Time-varying sliding mode control for a class of uncertain MIMO nonlinear system subject to control input constraint

To solve the regulator problem of a class of uncertain MIMO nonlinear systems subject to control input constraint, three types of time-varying sliding mode control laws are proposed. The sliding surfaces pass the initial value of the system at the initial time, and are shifted/rotated towards the predetermined ones. The controller parameters are optimized by genetic algorithm (GA). Lyapunov method is adopted to prove the stability and robustness to the parameter uncertainties and external disturbance. By mean of time-varying sliding mode control law, the reaching phase in the conventional sliding mode control is eliminated, and the system is guaranteed to have robustness from the very beginning. Taking the control of two-link manipulator and attitude tracking of rigid spacecraft as two examples, we illustrate the features of the time-varying sliding mode control. The simulation results show the validity of the control law to a class of uncertain MIMO systems. Better robustness against the uncertainties and external disturbance could be achieved by time-varying sliding mode control without violating the constraint on control input.