Parametric Transformation of a Quadratic Functional in a Linear Control System

Abstract

A linear-quadratic problem on a set of piecewise linear controls is considered. The control quality criterion is determined by indefinite matrices and contains control parameters for quadratic forms. A procedure for searching parameters based on the problem of minimizing the condition function of a general matrix of quadratic form with a restriction in the form of the condition of its sign definiteness. As a result of such regularization, the initial objective function acquires the property of strong convexity or concavity with all the positive consequences in terms of the effective solution of the corresponding optimization problems. An illustrative example is given that demonstrates the analytical solution of a parametric problem.

Keywords

• linear-quadratic problem with parameters
• spectral condition number
• optimization of parameters