Practically Predefined-Time Leader-Following Funnel Control for Nonlinear Multi-Agent Systems With Fuzzy Dead-Zone

Adaptive fuzzy practical predefined-time leader-following consensus with funnel performance is investigated for nonlinear multi-agent systems (MASs) subject to fuzzy dead zone (FDZ). The dead zone model is uncertain and fuzzy, which makes the developed scheme different from the existing work of funnel performance. Firstly, to avoid the “explosion of complexity” problem, an improved nonlinear predefined-time filter is introduced and the convergence time of filtering errors can be preset. Subsequently, a distributed controller is constructed via the dynamic surface technique, which can not only reduce the influence of FDZ nonlinearity on the system performance, but also realize the considered system is practical predefined-time stability (PPTS), while satisfying the transient and steady-state performance imposed by the funnel. Furthermore, unlike the literature for solving funnel-like performance, the inverse transform function and the complex Lyapunov function are not involved in the proposed method, which can avoid the potential singularity issue and complex control law. Finally, simulation examples are performed to verify the effectiveness of the developed algorithm.
Note to Practitioners
—Complex engineering systems are difficult to control with a single component, so the cooperative control of multi-agent systems (MASs) has attracted more and more attention due to its wide range of applications, such as multi-motor synchronization, spacecraft formation flying, etc. Consensus, as one of the important issues in MASs cooperative control, has become a research hotspot. Dead-zone (DZ) nonlinearity is one of the most common constraints in physical systems, which often occurs in electric servo motors, hydraulic servo valves, etc. In the existing literature, the DZ feature is definite and accurate. However, due to the physical characteristics of the actuator and the influence of the environment, there are often uncertainties in the DZ parameters. On the other hand, performance behaviors (convergence rate, maximum overshoot and maximum steady state error, etc.) often required to be pre-specified in practical applications. Therefore, the funnel-based leader-following consensus control is studied for MASs with fuzzy dead zone (FDZ) and predefined-time convergence.