Global quantized output feedback control of nonlinear systems under non-Lipschitz condition

Abstract

In this paper, a novel backstepping-based output feedback control algorithm is developed for uncertain nonlinear systems subject to both input and output quantization, while ensuring the prescribed transient performance. The development of this control approach involves several crucial steps that tackle specific challenges. Firstly, by creating invariant sets and choosing appropriate parameters, a prescribed performance control method is proposed. Subsequently, by leveraging the maximum values of relevant variables or functions within these invariant sets, the requirement for iterative differentiation of the virtual control signals in the controller design is circumvented. Furthermore, by simplifying the structure of the controller design, the effects arising from output quantization are effectively handled. Notably, the proposed method no longer requires the nonlinear function of the system model to satisfy global Lipschitz continuity, and it no longer yields semi-global results. Instead, it achieves global stability for the closed-loop system and provides clear guidance for the adjustment of its parameters. Finally, the effectiveness and advantages of the proposed quantized control approach are validated through a numerical case study.