Lyapunov optimal saturated control for nonlinear systems

A generalized feedback control law design methodology is presented that applies to systems under control saturation constraints. Lyapunov stability theory is used to develop stable saturated control laws that can be augmented to any unsaturated control law that transitions continuously at a touch point on the saturation boundary. The time derivative of the Lyapunov function, an error energy measure, is used as the performance index, which provides a measure that is invariant to the system dynamics, Lyapunov stability theory is used constructively to establish stability characteristics of the closed-loop dynamics, Lyapunov optimal control laws are developed by minimizing the performance index over the set of admissible controls, which is equivalent to forcing the error energy rate to be as negative as possible.