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# Singular perturbation methods in control : analysis and design

01 Jan 1986-

TL;DR: This SIAM Classics edition of the 1986 book, the original text is reprinted in its entirety (along with a new preface), providing once again the theoretical foundation for representative control applications.

Abstract: From the Publisher:
Singular perturbations and time-scale techniques were introduced to control engineering in the late 1960s and have since become common tools for the modeling, analysis, and design of control systems. In this SIAM Classics edition of the 1986 book, the original text is reprinted in its entirety (along with a new preface), providing once again the theoretical foundation for representative control applications.
This book continues to be essential in many ways. It lays down the foundation of singular perturbation theory for linear and nonlinear systems, it presents the methodology in a pedagogical way that is not available anywhere else, and it illustrates the theory with many solved examples, including various physical examples and applications. So while new developments may go beyond the topics covered in this book, they are still based on the methodology described here, which continues to be their common starting point.
Audience
Control engineers and graduate students who seek an introduction to singular perturbation methods in control will find this text useful. The book also provides research workers with sketches of problems in the areas of robust, adaptive, stochastic, and nonlinear control. No previous knowledge of singular perturbation techniques is assumed.
About the Authors
Petar Kokotovic is Director of the Center for Control Engineering and Computation at the University of California, Santa Barbara. Hassan K. Khalil is Professor of Electrical and Computer Engineering at Michigan State University. John O'Reilly is Professor of Electronics and Electrical Engineering at the University of Glasgow, Scotland.

##### Citations

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TL;DR: An accurate assessment of the so-called chattering phenomenon is offered, which catalogs implementable sliding mode control design solutions, and provides a frame of reference for future sliding Mode control research.

Abstract: Presents a guide to sliding mode control for practicing control engineers. It offers an accurate assessment of the so-called chattering phenomenon, catalogs implementable sliding mode control design solutions, and provides a frame of reference for future sliding mode control research.

2,082 citations

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TL;DR: A method is proposed for designing controllers with arbitrarily small tracking error for uncertain, mismatched nonlinear systems in the strict feedback form and it is shown that these low pass filters allow a design where the model is not differentiated, thus ending the complexity arising due to the "explosion of terms" that has made other methods difficult to implement in practice.

Abstract: A method is proposed for designing controllers with arbitrarily small tracking error for uncertain, mismatched nonlinear systems in the strict feedback form. This method is another "synthetic input technique," similar to backstepping and multiple surface control methods, but with an important addition, /spl tau/-1 low pass filters are included in the design where /spl tau/ is the relative degree of the output to be controlled. It is shown that these low pass filters allow a design where the model is not differentiated, thus ending the complexity arising due to the "explosion of terms" that has made other methods difficult to implement in practice. The backstepping approach, while suffering from the problem of "explosion of terms" guarantees boundedness of tracking errors globally; however, the proposed approach, while being simpler to implement, can only guarantee boundedness of tracking error semiglobally, when the nonlinearities in the system are non-Lipschitz.

1,901 citations

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TL;DR: In this paper, the problem of controlling a fixed nonlinear plant in order to have its output track (or reject) a family of reference (or disturbance) signal produced by some external generator is discussed.

Abstract: The problem of controlling a fixed nonlinear plant in order to have its output track (or reject) a family of reference (or disturbance) signal produced by some external generator is discussed. It is shown that, under standard assumptions, this problem is solvable if and only if a certain nonlinear partial differential equation is solvable. Once a solution of this equation is available, a feedback law which solves the problem can easily be constructed. The theory developed incorporates previously published results established for linear systems. >

1,639 citations

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TL;DR: A classification of a number of decentralized, distributed and hierarchical control architectures for large scale systems is proposed and attention is focused on the design approaches based on Model Predictive Control.

Abstract: The aim of this paper is to review and to propose a classification of a number of decentralized, distributed and hierarchical control architectures for large scale systems. Attention is focused on the design approaches based on Model Predictive Control. For the considered architectures, the underlying rationale, the fields of application, the merits and limitations are discussed, the main references to the literature are reported and some future developments are suggested. Finally, a number of open problems is listed.

1,234 citations

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TL;DR: This work reviews several approaches to temporal abstraction and hierarchical organization that machine learning researchers have recently developed and discusses extensions of these ideas to concurrent activities, multiagent coordination, and hierarchical memory for addressing partial observability.

Abstract: Reinforcement learning is bedeviled by the curse of dimensionality: the number of parameters to be learned grows exponentially with the size of any compact encoding of a state Recent attempts to combat the curse of dimensionality have turned to principled ways of exploiting temporal abstraction, where decisions are not required at each step, but rather invoke the execution of temporally-extended activities which follow their own policies until termination This leads naturally to hierarchical control architectures and associated learning algorithms We review several approaches to temporal abstraction and hierarchical organization that machine learning researchers have recently developed Common to these approaches is a reliance on the theory of semi-Markov decision processes, which we emphasize in our review We then discuss extensions of these ideas to concurrent activities, multiagent coordination, and hierarchical memory for addressing partial observability Concluding remarks address open challenges facing the further development of reinforcement learning in a hierarchical setting

1,175 citations

### Cites background from "Singular perturbation methods in co..."

...Further work is required for understanding how to build task hierarchies in such cases, and how to integrate this approach to related systems approaches such as singular perturbation methods [36, 46]....

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