Optimal nonlinear, but continuous, feedback control of systems with saturating actuators

This paper presents a modification of the optimal saturating feedback control laws given by Frankena and Sivan (1979) and Ryan (1982) for asymptotically stable systems. Unlike their results, which involve bang-bang action and singular extremals, the modified control law is continuous. Specifically, the new control law is linear inside of a cylinder set and saturated elsewhere. Using steady-state Hamilton-Jacobi-Bellman theory, this control law is shown to be optimal for a modified performance functional with a discontinuous integrand