A. P. Kurdyukov, O. G. Andrianova, A. A. Belov, D. A. Gol'din, “In between the $LQG/H_{2}$- and $H_{\infty }$-control theories”, Avtomat. i Telemekh., 2021, Issue 4,Pages 8

This article is cited in 9 papers

Surveys

In between the $LQG/H_{2}$- and $H_{\infty }$-control theories

A. P. Kurdyukov^ab, O. G. Andrianova^ab, A. A. Belov^a, D. A. Gol'din^a

^a Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, 117997 Russia
^b National Research University Higher School of Economics, Moscow, 101000 Russia

Abstract: 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.

Keywords: linear system, external disturbance rejection, robust control, robust filtering, robust stabilization, suboptimal control, optimal control, information theory, colored noise, robust stability, system with uncertainties, descriptor system, bounded real lemma.

Received: 29.06.2020
Revised: 09.10.2020
Accepted: 08.12.2020

DOI: 10.31857/S0005231021040024