Adaptive nonsingular fast terminal sliding-mode control for the tracking problem of uncertain dynamical systems. (June 2018) - Boukattaya, Mohamed; Mezghani, Neila; Damak, Tarak
Abstract: In this paper, robust and adaptive nonsingular fast terminal sliding-mode (NFTSM) control schemes for the trajectory tracking problem are proposed with known or unknown upper bound of the system uncertainty and external disturbances. The developed controllers take the advantage of the NFTSM theory to ensure fast convergence rate, singularity avoidance, and robustness against uncertainties and external disturbances. First, a robust NFTSM controller is proposed which guarantees that sliding surface and equilibrium point can be reached in a short finite-time from any initial state. Then, in order to cope with the unknown upper bound of the system uncertainty which may be occurring in practical applications, a new adaptive NFTSM algorithm is developed. One feature of the proposed control law is their adaptation techniques where the prior knowledge of parameters uncertainty and disturbances is not needed. However, the adaptive tuning law can estimate the upper bound of these uncertainties using only position and velocity measurements. Moreover, the proposed controller eliminates the chattering effect without losing the robustness property and the precision. Stability analysis is performed using the Lyapunov stability theory, and simulation studies are conducted to verify the effectiveness of the developed control schemes. Highlights: The novelty of the approach presented here can be understood by considering the following points: Unlike the existing robust TSM approaches [26–30 ] which are formulated under the assumption that the bound of the system uncertainty and disturbances are usually required to be known in advance, an adaptive parameter-tuning procedure is proposed here to estimate the unknown upper bounds. Therefore, the bound of the lumped uncertainty is unnecessary. Compared with the existing adaptive TSM control [31–37 ] which cannot guarantee singularity avoidance, the novel adaptive control law does not exhibit any singularity problem. Furthermore, the convergence rate of the system state is improved when the system state is far away from the equilibrium. Unlike [33, 34 ] where the acceleration signal is needed for the control design, the proposed approaches need only position and velocity information, which can be easily obtained using appropriate sensors.