Application of periodic Bernoulli polynomials in approximating the solution of linear time-delay optimal control problems

Abstract

In this paper, a numerical method based on application of periodic Bernoulli polynomials for solving optimal control of linear time-delay systems with quadratic performance index is presented. Some important properties of Bernoulli polynomials are reviewed and a new operational matrix of delay based on these functions is introduced. Also an error bound for approximating a function with periodic Bernoulli polynomials is presented. Using operational matrices of differentiation, delay and the integration of the cross product of two Bernoulli polynomials, the linear time delay optimal control problem with quadratic objective function is converted to a nonlinear optimization problem. Finally, numerous illustrative examples are studied to show the efficiency and accuracy of the proposed method compared with some other methods.