Fast robust adaptive tracker for uncertain nonlinear second-order systems with time-varying uncertainties and unknown parameters

This paper considers the problem of robust adaptive tracking control of nonlinear second-order systems subjected to matched and unmatched uncertainties. This paper presents a control law derived by a new form of fast terminal sliding mode control that is combined with global sliding mode scheme. An adaptation mechanism is also employed to estimate the unknown parameters of the system. The proposed control law guarantees the finite-time convergence of the sliding variable in the presence of uncertainties and unknown parameters. By elimination of the reaching phase, the robustness of the system is guaranteed throughout the entire response. Furthermore, there is no need for the upper bound of the system uncertainties or external disturbance to be known in advance. This feature makes the proposed controller more flexible in terms of implementation. The robustness of the proposed scheme is established by means of the Lyapunov stability theorem.