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"In practical control systems, actuators may inevitably undergo failures and a variety of nonsmooth nonlinearities, such as backlashes, hysteresis and dead-zones, influence their e ectiveness in executing the control commands. These actuator imperfections, often uncertain in time, pattern and values, can lead to deteriorated performance or even instability of the system if they are not well handled. In particular, when the system parameters are poorly known, the compensation problem becomes more complicated. Adaptive control has been proved to be a promising tool to solve the problem, but some important issues, such as guaranteeing transient performance of adaptive failure compensation control systems and accommodating intermittent failures, are still worth investigating.

On the other hand, subsystems are often interconnected in large-scale systems of increasing complexity, whereas the interactions between any two subsystems are di□cult to identify or measure. The decentralized adaptive control technique is an e□cient and practical strategy for such interconnected systems. It is aimed at designing a local controller for each subsystem which uses only local information while the stability and performance of the whole system are guaranteed. Nevertheless, when adaptive control approaches are applied to deal with system uncertainties, the analysis of the entire system is quite challenging. Besides, advances in communication techniques enable information exchanges among distinct subsystems so that certain collective objectives, such as consensus and formation control, can be attained by designing subsystem interactions carefully.

This book is a compilation of the latest results on designing and analyzing adaptive backstepping control systems involving treatment on actuator failures, subsystem interactions and nonsmooth nonlinearities. Some novel work related to adaptive failure compensation, decentralized adaptive control and distributed adaptive coordinated control is also discussed in this book. In this book the authors aim to introduce novel solutions to a number of hot-spot and challenging problems in the area of adaptive control. In the reviewer's opinion, it is a meaningful work for achieving this objective. This book is organized into 11 chapters. The first chapter is devoted to a brief introduction and elaborates the state of the art of related research areas and motivation of this work. The second chapter gives the concepts of adaptive backstepping control design and related analysis.

The main content of this book, consisting of Chapters 3{10, provides the novel solutions adopting a backstepping design tool for a number of hot-spot and challenging problems in the area of adaptive control, which can be divided into two parts. The first part introduces three di erent backstepping-based adaptive actuator failure compensation methods for di erent cases. In Chapter 3, the relative degree restriction corresponding to the redundant actuators is relaxed by introducing a pre-filter, for each actuator, in designing an output-feedback controller for the systems with a total loss of e ectiveness (TLOE) type of failure. A set-point regulation problem for linear systems is considered to illustrate the design idea, and the result is extended to tracking control of nonlinear systems. Chapter 4 analyzes the transient performance of the adaptive systems in failure cases, and proposes a new adaptive backstepping-based failure compensation scheme to guarantee a prescribed transient performance of the tracking error. Chapter 2 Mathematical Reviews Clippings December 2018 5 presents a modular design-based adaptive backstepping control scheme by using a projection operation technique to ensure system ability in the presence of intermittent actuator failures.

The second part addresses some advances in decentralized adaptive backstepping control of uncertain interconnected systems. By using the standard adaptive backstepping technique, Chapter 6 proposes a decentralized control method for a class of interconnected systems with dynamic interconnections and unmodeled dynamics depending on subsystem inputs and outputs. In Chapter 7, two decentralized output-feedback adaptive backstepping control schemes are presented to acquire stabilization of uncertain interconnected systems with hysteresis. In the presence of external disturbance, Chapter 8 designs decentralized adaptive controllers for achieving output tracking of nonlinear interconnected systems. In Chapter 9, the problem of decentralized adaptive tracking is investigated for a class of interconnected systems with unknown time-varying delays and with the input of each loop preceded by unknown dead-zone nonlinearity. Chapter 10 discusses the output consensus tracking for a group of nonlinear subsystems in parameter strict-feedback form under the condition of a directed communication graph, and presents a distributed adaptive backstepping control approach to achieve an asymptotic
consensus tracking.

Finally, Chapter 11 concludes the book by summarizing the main approaches and contributions and discussing some promising open problems in the areas of adaptive failure compensation, decentralized adaptive control and distributed adaptive coordinated control.

In this reviewer's opinion, this book presents innovative technologies for designing and analyzing adaptive backstepping control systems involving treatment on actuator failures, subsystem interactions and nonsmooth nonlinearities. Among the novelties are (1) relaxation of the relative degree condition imposed on redundant actuators; (2) improvement of transient performance of adaptive control systems in the presence of uncertain actuator failures; (3) adaptive compensation for intermittent actuator failures; (4) decentralized adaptive stabilization of uncertain interconnected systems with dynamic interactions depending on subsystem input directly; (5) decentralized adaptive tracking of uncertain interconnected systems; (6) decentralized adaptive control of uncertain interconnected systems with nonsmooth nonlinearities (such as hysteresis, dead-zone) and time delay; (7) distributed adaptive coordinated control of uncertain multi-agent systems under a directed graph condition.

The following are also worth mentioning: (1) In Chapters 3 and 4, an assumption is imposed that one actuator may only fail once and the failure mode will remain unchanged afterwards. This assumption is removed and the adaptive backsteppingbased compensation control problem for intermittent actuator failures is investigated in Chapter 5. (2) Unlike state feedback control in Chapters 2, 4, 5 and 10, output-feedback control is adopted in Chapters 3 and 6{9. Especially, by considering the e ects caused by the uncertain actuator failures, some modified state estimation filters are designed in Chapter 3. Besides, the standard filters are adopted without any modification in Chapters 6{9 to estimate the local state variables. (3) The authors analyze the fact that transient performance of the adaptive system cannot be adjusted through changing controller design parameters when actuator failures occur. Then a modified controller design scheme based on a prescribed performance bound is designed in Chapter 4, such that the transient performance is ensured and can be improved by varying certain design parameters. (4) Compared with decentralized stabilization in Chapters 6 and 7, the main challenge of decentralized tracking in Chapters 8 and 9 comes from compensating for the e ects the subsystem reference inputs have on local tracking errors through interactions. Thus, in Chapters 8 and 9, a new smooth function is used to compensate for these 3 Mathematical Reviews Clippings December 2018 e ects. (5) Chapters 6{10 are all devoted to designing local adaptive controllers for each subsystem in a group of uncertain interconnected systems. Specifically, subsystem interactions are utilized in Chapter 10, rather than compensated for as in Chapters 6{9, for completing a certain collective mission. Though a series of innovative technologies are presented for designing and analyzing adaptive backstepping control systems involving treatment on actuator failures, subsystem interactions and nonsmooth nonlinearities, some challenging open problems in the areas of adaptive failure compensation, decentralized adaptive control and distributed adaptive coordinated control are also mentioned in this book.

In general, as a collection of cutting-edge research results on adaptive failure compensation, decentralized/distributed adaptive control of interconnected systems and related areas, this book provides some innovative technologies for designing and analyzing adaptive backstepping control systems involving treatment on actuator failures, subsystem interactions and nonsmooth nonlinearities, and undoubtedly enriches nonlinear system theory and adaptive control theory. It is a valuable reference for interested researchers and engineers."

- Zhaoxu Yu - Mathematical Reviews Clippings - December 2018

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