Numerical treatment of non-linear optimal control problems involving piecewise constant delay

An efficient approximation scheme for solving non-linear optimal control problems with a piecewise constant delay function is introduced. The proposed method is based on a hybrid of block-pulse functions and Lagrange interpolating polynomials using the well-known Legendre–Gauss–Lobatto points. A direct approach is applied to transform the main problem into a finite-dimensional optimization problem whose solution is much easier than the original one. The operational matrix of derivative associated with the hybrid functions is constructed. The necessary conditions of optimality corresponding to non-linear piecewise constant delay systems are derived. Several numerical experiments are investigated to evaluate the performance and computational efficiency of the proposed procedure. The method is easy to implement and provides very accurate results.