In Between the $$LQG/H_{2}$$- and $$H_{\infty } $$-Control Theories

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.