Suboptimal Feedback Control of Nonlinear Distributed Parameter Systems by Stable Manifold Method

Abstract

Abstract This paper proposes a suboptimal feedback controller design for nonlinear distributed parameter systems via the stable manifold method. The stable manifold method provides approximate stabilizing solutions of Hamilton-Jacobi (HJ) equations in nonlinear optimal control theory. We apply this method to a reduced-order system obtained from the proper orthogonal decomposition (POD) and Galerkin projection. The feasibility of the design is demonstrated by the numerical example of feedback controls of the viscous Burgers' equation.