Finite-time tracking for state-constrained strict-feedback systems without feasibility conditions

This paper investigates the finite-time tracking control problem for a class of nonlinear strict-feedback systems subject to asymmetric and time-varying full-state constraints. The proposed method is able to achieve practical finite-time tracking stability without the feasibility conditions, that is, the tracking error converges to a small region around zero in a finite time that can be explicitly expressed and adjusted, which is different from most existing results on strict-feedback systems subject to constraints where only ultimately uniformly bounded results are obtained and the feasibility conditions are normally required. Three major design steps are utilized. Firstly, by introducing a novel barrier function, the technical obstacle associated with the feasibility conditions is removed; Secondly, to circumvent the technical difficulty in finite-time stability analysis, a time-varying index is introduced and incorporated into the adaptive law; And thirdly, both a linear feedback term and a fractional feedback term are included into the virtual filter of the dynamic surface control-based method. It is the combination of these design skills that allows the practical finite-time tracking results to be established. The effectiveness of the proposed scheme is verified by the numerical simulation.