Command filtered robust control of nonlinear systems with full-state time-varying constraints and disturbances rejection

For the barrier Lyapunov function-based control of full-state time-varying constrained systems via the traditional backstepping technology, due to repeated differentiations of virtual control functions involving time-varying barriers, the adverse effects of “explosion of complexity” caused by the backstepping iteration are more serious, which even makes it impossible to implement for high-order systems. In order to eliminate this negative influence, we take advantage of the command filtered backstepping approach which introduces a command filter to approximate the constructed virtual control law in each procedure of the backstepping design. More importantly, the approximate errors arising from the introduced filters will be removed by constructing a series of compensating signals. Meanwhile, some relatively conservative assumptions will be released compared with existing control strategies. Furthermore, largely unknown external disturbances that may exist in the system will be estimated in real-time via high-gain disturbance observers and then compensated feedforwardly in designing the controller. Specially, the scheme of the resulting control algorithm is simple and online computation time is saved. Finally, the stability of the whole closed-loop system and the control performance is strictly certificated, respectively.