Parametric Regularization of the Functional in a Linear-quadratic Optimal Control Problem

Abstract

A linear-quadratic optimal control problem with parameters and arbitrary matrices in the quadratic cost functional is considered on the set of stepwise control functions. As a quality criterion of the admissible set of parameters it is proposed to choose a condition number of the final matrix, which is expressed through the boundaries of its spectrum. As a result, parameter optimization problems are constructed which provide a strong convexity of the objective function on control variables together with relatively good conditionality of the corresponding quadratic programming problem. A similar approach is realized for the minimax problem. In this case, the objective function acquires a convex-concave structure and the choice of parameters is based on minimization of some convolution of two condition numbers.

Keywords

• linear-quadratic optimal control problem
• cost functional with parameters
• parameter optimization
• minimization of the condition number