LMI-based H_∞ boundary practical consensus control for nonlinear multi-agent systems with actuator saturation

This paper mainly addresses the practical consensus problem of nonlinear multi-agent systems modeled by reaction-diffusion equations subject to the bounded external disturbances. Different from the existing consensus control methods associated with spatiotemporal dynamics, the proposed H_∞ Neumann boundary controller based on distributed measurement data can guarantee the optimal disturbance attenuation performance under the actuator saturation. Initially, a consensus spatiotemporal error model is constructed by introducing the Kronecker product and equivalent directed graph. Subsequently, a linear matrix inequalities (LMIs)-based sufficient condition is derived by combining the improved Lyapunov-based approach and H_∞ norm. Then, an optimization problem is proposed by applying invariant set, such that the consensus errors can converge to a minimized bounded region in the presence of actuator saturation. Finally, comparison simulations on the synchronization of FitzHugh-Nagumo (FHN) model are given to demonstrate the effectiveness of proposed methodology.