Advances in Dynamic Games and Applications by Eitan Altman, Tamer Başar, Naira Hovakimyan (auth.), Jerzy

By Eitan Altman, Tamer Başar, Naira Hovakimyan (auth.), Jerzy A. Filar, Vladimir Gaitsgory, Koichi Mizukami (eds.)

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Uchida 36 then the controller (r) solving the problem [P] is given as i u = Ax - B(x)B T (x)Xx =- B T + y-2 B\ Bf Xx + TCJ (y - C2X), (x)Xx. (26) (27) Moreover, the closed-loop system (E, r) is internally stable in the maximum hyperellipsoid that is contained in the domain <1>2. 1. 1 of[7]. 1 corresponds. This paper gives another type of controller as shown for linear systems in [3] and [10]. 2. We use condition (C23) (or (C13» to obtain the largest domain possible. , in [7]), the higher-order terms of condition (C23) (or (C13», with respect to the state, are contained in a "gap" of the inequality (24) (or (18» and condition (C23) (or (C13» becomes useless.

The basic approach to the problem here is game-theoretic, which associates a particular differential game with the disturbance attenuation problem. Here we only consider the finite horizon case, with the extension to the infinite-horizon problem to be dealt with in another forthcoming paper. Under a 50 M Xiao and T B~ar rather weak assumption on the infinitesimal generator A (which is that A generates a Co-semigroup on X), we develop a general theory for existence and characterization of disturbance attenuating time-varying state-feedback controllers for H'~o problems in infinite dimensions.

5] Grace, A Optimization Toolbox User's Guide. The MathWorks, 1994. , T. Sugie, and T. Yoshikawa. Internal Stability and L 2 gain of Nonlinear Systems-Derivation of Bounded Real Condition. 6 659-667,1993. In Japanese. [7] Isidori, A. Hoo Control via Measurement Feedback for Affine Nonlinear Systems. International Journal ofRobust and Nonlinear Control, 4, 553-574, 1994. [8] Ito, K. and T. Tsuji. The Bilinear Characteristics of Muscle-Skeletomotor System and the Application to Prosthesis Control.

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