Optimal polynomial feedback laws for finite horizon control problems

A learning technique for finite horizon optimal control problems and its approximation based on polynomials is analyzed. It allows to circumvent, in part, the curse dimensionality which is involved when the feedback law is constructed by using the Hamilton-Jacobi-Bellman (HJB) equation. The convergence of the method is analyzed, while paying special attention to avoid the use of a global Lipschitz condition on the nonlinearity which describes the control system. The practicality and efficiency of the method is illustrated by several examples. For two of them a direct approach based on the HJB equation would be unfeasible.