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

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.