Numerical computation of state feedback controllers for systems with persistent outputs

In this paper, we consider the problem of computing a state feedback controller for a class of nonlinear plants without requiring asymptotic stability of the resulting closed loop system. A simple generalization of the L₂-gain inequality which permits persistent outputs is used as the objective in the control design. By considering notions of dissipation and available storage, the controller can be computed by solving a Hamilton-Jacobi-Bellman-Isaac PDE. Although this PDE rarely admits analytical solutions, finite differences may be applied to compute an approximation to both the available storage and the desired state feedback controller. Due to problems with convergence of conventional Jacobi value space iterations, a mixed policy space/value space algorithm is applied