A direct approach using the shifted Legendre series expansion for near optimum control of linear time-varying systems with multiple state and control delays

Abstract

A computationally efficient method, which uses finite orthogonal expansions to approximate state and control variables, is developed to obtain suboptimal control for time-varying systems with multiple state and control delays and with quadratic cost. Shifted Legendre polynomials form the basis of expansions as a consequence of their useful properties. The Galerkin method is used to reduce the problem to one of minimizing a quadratic form with linear algebraic constraints. The solution of a coupled two-point boundary-value problem with both delayed and advanced terms, which is always required in applying the Pontryagin's maximum principle to the optimization of delay systems, is thus avoided.