Adaptive $H_{\infty }$-optimal control

For linear dynamic plants, we consider a new class of controllers with adjustable parameters synthesized so as to reduce the integral indicators of the influence of initial and exogenous disturbances. The controller parameters are adjusted according to a differential equation in the direction of decrease of a local objective function. The conditions are stated under which the control objective is achieved, and the losses in comparison with time-invariant linear-quadratic and $H_{\infty }$-optimal controllers are given, including the case of degenerate functionals. It is shown how these controllers are used in adaptive linear-quadratic and $H_{\infty }$-optimal control for indeterminate plants whose parameters belong to a given polyhedron as well as in adaptive tracking of the reference model output.