Event-Trigger-Based Fuzzy Adaptive Finite-Time Control for Uncertain Nonlinear Systems with Unmeasurable States

This article delves into the fuzzy finite-time adaptive control problem for uncertain nonlinear systems where state measurements are unavailable, nonlinear functions are unknown, and communication is limited. To emulate the unknown nonlinear relationships within the control methodology, we exploit fuzzy logic systems, while also proposing a state observer to address the challenge of unobservable states. To avoid the “complexity explosion” problem intrinsic to conventional backstepping techniques, the controller is developed based on the dynamic surface control methodology, which incorporates first-order filters to successfully alleviate this issue. An event-triggered approach is introduced to alleviate the computational and communication overhead. By leveraging the finite-time control approach, an adaptive finite-time fuzzy control algorithm is constructed using the adaptive backstepping technique. An event-triggered mechanism is designed to reduce communication frequency, while rigorously maintaining closed-loop stability and ensuring a positive minimum inter-event time to avoid Zeno behavior. The proposed finite-time controller achieves finite-time stability of the controlled systems, thereby guaranteeing that all system signals remain bounded within a finite time, despite the presence of unmeasurable states, unknown nonlinear functions, and limited communication constraints. This paper differentiates itself from recent related studies by proposing a co-designed observer–controller framework that rigorously guarantees finite-time stability under an event-triggered communication mechanism, thereby effectively addressing the multiple concurrent challenges of state estimation, rapid convergence, and limited network resources. Simulation examples are conducted to illustrate the effectiveness and feasibility of the derived control algorithm.