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The worst perturbation and minimax control for continuous linear systems: Solutions of the inverse problems. (English. Russian original) Zbl 0926.93021

Autom. Remote Control 58, No. 4, Pt. 1, 535-541 (1997); translation from Avtom. Telemekh. 1997, No. 4, 22-30 (1997).
This paper mainly considers the following linear continuous system: \[ \dot x= Ax+ Bu+ Fv, \] where \(x\in \mathbb{R}^m\) is a state, \(u\in \mathbb{R}^k\) is a control and \(v\in \mathbb{R}^l\) is an \(L^2\)-perturbation and \(A\), \(B\) and \(F\) are some matrices. The cost functional is \[ J_2(u,v)= \int^\infty_0 (x^TQ_u x+ u^Tu- \gamma^2 v^Tv)dt \] with \(Q_u= Q^T_u\geq 0\) and \(\gamma\neq 0\). The author solves the inverse minimax control problem for this system by a local approach and by the Lyapunov-function method. The solution is derived from the inverse worst perturbation problem. The criterion which is expressed in the form of a frequency inequality, demonstrates that the feedbacks for minimax controls form a subset of the stable feedbacks for optimal controls under no perturbation relative to a quadratic functional with nonnegative-definite weight matrix.
Reviewer: S.Shih (Tianjin)

MSC:

93B36 \(H^\infty\)-control
93C73 Perturbations in control/observation systems
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