Universal controllers in model matching optimal control problems for unknown external signals

Linear-quadratic model matching optimal control problems are studied for unknown external signals and noise in the control plant. Given natural assumptions for two practically significant classes of external signals (stochastic with an unknown, rapidly decreasing spectral density and polyharmonic with the known spectrum and unknown amplitudes), controllers universal in the sense that they generate an optimal or approximately optimal process in the problem for any signal from the stated class are proved to exist. Linear controllers are shown to exist among them, with the class of linear universal controllers described exhaustively.