Effective Fixed-Time Control for Constrained Nonlinear System

TL;DR

This paper introduces an adaptive fixed-time control approach for constrained nonlinear systems, combining state transformation, event-triggered strategies, and stability analysis to improve control efficiency and reduce communication load.

Contribution

It presents a novel fixed-time control method with an innovative state transformation and a multi-threshold event-triggered strategy that eliminates the need for continuous state monitoring.

Findings

Reduces control command updates significantly

Maintains high tracking accuracy under constraints

Ensures stability with convergence time independent of initial conditions

Abstract

In this paper, we tackle the state transformation problem in non-strict full state-constrained systems by introducing an adaptive fixed-time control method, utilizing a one-to-one asymmetric nonlinear mapping auxiliary system. Additionally, we develop a class of multi-threshold event-triggered control strategies that facilitate autonomous controller updates, substantially reducing communication resource consumption. Notably, the self-triggered strategy distinguishes itself from other strategies by obviating the need for continuous real-time monitoring of the controller's state variables. By accurately forecasting the subsequent activation instance, this strategy significantly optimizes the efficiency of the control system. Moreover, our theoretical analysis demonstrates that the semi-global practical fixed-time stability (SPFTS) criterion guarantees both tracking accuracy and closed-loop stability under state constraints, with convergence time independent of initial conditions. Finally, simulation results reveal that the proposed method significantly decreases the frequency of control command updates while maintaining tracking accuracy.