A quasi-optimal Variable Structure Control scheme based on Control Lyapunov Function

In this paper, the Variable Structure Control (VSC) method is integrated with a nonlinear suboptimal control method based on Control Lyapunov Function (CLF). According to the system nominal part, a CLF is first constructed in general to facilitate the nonlinear optimal system design and Sontagpsilas formula is used in particular to generate a suboptimal controller. To take system uncertainties into account, the VSC mechanism is designed based on the CLF. By integration, the suboptimal control and VSC are made to function in a complementary manner. When the system state is far away from the equilibrium and the system nominal part is predominant, the nonlinear optimal control part will govern the system response as well as drive the system state approach the equilibrium in an optimal fashion. On the contrary, when approaching the equilibrium such that system perturbations become the main factor, the VSC will take over the control task to warrant the desired robustness property and achieve precise control.