Adaptive Finite-time Tracking Control for Constrained Pure-feedback Systems With Time-varying Delays and Unknown Initial States

This paper investigates the adaptive finite-time tracking control problem for a class of constrained pure-feedback systems with time-varying delays and unknown initial states. By designing a novel shifting function and using the state transformation, there is no need to know the initial value of states. Instead of employing barrier Lyapunov functions, the modified nonlinear state-dependent functions are constructed to solve the deferred state constraints, avoiding the feasibility conditions on virtual controllers. The effect of time-varying delays is eliminated by combining the radial basis function neural networks with a finite covering lemma, and the requirement that the derivative of time-varying delays should be less than one in Lyapunov-Krasovskii functional method is relaxed. The asymmetric saturation nonlinearity is solved by designing an auxiliary system. The system coordinate transformation is employed to solve the design difficulty brought by the nonaffine structure. Then, an adaptive finite-time tracking control scheme is developed based on the command filtered backstepping technique. The developed control scheme can not only make all states satisfy the asymmetric time-varying constraints after a predefined time, but also guarantee the finite-time tracking performance. Finally, simulation examples are given to demonstrate the effectiveness of the proposed scheme.