Analytical Design of the Optimal Controllers in Linear-Quadratic Problems of Controlling Systems with Distributed Parameters under Uniform Estimates of Target Sets

Abstract

A constructive method for synthesizing the optimal control of deterministic and not completely determined systems with distributed parabolic parameters under the conditions of the prescribed accuracy of a uniform approximation of the terminal plant state to the required spatial distribution of the controlled variable is proposed. This approach is based on the earlier developed alternance method for constructing optimal open-loop control algorithms, which extends the results of the theory of nonlinear Chebyshev approximations to a wide range of parameterizable optimal control problems and takes into account fundamental features of the domain. It is shown that the optimal controller equations are reduced to linear output feedback equations with time-dependent coefficients that are calculated based on incomplete measurements of the system’s state with an error that decreases as the number of modal components of the controlled variable that are taken into account increases.