Optimal Control of Constrained Time Delay Systems

In this paper, a new approach based on embedding method for finding an approximate solution for a wide range of nonlinear optimal control problems with delays in state and control variables subject to mixed-control state constraints is introduced. First, the problem is transformed to a new optimal measure problem which is an infinite dimensional linear programming problem and then this new problem is approximated by a finite dimensional one. The approximate values of the optimal control, optimal state and optimal objective function are obtained by solving the corresponding finite dimensional linear programming problem. The effectiveness and applicability of the proposed idea is illustrated by several numerical examples. Mathematics Subject Classification: 49J15; 28A12; 90C05.