The Global Inverse Optimal Design with Robustness to Some Uncertainties

In this paper, by employing the new characterization of control Lyapunov function, an inverse optimal controller is designed for the nonlinear system. The controller guarantee robustness against some input dynamic uncertainties and in the cost functional, the penalty on the control is not always quadratic. It is shown that the Lyapunov function guaranteeing closed-loop stability is a solution to the Hamilton-Jacobi-Bellman equation. With this method an inertia-wheel pendulum system is put forward to verify our conclusion. The control law for the pendulum system is designed to make the system global asymptotically stability on one of its equilibrium point, and computer simulations are given for illustration.