Robust, near time-optimal control of nonlinear second order systems with model uncertainty

In this paper, a robust optimal control algorithm is presented for the nonlinear second order systems with model uncertainty. To do so, the bang-bang principle, singular control and sliding-mode control are combined. The state space is divided into three regions to implement the control algorithm. In each region, the appropriate linear and nonlinear feedback control law is used satisfying the dynamic system equations. The algorithm blends smoothly not to give stress on the system. Comparison with pure time optimal control (bang-bang) shows the stability and robustness of the proposed algorithm and the closeness to minimum time.