Finite-time tracking control for a class of uncertain strict-feedback nonlinear systems with state constraints: A smooth control approach

This article is concerned with the finite-time tracking control problem for a class of strict-feedback nonlinear systems involving state constraints, unknown nonlinearities, and nonvanishing disturbances. Unlike the literature that mainly focuses on a C{0} finite-time controller, in this article, a novel C^{1} smooth finite-time adaptive neural network (NN) controller is proposed by employing a smooth switch between the fractional and cubic form state feedback. The proposed controller not only avoids the singularity but also makes it possible to implement the dynamic surface control (DSC) technique. By applying the adaptive NN control technique, together with barrier Lyapunov functions (BLFs) and a generalized first-order filter including both linear and fractional terms, the desired fast finite-time control performance of the closed-loop nonlinear systems can be guaranteed, and meanwhile, the state constraints are never violated. Under the proposed control scheme, the tracking control problems of nonlinear systems with output constraint and full-state constraints are, respectively, discussed. It is explicitly shown that all the internal error signals are driven to converge into small regions in a finite time. Finally, the effectiveness of the control scheme is also confirmed by the applications to the control of a second-order nonlinear system and an uncertain ship autopilot.