Solutions of Nonlinear Optimal Regulator and H∞ Control Problems via Galerkin Methods

This paper proposes a general framework for the numerical solution of nonlinear optimal control arising in optimal regulators and some related H-infinity problems. This approach is based on Galerkin methods, commonly used today in computational physics for the solution of partial differential equations appearing for example in structural mechanics, fluid mechanics or heat-conduction problems. It leads to approximations of optimal control laws in closed-loop form. From the viewpoint of stability and robustness, these approximations are stabilizing under mild sufficient conditions. Some examples are provided that demonstrates the effectiveness of this approach.