Cooperative learning event-triggered control for discrete-time nonlinear multi-agent systems by internal and external interaction topology

This paper investigates distributed cooperative learning event-triggered control for discrete-time strict-feedback nonlinear multi-agent systems with an identical system structure and different recurrent reference orbits. A clever system decomposition method is firstly proposed to divide every n$$ n $$-order agent system into n$$ n $$ first-order subsystems, which makes it possible to solve the tough problem that every estimated neural weight cannot converge to an unique ideal value based on the existing control scheme. By constructing two interaction typologies, a novel distributed cooperative weight updating law is designed by the introduction of the internal interaction terms between n$$ n $$ subsystems of every agent, the external interaction terms between agents, and the triggering mechanism between agents. With the combination of the graph multiplication operation, the consensus theory and the matrix null space property, the proposed cooperative event-triggered control scheme guarantees that every agent can track their corresponding recurrent reference trajectories. And further the exponential convergence of all agents' neural estimated weights to a close vicinity around their mutual and unique ideal weights is verified under the condition that the directed interaction topology between agents is strongly connected and balanced. Such a weight convergence makes the proposed scheme has some significant advantages including the small data storage space, the convenient knowledge reuse, the good generalization ability, and the low communication burden. By reinvoking the saved constant weights, a static learning controller is presented for the high-performance control of similar diversified tracking tasks. Simulation studies and some comparisons are given to show the advantages and effectiveness of the presented scheme.