Observer-based prescribed-time adaptive fuzzy formation control for nonlinear multi-agent systems

This article focuses on the issue of observer-based fuzzy adaptive prescribed-time formation tracking control for nonlinear multi-agent systems (MASs). Unknown nonlinear dynamics are identified using Fuzzy logic systems (FLSs). By introducing the time-varying gain function, a fuzzy high-gain state observer is constructed to identify unmeasurable states. Then, with the help of the time-domain mapping technique, the prescribed-time control issue of finite-time domain can be converted to asymptotic tracking control of infinite-time domain. Furthermore, a nonlinear filter is constructed to avoid the issue of computational complexity. Combining the developed high-gain observer and smooth projection operator, an adaptive fuzzy prescribed-time formation output feedback control algorithm is proposed. Anchored in the Lyapunov stability and Barbalat Lemma, the presented control algorithm demonstrates all signals of the controlled system are bounded within prescribed time, the observe and formation errors can asymptotically converge to zero within prescribed time, and all signals of the closed-loop system are bounded. Finally, the effectiveness and feasibility of the developed control approach and theory can be verified by simulations.