LMI-based [formula omitted] 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. • This paper addresses the problem of practical consensus with spatiotemporal dynamics. • The multi-agent system is modeled by a nonlinear reaction–diffusion equation. • An H ∞ boundary consensus control is proposed to suppress the external disturbances. • The controller needs a fewer actuators than ones distributed inner spatial domain. • The controller gives a tradeoff between optimal performances and actuator saturation. [ABSTRACT FROM AUTHOR]