On the convergence of successive Galerkin approximation for nonlinear output feedback H∞ control

Although the formulation of the nonlinear theory of H∞ control has been well developed, solving the Hamilton–Jacobi–Isaacs equation remains a challenge and is the major bottleneck for practical application of the theory. Several numerical methods have been proposed for its solution. In this paper, results on convergence and stability for a successive Galerkin approximation approach for nonlinear H∞ control via output feedback are presented. An example is presented illustrating the application of the algorithm.