Linear programming based optimality conditions and approximate solution of a deterministic periodic optimal control problem in discrete time (Q2169814)

In the paper, the author shows that linear programming formulations may be used to construct near optimal controls in problems of periodic optimization of systems evolving in discrete time. First, the discrete time analog of the Hamilton-Jacobi-Bellman (HJB) inequality is defined. Then a variational maxmin problem which is equivalent to the ``discrete time HJB inequality'' is introduced. The author shows that, under certain controllability conditions, solutions for approximating maxmin problems exist and yield approximate solutions of the ``discrete time HJB inequality''. It is established that solutions of the approximating maxmin problems may be used for the construction of a near optimal control in the periodic optimization problem. A numerical example is included to demonstrate these results.