On the optimal and suboptimal VSC approaches for nonlinear uncertain systems

The variable structure control (VSC) method is integrated with a nonlinear suboptimal control method based on the control Lyapunov function. 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, once approaching the equilibrium such that system perturbation becomes the main factor, the VSC will take over the control task to warrant the designed robustness property and achieve precise control