A Fuzzy Gain-Scheduled Time Base Generator for Fixed-Time Leader-Following Tracking Consensus of Feedforward Nonlinear Multi-Agent Systems

Abstract

This paper proposes a fuzzy gain-scheduled time base generator (FGS-TBG) framework for prescribed fixed-time leader-following consensus of Lipschitz feedforward nonlinear multi-agent systems (FNMASs) with a dynamic leader under distributed output feedback. Existing TBG-based fixed-time consensus methods mostly rely on static leader assumptions and constant tuning parameters, limiting their adaptability to dynamic reference trajectories and causing redundant control energy consumption; meanwhile, most are designed for integrator-type or linear systems, leaving a notable research gap for FNMASs. To address the static-leader limitation, we first develop a smooth TBG-based distributed observer and a distributed output-feedback consensus protocol for FNMASs with a dynamic leader. Our scheme accommodates a user-defined nonzero leader control input and guarantees prescribed fixed-time leader-following tracking consensus independent of the initial conditions. To boost the adaptability of fixed-parameter TBG schemes, we further develop an FGS-TBG strategy for online intelligent tuning of TBG gains. Instead of approximating unknown nonlinear dynamics as in traditional adaptive fuzzy control, the fuzzy system only schedules TBG gains, retaining all inherent theoretical characteristics of TBG while enhancing adaptability and cutting redundant control energy. We establish the fixed-time convergence of the closed-loop system through Lyapunov analysis. Comparative simulations verify that the proposed framework achieves superior adaptability and lower control cost while maintaining the prescribed fixed-time performance.