Optimal control of linear multi-delay systems based on a multi-interval decomposition scheme

This paper presents a novel approximation scheme to the numerical treatment of linear time‐varying multi‐delay systems with a quadratic performance index. A direct approach based on a hybrid of block‐pulse functions and Chebyshev polynomials is successfully developed. The operational matrix of delay associated to multi‐delay systems is constructed by an efficient manner. The excellent properties of hybrid functions together with the operational matrices of integration, delay, and product are then used to transform the optimal control problem into a mathematical optimization problem whose solution is much more easier than the original one. The procedure described in the current paper can be regarded as a multi‐interval decomposition scheme. The convergence of the proposed method is verified numerically. A wide variety of multi‐delay systems are investigated to demonstrate the effectiveness and computational efficiency of the proposed numerical scheme. The method has a simple structure, is easy to implement, and provides very accurate solutions.