Optimal quadratic control of linear time delay systems: One approach to numerical solution

A finite-horizon linear-quadratic optimal control problem for systems with point-wise and distributed state delays is considered. Based on well known control optimality conditions, the solution of this problem is reduced to solution of the set of three Riccati-type matrix differential equations: an ODE and two first-order PDEs with two and three independent variables. In the paper, this set of Riccati-type equations is further reduced to a set of two equations. One of these equations is the ODE, while the other is a partial integro-differential equation. A numerical procedure of solution of this new set of equations is proposed. An illustrative example is presented.