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In between the \(LQG/H_2\)- and \(H_{\infty } \)-control theories. (English. Russian original) Zbl 1466.93041

Autom. Remote Control 82, No. 4, 565-618 (2021); translation from Avtom. Telemekh. 2021, No. 4, 8-76 (2021).
Summary: In this survey, we discuss various approaches to control theory that have arisen in the recent decades and reflect the desire to reach a trade-off between the \(LQG /H_2 \)-control theory and the \(H_{\infty } \)-control theory. The theories of the kind include the theory of risk-sensitive controllers, the theory of suboptimal control with a constraint on the \(H_{\infty } \)-entropy functional, the mixed \(H_2/H_{\infty } \)-control theory, the minimax \(LQG \)-control theory, the anisotropy-based theory, and some others. The survey discusses in more detail the anisotropy-based control theory, which includes both the \(LQG/H_2\)- and the \(H_{\infty } \)-theory within a single statement of the problem.

MSC:

93B36 \(H^\infty\)-control
93D09 Robust stability
93B11 System structure simplification
93-02 Research exposition (monographs, survey articles) pertaining to systems and control theory
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References:

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