Hybrid Functions Approach for Variational Problems and Optimal Control of Delay Systems

Abstract

In this chapter, a numerical method for solving variational problems and optimal control of delay systems is presented. The method is based upon hybrid functions approximation. The properties of hybrid functions consisting of block-pulse functions and Bernoulli polynomials are presented. The operational matrices of integration, product, delay and the integration of the cross product of two hybrid functions of block-pulse and Bernoulli polynomials vectors are given. These matrices are then utilized to reduce the solution of variational problems, delay systems and the optimal control of delay systems to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.KeywordsDelay systemsoptimal controlvariational problemshybridblock-pulseBernoulli polynomials