adaptive control system design and analysis. The discrete-time contents are mainly in Sections 1.5.3 (adaptive control system examples), 2.7 and 2.8 (systems and signals), 3.6 (adaptive parameter estimation), 3.7.2 (robustness of parameter estimation), 3.8.2 (robust parameter estimation), 4.5 (state feedback adaptive control), Chapter 6 (model reference adaptive control), Sections 7.3 (indirect model reference adaptive control and adaptive pole placement control), 9.2 (multivariable model reference adaptive control), and 10.2--10.5 (adaptive actuator nonlinearity inverse control) (both in a unified continuous- and discrete-time framework). The rest of the book is for continuous-time adaptive control design and analysis.

If used as a textbook for students with knowledge of linear control systems, as a suggestion based on experience at the graduate level, the instruction may start with Sections 1.4 and 1.5 as an introduction to adaptive control (one or two lectures, 75 minutes each). Some basic knowledge of systems, signals, and stability may be taken from Sections 2.1--2.6 (system modeling, signal norms, Lyapunov stability, Gronwall-Bellman lemma, small-gain lemma, strictly positive realness and Lefschetz-Kalman-Yakubovich lemma, signal convergence lemmas including Lemmas 2.14, 2.15, and 2.16 (Barbalat lemma) for four or five lectures). Adaptive parameter estimation can be taught using Sections 3.1--3.6 in four or five lectures, including some reading assignments of robustness results from Sections 3.7 and 3.8. The design and analysis of adaptive control schemes with state feedback are presented in Sections 4.1--4.4 (three lectures), while the discrete-time results in Section 4.5 can be used as reading materials. Continuous-time model reference adaptive control in Chapter 5 can be covered in seven or eight lectures (Sections 5.1--5.5, with Section 5.6 as a reading assignment). Indirect adaptive control in Chapter 7 may need four lectures. One lecture plus reading is recommended for Chapter 8. Chapters 9 and 10 are for advanced study as either extended reading or project assignments. Further reading can be selected from the included extensive list of references on adaptive systems and control.

In this book, for a unified presentation of continuous- and discrete-time adaptive control designs in either the time or frequency domain, the notation y(t) = G(D)[u](t) (or y(D) = G(D)u(D)) represents, as the case may be, the time-domain output at time t (or frequency-domain output) of a dynamic system characterized by a dynamic operator (or transfer function) G(D) with input u(tau), tau < = t (or u(D)), where the symbol D is used, in the continuous-time case, as the Laplace transform variable or the time differentiation operator D[x](t) = dot{x}(t), t in [0, infty), or, in the discrete-time case, as the z-transform variable or the time advance operator D[x](t) = x(t + 1), t in {0, 1, 2, 3, ...}, with x(t) == x(tT) for a sampling period T > 0.

Adaptive control as knowledge has no limit and as theory is rigorous. Adaptive control is a field of science. The universe is mysterious, diverse, and vigorous. The world is complicated, uncertain, and unstable. Adaptive control deals with complexity, uncertainty, and instability of dynamic systems. Taoist philosophy emphasizes simplicity, balance, and harmony of the universe. A goal of this book is to give a simplified, balanced, and harmonious presentation of the fundamentals of adaptive control theory, aimed at improving the understanding of adaptive control, which, like other control methodologies, brings more simplicity, balance, and harmony to the dynamic world.

This book has benefited from many people's help. First, I am especially grateful to Professors Petros Ioannou and Petar Kokotovic. I was introduced to the field of adaptive control by Professor Ioannou, and his continuous support and vigorous instruction were most helpful to my study and research in adaptive control. Professor Kokotovic has been a great mentor, and his persistent enthusiasm and continual encouragement have been most valuable to me in the writing of this book. Their robust adaptive control theory has been most influential to my research in adaptive control.

I would like to particularly acknowledge Professors Karl Astrom, Graham Goodwin, Bob Narendra, and Shankar Sastry for their work on adaptive control, which inspired me in research and in writing this book. I would like to thank Professors Brian Anderson, Anu Annaswamy, Er-Wei Bai, Bob Bitmead, Stephen Boyd, Marc Bodson, Carlos Canudas de Wit, Han-Fu Chen, Aniruddha Datta, Michael Demetriou, Manuel De la Sen, Gang Feng, Li-Chen Fu, Sam Shu-Zhi Ge, Lei Guo, Lui Hsu, Alberto Isidori, Zhong-Ping Jiang, Dr. Ioannis Kanellakopoulos, Professor Hassan Khalil, Dr. Bob Kosut, Professors Gerhard Kreisselmeier, P. R. Kumar, Yoan Landau, Frank Lewis, Wei Lin, Lennart Ljung, Rogelio Lozano, Iven Mareels, David Mayne, Rick Middleton, Steve Morse, Romeo Ortega, Marios Polycapou, Laurent Praly, Drs. Darrel Recker, Doug Rhode, Professors Gary Rosen, Jack Rugh, Ali Saberi, Mark Spong, Yu Tang, T. J. Tarn, David Taylor, Chang-Yun Wen, John Ting-Yung Wen, and Erik Ydstie, whose knowledge of adaptive systems and controls helped my understanding of the field.

I especially thank Professors Murat Arcak, Ramon Costa, Dr. Suresh Joshi, Professor Miroslav Krstic, Dr. Jing Sun, and Professor Kostas Tsakalis for their knowledge and comments, which helped me in writing this book.

I am thankful to my graduate students Michael Baloh, Lori Brown, Jason Burkholder, Shu-Hao Chen, Tinya Coles, Warren Dennis, Emin Faruk Kececi, Yi Ling, Xiao-Li Ma, Raul Torres Muniz, Nilesh Pradhan, Gray Roberson, Min-Yan Shi, Xi-Dong Tang, Avinash Taware, Ming Tian, Timothy Waters, and Xue-Rui Zhang, and to computer scientists Chen-Yang Lu and Ying Lu, and engineer Yi Wu, for their earnest study, stimulating discussion, and interesting applications of adaptive control.

I would also like to express my thanks to my colleagues at the University of Virginia for their support, in particular, to Professors Milton Adams, Paul Allaire, Jim Aylor, Zong-Li Lin, Jack Stankovic, Steve Wilson, and Houston Wood, for their collaboration and help in my teaching and research.

Finally, I gratefully acknowledge that my study and research on adaptive control, which led to many of the results in this book, were supported by grants from the U.S. National Science Foundation and by a scholarship from the Chinese Academy of Sciences.

Gang Tao
Charlottesville, Virginia

Adaptive Control of Systems with Actuator Failures


Gang Tao, Shuhao Chen, Xidong Tang, Suresh M. Joshi

(published by Springer, March 2004; ISBN 1-85233-788-5)


Errata and Remarks: errata-remarks.pdf


Actuator failures in control systems may cause severe system performance deterioration and even lead to catastrophic closed-loop system instability. For example, many aircraft accidents were caused by operational failures in the control surfaces, such as rudder and elevator. For system safety and reliability, such actuator failures must be appropriately accommodated. Actuator failure compensation is an important and challenging problem for control systems research with both theoretical and practical significance.

Despite substantial progress in the area of actuator failure compensation, there are still many important open problems, in particular those involving system uncertainties. The main difficulty is that the actuator failures are uncertain in nature. Very often it is impossible to predict in advance which actuators may fail during system operation, when the actuator failures occur, what type and what values of the actuator failures are. It may also be impractical to determine such actuator failure parameters after a failure occurs. It is appealing to develop control schemes that can accommodate actuator failures without explicit knowledge of the occurrences of actuator failures and the actuator failure values. Adaptive control, which is capable of accommodating system parametric, structural, and environmental uncertainties, is a suitable choice for such actuator failure compensation schemes.

This book presents our recent research results in designing and analyzing adaptive control schemes for systems with unknown actuator failures and unknown parameters. The main feature of the adaptive actuator failure compensation approach developed in this book is that no explicit fault detection and diagnosis procedure is used for failure compensation. An adaptive law automatically adjusts the controller parameters based on system response errors, so that the remaining functional actuators can be used to accommodate the actuator failures and systems parameter uncertainties.

The book is in a comprehensive and self-contained presentation, while the developed theory is in a general framework readily applicable to specific practical adaptive actuator failure compensation problems. The book can be used as a technical reference for graduate students, researchers, and engineers from fields of engineering, computer science, applied mathematics, and others who have a background in linear systems and feedback control at the undergraduate level. It can also be studied by interested undergraduate students for their thesis projects.

This book is focused on adaptive compensation of actuator failures characterized by the failure model that some unknown control inputs may get stuck at some unknown fixed (or varying) values at unknown time instants and cannot be influenced by the control signals. The type of fixed-value actuator failures, referred to as ``lock-in-place'' actuator failures, is an important type of actuator failures and is often encountered in many critical control systems. For example, in aircraft flight control systems, the control surfaces may be locked in some fixed places and hence lead to catastrophic accidents. Varying value failures can occur, for example, due to hydraulics failures that can produce unintended movements in the control surfaces of an aircraft.

For actuator failure compensation, a certain redundancy of actuators is needed. For a system with multiple actuators, one case is that all actuators have the same physical characteristics; for example, they are segments of a multiple-segment rudder or elevator for an aircraft. For this case, a reasonable (natural) design for the applied control inputs is one with equal or proportional actuation for each actuator, that is, all control inputs are designed to be equal or proportional to each other. This actuation scheme is employed throughout the book, except for Chapter 5, where a multivariable design is used for the case when the actuators are divided into several groups and each group has actuators of the same physical characteristics (for example, an aircraft has a group of four engines and a group of three rudder segments), and within each group, an equal or proportional actuation is used.

With 12 chapters, the book systematically develops adaptive state tracking and output tracking control schemes for systems with parameter and actuator failure uncertainties. Designs and analysis for both linear systems and nonlinear systems with unknown actuator failures are covered. Key issues for adaptive actuator failure compensation, namely, design condition, controller structure, error equations, adaptive laws for updating the controller parameters, analysis of stability and tracking properties, are given in detail. Extensive simulation results are presented to verify the desired closed-loop system performance. This work is aimed at developing a theoretical framework for adaptive control of systems with actuator failures, to provide guidelines for designing control systems with guaranteed stability and tracking performance in the presence of system parameter uncertainties and failure uncertainties.

Chapter 1 presents some background material. Basic concepts and fundamental principles of adaptive control systems are introduced. The actuator failure compensation problems for linear systems and nonlinear systems are formulated. An overview of several existing actuator failure compensation design methods, including multiple models, switching and tuning designs, fault diagnosis designs, adaptive designs, and robust designs, is also given.

Chapters 2--8 address the adaptive actuator failure compensation problems for linear time-invariant systems with unknown actuator failures. Chapter 2 presents several model reference state feedback state tracking designs. For a linear time-invariant system with m actuators, the adaptive actuator failure compensation problem for up to m - 1 unknown actuator failures is investigated. Designs for three types of actuator failures: ``lock-in-place,'' parametrizable time-varying, and unparametrizable time-varying, are developed. Conditions and controller structures for achieving plant-model state matching, adaptive laws for updating the controller parameters, and analysis of closed-loop stability and asymptotic state tracking properties are addressed in a unified and comprehensive framework. State feedback actuator failure compensation designs for a class of multi-input systems are also derived. A more general case of up to m - q (q > = 1) unknown actuator failures is then addressed. Necessary and sufficient conditions for actuator failure compensation are derived. It is shown that the number of fully functional actuators is crucial in determining the actuation range that specifies the compensation design conditions in terms of system actuation structures. Such conditions are required for both a nominal design using system and failure knowledge and an adaptive design without such knowledge. An adaptive actuator failure compensation control scheme based on such system actuation conditions is developed for systems with unknown dynamics parameters and unknown ``lock-in-place'' actuator failures. Simulation results are presented to verify the desired system performance with failure compensation.

Chapter 3 investigates the state feedback output tracking problem for single-output linear time-invariant systems with any up to m - 1 uncertain failures of the total m actuators. In particular, adaptive rejection of the effect of certain unmatched input disturbances on the output of a linear time-invariant system is addressed in detail. A lemma that presents a novel basic property of linear time-invariant systems is derived to characterize system conditions for plant-model output matching. An adaptive disturbance rejection control scheme is developed for such systems with uncertain dynamics parameters and disturbances. This adaptive control technique is applicable to control of systems with actuator failures whose failure values, failure time instants, and failure patterns are unknown. A solution capable of accommodating the ``lock-in-place'' and time-varying actuator failures in the presence of any up to m - 1 uncertain failures of the total m actuators is presented to this adaptive actuator failure compensation problem. The developed adaptive actuator failure compensation schemes ensure closed-loop stability and asymptotic output tracking despite the uncertainties in actuator failures and system parameters. Simulation results verify the desired system performance in the presence of unknown actuator failures.

Chapter 4 develops a model reference adaptive control scheme using output feedback for output tracking for linear time-invariant systems with unknown actuator failures. An effective output feedback controller structure is proposed for actuator failure compensation. When implemented with true matching parameters, the controller achieves desired plant-model output matching, and when implemented with adaptive parameter estimates, the controller achieves closed-loop stability and asymptotic output tracking, which is also verified by simulation results. Compensation of varying failures is achieved based on an output matching condition for a system with multiple inputs whose actuation vectors may be linearly independent.

Chapter 5 deals with the output tracking problem for multi-output linear time-invariant systems using output feedback. Two adaptive control schemes based on model reference adaptive control are developed for a class of multi-input multi-output systems with unknown actuator failures. An effective controller structure is proposed to achieve the desired plant-model output matching when implemented with matching parameters. Based on design conditions on the controlled plant, which are also needed for nominal plant-model output matching for a chosen controller structure, two adaptive controllers are proposed and stable adaptive laws are derived for updating the controller parameters when system and failure parameters are unknown. All closed-loop signals are bounded and the system outputs track some given reference outputs asymptotically, despite the uncertainties in failures and system parameters. Simulation results are presented to demonstrate the performance of the adaptive control system in the presence of unknown rudder and aileron failures in an aircraft lateral dynamic model.

Chapter 6 studies adaptive pole placement control for linear time-invariant systems with unknown actuator failures, applicable to both minimum and nonminimum phase systems. A detailed analysis shows the existence of a nominal controller (when both system and actuator failure parameters are known) that achieves the desired pole placement, output tracking, and closed-loop signal boundedness. For that case when both system and failure parameters are unknown, an adaptive control scheme is developed. A simulation study with a linearized lateral dynamic model of the DC-8 aircraft is presented to verify the desired actuator failure compensation performance.

Chapter 7 applies several adaptive control schemes developed in the previous chapters to a linearized longitudinal dynamic model of a transport aircraft model. The tested adaptive schemes include state feedback design for state tracking, state feedback design for output tracking, and output feedback design for output tracking. Various actuator failures are considered. Extensive simulation results for different cases are presented to demonstrate the effectiveness of the adaptive actuator failure compensation designs.

Chapter 8 presents a robust adaptive control approach using output feedback for output tracking for discrete-time linear time-invariant systems with uncertain failures of redundant actuators in the presence of the unmodeled dynamics and bounded output disturbance. Technical issues such as plant-model output matching, adaptive controller structure, adaptive parameter update laws, stability and tracking analysis, and robustness of system performance are solved for the discrete-time adaptive actuator failure compensation problem. A case study is conducted for adaptive compensation of rudder servomechanism failures of a discrete-time Boeing 747 dynamic model, verifying the desired adaptive system performance.

Chapters 9--11 deal with actuator failure compensation problems for nonlinear systems. Chapter 9 formulates such problems and develops adaptive control schemes for feedback linearizable systems. Different structure conditions that characterize different classes of systems amenable to actuator failure compensation are specified, with which adaptive state feedback control schemes are developed for systems with uncertain actuator failures.

Chapter 10 addresses actuator failure compensation problems for nonlinear systems that can be transformed into parametric-strict-feedback form with zero dynamics. Two main cases are studied for adaptive actuator failure compensation: systems with stable zero dynamics, and systems with extra controls for stabilization. Design conditions on systems admissible for actuator failure compensation are clarified. Adaptive state feedback control schemes are developed, which ensure asymptotic output tracking and closed-loop signal boundedness despite the uncertainties in actuator failures as well as in system parameters. An adaptive control scheme is applied to a twin otter aircraft longitudinal nonlinear dynamics model in the presence of unknown failures in a two-segment elevator servomechanism. Simulation results verify the desired adaptive actuator failure compensation performance.

Chapter 11 presents an adaptive control scheme that achieves stability and output tracking for output-feedback nonlinear systems with unknown actuator failures. A state observer is designed for estimating the unavailable system states, based on a chosen control strategy, in the presence of actuator failures with unknown failure values, time instants, and pattern. An adaptive controller is developed by employing a backstepping technique, for which parameter update laws are derived to ensure asymptotic output tracking and closed-loop signal boundedness, as shown by detailed stability analysis. An extension of the developed adaptive actuator failure compensation scheme to nonlinear systems whose dynamics are state-dependent is also given to accommodate a larger class of nonlinear systems. An application to controlling the angle of attack of a nonlinear aircraft model in the presence of elevator segment failures is studied, with simulation results presented to illustrate the effectiveness of the failure compensation design.

Chapter 12 presents concluding remarks and suggests a list of theoretical and practical topics for further research in this area of adaptive control.

To help the readers understand the basic designs of adaptive control in the absence of actuator failures, the book includes an appendix that presents the schemes of model reference adaptive control using state feedback for state tracking, state feedback for output tracking, output feedback for output tracking, and multivariable design, as well as adaptive pole placement control. Key issues such as a priori system knowledge, controller structure, plant-model matching, adaptive laws, and stability are addressed.

This book describes adaptive actuator failure compensation approaches for effectively controlling uncertain dynamic systems with uncertain actuator failures. It addresses the theoretical issues of actuator failure models, controller structures, design conditions, adaptive laws, and stability analysis, with extensive simulation results on various aircraft system models. Design guidelines provided here may be used to develop advanced adaptive control techniques for control systems with controller adaptation and failure compensation capacities to improve reliability, maintainability, and survivability. The research leading to this book was supported by the National Aeronautics and Space Administration (NASA). However, the views and contents of this book are solely those of the authors and not of NASA.


We would like to express our thanks to Professors Karl Astrom, Petros Ioannou, Petar Kokotovic, Frank Lewis, and Kumpati Narendra for their knowledge and encouragement, to Dr. Jovan Boskovic for his inspiring work, to Professor Marios Polycapou for his help, to Professor Jack Stankovic for his interest and support, to Professors Michael Demetriou and Hong Wang for their comments, to Dr. Xiao-Li Ma for her contribution to Chapter 2, to Mr. Juntao Fei for his contribution to Chapter 8, to Mr. Richard Hueschen for his useful discussion about transport aircraft dynamics and actuator configurations, to Drs. Emin Faruk Kececi and Avinash Taware for their discussion, to Professors Zong-Li Lin and Steve Wilson for their support, and to the anonymous reviewers for their comments, which all have been continually motivating and highly beneficial to our related research, whose results have been reported in this book.

The first three authors wish to gratefully acknowledge the support by the NASA Langley Research Center to this work.

We are especially grateful to our families for their love and their support to our research work, which made this project possible.

Gang Tao, Shuhao Chen, Xidong Tang
Charlottesville, Virginia

Suresh M. Joshi
Hampton, Virginia

Advances in Control Systems Theory and Applications


Gang Tao and Jing Sun (editors)

(published by USTC Press, 2009)


Control systems theory, as an interdisciplinary science that deals with basic principles underlying the analysis and synthesis of interconnected systems, has had an enormous impact on the development of basic physical science, social economy, and advanced technology. Over the last 50 years, the advancement in control theory and its applications have played a crucial and prominent role to enable engineering activities in improving social infrastructure, life quality, and environment. Advanced theory for feedback control and other control mechanisms provides foundation and new insights to other branches of physical sciences such as communication, biomedical, and micro-nano systems. New control design tools have helped to streamline the system design and integration tasks for many industries, such as the process and automotive industry, thereby leading to more effective and robust products and processes. Widespread applications of micro-processors, distributed actuators and sensors, and real-time computing have further extended the domains of control application and made feedback even more ubiquitous, covering macro systems such as aircrafts, automobiles as well as micro entities like biology cells and nano-devices.

While it is evident that control theory has enabled many technological breakthroughs in aerospace, automotive, biomedical and other fields, it is equally convincing that new developments emerged in other fields have offered new challenges and opportunities for control engineers and researchers. It is this healthy cross-fertilization between the control theory and its application domains that has propelled the immense progresses of the control systems theory and led to the vast amount of scientific and technical publications in the literature. The field is developing and expanding rapidly with the stimulation of emerging challenges and the encouragement of the promising solutions.

This book presents a collection of diverse topics on some recent advances in control systems theory and applications, contributed by the authors who have enthusiastically and persistently worked in this exciting field. Moreover, most of the authors are alumni of the University of Science and Technology of China (USTC), who studied in their Alma Mater during different time periods of her glorious 50 years. The publication of this book is also intended to be a celebratory event for the 50th anniversary of the founding of USTC, a commemoratory testimony to those authors' Alma Mater for her dedication and contributions to education and research.

Book Summary

The book consists of 15 chapters whose topics range from different areas of control systems theory to various control applications: from adaptive control, control of bifurcations, digital control, fault tolerance control, H_infty control, learning control, neural and fuzzy control, nonlinear control, optimization, parameter estimation, predictive control, robust control, stochastic control, system identification, variable structure control, to aircraft flight control, building vibration control, computer control systems, medical robots, portfolio management, robot formation and control, and smart structures. The 15 chapters, with their titles and authors (and their USTC class numbers), are summarized as follows.

Chapter 1: A Sensitivity-Based View to the Stochastic Learning and Optimization, by Xi-Ren Cao (6204), Fang Cao (9862)

Chapter 2: Brief Review of Research on Robust Pole Clustering and Robust Structural Control, by Sheng-Guo Wang (6206)

Chapter 3: Two Challenging Problems in Control Theory, by Minyue Fu (7765)

Chapter 4: Developments in Receding Horizon Optimization-based Controls: Towards Real-time Implementation for Nonlinear Systems with Fast Dynamics, by Jing Sun (7765), Reza Ghaemi, Ilya Kolmanovsky

Chapter 5: Multivariable Model Reference Adaptive Control, by Gang Tao (7765)

Chapter 6: On Computer-Controlled Variable Structure Control Systems, by Bing Wang, Xinghuo Yu (7765), Xiangjun Li, Changhong Wang

Chapter 7: Multi-Robot Formation Control Based on Feedback from Onboard Sensors, by Tove Gustavi, Maja Karasalo, Xiaoming Hu (7865)

Chapter 8: Semiactive Control Strategies for Vibration Reduction in Smart Structures, by Ningsu Luo (7865)

Chapter 9: Identification and Control of Nonlinear Dynamic Systems via a Constrained Input-Output Neurofuzzy Network, by Marcos Gonzalez-Olvera, Yu Tang (7868)

Chapter 10: Decomposition-Based Robot Control, by Guangjun Liu (7965)

Chapter 11: From Adaptive Observers to Decoupled State and Parameter Estimations, by Qinghua Zhang (8110)

Chapter 12: Reduced-Order Controllers for the H_infty Control Problem with Unstable Invariant Zeros or Infinite Zeros, by Xin Xin (8210)

Chapter 13: Recent Advances in Bifurcation Control, by Hua O. Wang (8364)

Chapter 14: Intelligent Medical Robot Application: Tele-Neurosurgical Robot Case Study, by Weimin Shen, Jianjun (Jason) Gu (8700), Yanjun Shen

Chapter 15: Applications of Stochastic Control Theory in Portfolio Management, by Tao Pang (9001).

Dedication and Appreciation

On the behalf of the USTC alumni authors of this book, we would like to express our heartfelt gratitude to the teachers of our Alma Mater, who, with their enthusiasm and dedication, led us to this fascinating field and taught us the knowledge and skills that allowed us to explore the subject in various directions presented in this book. Our experience at our Alma Mater had been life enriching, and it shaped our personal and professional life in numerous ways. This book is specially edited and dedicated to our Alma Mater at her 50th anniversary in the special year of 2008. We would also like to express our appreciation to the contributions of other authors to this book, for joining this effort and making this special edition possible.

In addition, all the authors of this book would like to thank our colleagues for their intellectual stimulation and collaboration in our research, our students for their diligent and conscientious effort and for being our continuous inspiration, and our universities and our research sponsors for their support to our professional duties and research activities.

Gang Tao and Jing Sun (USTC Class 7765)