Optimal control of linear pantograph-type delay systems via composite Legendre method

In this paper, linear-quadratic optimal control problems involving proportional delay are investigated. The necessary optimality conditions for these systems are derived. A direct approach is used to transform the delayed optimal control problem into a quadratic programming problem. The proposed discretization technique is based on an adaptive method using composite Legendre polynomials. Some useful error bounds are established. The corresponding delay and product operational matrices are constructed. Several illustrative examples are investigated to show the usefulness and effectiveness of the proposed discretization procedure. The method has a simple structure. (C) 2020 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.