Adaptive output-feedback tracking for nonlinear systems with unknown control direction and generic inverse dynamics

Abstract

This paper studies adaptive output-feedback tracking for a class of typical uncertain nonlinear systems. In the context of unknown control direction, a generic uncertainty encountered inevitably in practice is adequately taken into consideration, i.e., the ISpS (input-to-state practically stable) inverse dynamics acting as the dynamic differences between the real plants and the models. Besides, the systems in question also permit two critical ingredients, i.e., unmeasured-state dependent nonlinearities and arbitrary function-of-output growth on unknown system nonlinearities. The three ingredients together largely challenge the feasibility/availability of practical tracking by means of output feedback. Nevertheless, a new control strategy is proposed by flexibly integrating the dynamic compensation based on Nussbaum-type gain, backstepping design technique together with the refined pseudo-sign and pseudo-dead-zone functions that were introduced for the first time in our previous studies. The two refined functions, which are sufficiently smooth, can moderately avoid the use of smooth domination/treatment in control design and can potentially render the attained control strategy tighter and less conservative. Moreover, to keep the order of the closed-loop system at a low level, an n-dimensional filter with a dynamic high gain is delicately devised instead of a 2n-dimensional one used in the relevant literature. It turns out that the proposed adaptive output-feedback controller is capable of guaranteeing the global boundedness of all states of the resulting closed-loop system, while steering the system tracking error to enter, in finite time, a prescribed λ-neighborhood of the origin and keeping it inside thereafter. A simulation example is provided to demonstrate the proposed approach.