Global Tracking Control With Tunable Transient Performance Under Deferred Time-varying Constraints

In this article, we present a global output tracking control method for nonlinear strict-feedback systems under deferred asymmetric time-varying constraints and various initial conditions. Different from most existing results that require initial satisfaction of the constraining conditions, the proposed solution makes use of the proof-by-contradiction method, which, with the aid of the tunable normalized tracking signal and two novel error transformation functions, enables the control scheme with several salient features: 1) the deferred constraint (time-varying and asymmetric) is directly addressed, while completely avoiding the explosion of complexity arising from repeatedly/recursively differentiating virtual controllers as typically involved in the backstepping control of nonlinear strict-feedback systems; 2) stable output tracking with tunable transient behavior and prescribed steady-state performance is ensured under any unknown initial conditions without the need for human intervention; 3) there is no need for neural network (NN)-based approximators, command filters or auxiliary dynamic surface control (DSC)-based design and analysis, thus substantially reducing the control synthesis complexity; and 4) neither a priori knowledge of system nonlinearities nor estimation of their bounds is required. Two numerical examples are provided to verify the benefits and efficiency of the proposed method.