Disturbance rejection for classes of nonlinear systems

Abstract

This paper addresses the problem of non-adaptive global robust disturbance rejection for two distinct classes of nonlinear systems. The first class, denoted by C1, consists of nonlinear systems in strict-feedback form, with linear and Hurwitz zero-dynamics (whose states are unavailable for feedback), and enhanced - within this work - by forcing, unmatched, additive disturbances. Nonlinear tools are herein employed to demonstrate that the proposed control architecture - based on the high-gain paradigm - achieves closed-loop input-to-state stability with respect to the forcing disturbances, along with global asymptotic convergence towards an attractor which can be rendered as small as desired. Then, owing to the established input-to-state stability property, a uniformly bounded control action is additionally embedded within the control architecture. The additional unit, designed following the sliding-mode paradigm, is aimed at improving the disturbance rejection task, by potentially lowering the required high-gain control expenditure. The second class of systems, denoted by C2, is constituted by minimum-phase, uncertain, nonlinear systems with relative degree greater than one, featuring possibly unbounded, with possibly unbounded derivatives, output-dependent nonlinearities, with matched additive forcing disturbances. To solve the problem of output-feedback, non-adaptive, global robust disturbance rejection for systems within C2, first, an open-loop observer is employed in lieu of a classic dynamic extension adopted in earlier works, as the latter is no longer implementable due to the presence of unknown forcing disturbances. Subsequently, the results derived for C1 are then adapted to C2, to yield an output-feedback dynamic controller providing closed-loop global uniform boundedness, along with asymptotic regulation towards an attractor which can be rendered as small as desired.