Hoptimal control and related minimax design problems
by Tamer Basar , P. Bernhard

Persian Title: کنترل Hبهینه و مشکلات طراحی مینیماکس مرتبط

Summary and Info
One of the major concentrated activities of the past decade in control theory has been the development of the socalled "Hinfinityoptimal control theory", which addresses the issue of worstcase controller design for linear plants subject to unknown disturbances and plant uncertainties. Among the different timedomain approaches to this class of worstcase design problems, the one that uses the framework of dynamic, differential game theory stands out to be the most natural. This is so because the original Hinfinity control problem (in its equivalent timedomain formulation) is in fact a minimax optimization problem, and hence a zerosum game, where the controller can be viewed as the minimizing player and disturbance as the maximizing player. Using this framework, the authors present in this book a complete theory that encompasses continuoustime as well as discretetime systems, finite as well as infinite horizons, and several different measurement schemes, including closed loop perfect state, delayed perfect state, samples state, closedloop imperfect state, delayed imperfect state and sampled imperfect state information patterns. They also discuss extensions of the linear theory to nonlinear systems, and derivation of the lower dimensional controller for systems with regularly and singularly perturbed dynamics. This is the second edition of a 1991 book with the same title, which, besides featuring a more streamlined presentation of the results included in the first edition, and at places under more refined conditions, also contains substantial new material, reflecting new developments in the field since 1991. Among these are the nonlinear theory; connections between Hinfinityoptimal control and risk sensitive stochastic control problems; Hinfinity filtering for linear and nonlinear systems; and robustness considerations in the presence of regular and singular perturbations. Also included are a rather detailed description of the relationship between frequencyand timedomain approaches to robust controller design, and a complete set of results on the existence of value and characterization of optimal policies in finite and infinitehorizon LQ differential games. The authors believe that the theory is now at a stage where it can easily be incorporated into a secondlevel graduate course in a control curriculum, that would follow a basic course in linear control theory covering LQ and LQG designs. The framework adopted in this book makes such an ambitious plan possible. For the most part, the only prerequisite for the book is a basic knowledge of linear control theory. No background in differential games, or game theory in general, is required, as the requisite concepts and results have been developed in the book at the appropriate level. The book is written in such a way that makes it possible to follow the theory for the continuous and discretetime systems independently (and also in parallel).
More About the Author
Tamer Başar, (born January 19, 1946 in Istanbul, Turkey) is a Turkish control theorist who holds the Swanlund Endowed Chair of the Center for Advanced Study and Professor in the Department of Electrical and Computer Engineering at the University of Illinois at UrbanaChampaign, USA.
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