Backstepping based all states trajectories tracking for strict-feedback systems

In this letter, we address all states trajectories tracking problem, in which the reference trajectories can be selected arbitrarily. Moreover, the relation between the amounts of reference trajectories and that of states is analyzed. Then, based on backstepping method, we offer the systematic procedure for designing proper controllers for strict feedback form nonlinear systems with all states available. The advantage of this approach is that global exponential tracking is achieved. Moreover it can quickly track any reference trajectory. Simulation results are provided to validate the effectiveness of the approach.