Nonlinear Robust and Optimal Control via Proper Orthogonal Decomposition

Abstract

In this paper, a methodology based on proper orthogonal decomposition (POD) for computing approximate closed-loop optimal or robust control laws for finite-dimensional nonlinear systems is proposed. The solution can be obtained on any arbitrary domain of the state space represented by a multidimensional grid. The method only requires the computation of a limited number of well-conditioned two-point boundary value problems and a simple backwards integration of a reduced model of the Hamilton-Jacobi-Bellman or Hamilton-Jacobi-Isaacs equation associated to the control problem. Two illustrative examples demonstrate the effectiveness of the approach.