Control Lyapunov functions: new ideas from an old source

A control design method for nonlinear systems based on control Lyapunov functions and inverse optimality is analyzed. This method is shown to recover the LQ optimal control when applied to linear systems. More generally, it is shown to recover the optimal control whenever the level sets of the control Lyapunov function match those of the optimal value function. The method can be readily applied to feedback linearizable systems, and the resulting inverse optimal control law is generally much different from the linearizing control law. Examples in two dimensions are given to illustrate both the strengths and the weaknesses of the method.