Showing papers by "Petar V. Kokotovic published in 1986"

Singular perturbation methods in control : analysis and design

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.

On vanishing stability regions in nonlinear systems with high-gain feedback

Abstract: When local stabilization of nonlinear systems is achieved by linear feedback, the resulting stability region may vanish as the feedback gains increase. This is demonstrated by examples in which neglected nonlinearities create an unstable limit cycle around an asymptotically stable equilibrium. As the feedback gains tend to infinity the unstable limit cycle shrinks to the equilibrium. If a feedback linearization design is applied, the same instability mechanism may occur when the nonlinearities are not precisely known.

A corrective feedback design for nonlinear systems with fast actuators

Abstract: Recent two-time-scale results can be derived from a geometric framework which allows further extensions and computational improvements. In this note the two-time scale behavior of singularly perturbed systems is exploited to design slow and fast controls and to combine them into a composite control. As an illustration, we present a corrective design to compensate for fast actuator dynamics modeled as singular perturbations.

A geometric approach to composite control of two-time-scale systems

Abstract: The basic results from center manifold theory ([1], [2], [3], [4]) are applied to singularly perturbed nonlinear control systems. Under certain assumptions, the existence of a local, control dependent, invariant manifold allows us to relate asymptotic properties as t ? ? of the singularly perturbed control system to those of a reduced order control system. Moreover, with the use of composite control strategy, the asymptotic properties as ? ? 0 of the original control system and the reduced order one are also related via a version of Tikhonov's theorem given in [13].

Stability of Slow Adaptation for Non-SPR Systems with Disturbances

Abstract: Using the theory of integral manifolds, followed by the method of averaging. sufficient conditions are given for the existence of a bounded uniformly asymptotically stable (u.a.s.) solution of the model reference adaptive control system. These conditions, which do not require any matching assumptions or knowledge of the order of the plant, provide an estimate of the region of attraction and a bound on the average squared tracking error for which the u.a.s. property of the solution is preserved.