ON THE LINEAR QUADRATIC DYNAMIC OPTIMIZATION PROBLEMS WITH FIXED-LEVELS CONTROL FUNCTIONS

Abstract

This paper deals with a constrained LQ-type optimal control problem (OCP) in the presence of fixed levels input restrictions.  We consider control processes governed by linear differential equations with a priori known control switching structure.  The set of admissible inputs reflects some important natural engineering applications and moreover, can also be interpreted as a result of a quantization procedure applied to the original dynamic system.  We propose a novel implementable algorithm that makes it possible to calculate a (numerically consistent) approximative solution to the constrained LQ-type OCPs under consideration.  Our contribution mainly discusses theoretic aspects of the proposed solution scheme and contains an illustrative numerical example.