Event-triggered robust cooperative stabilization in nonlinearly interconnected multiagent systems

Abstract

By way of the graph theoretic tools, we model closed-loop large-scale systems as two-layer multiagent systems with the agent layer describing nonlinearly interconnected dynamics and the control layer designed to stabilize the system by communications in agents’ neighborhoods. We consider a scenario in which the effect of dynamical interactions over the agent layer appears through some nonlinear functions which are in the range space of the control input matrix, yet the underlying agent layer interconnection topology and the associated nonlinearities are not known to the control layer designer. We develop a static linear cooperative algorithm and, having endowed each local controller with several buffers, we schedule the control layer information exchange events in a non-periodic non-synchronous manner. We combine graph theoretic and event triggering ideas with an optimal control formulation, and propose a design procedure to obtain the required robust control gain. We prove that all trajectories of the closed-loop multiagent system will exponentially converge to the origin in the presence of time-varying nonlinearly interconnected modeling uncertainties over agent layer. For the same cooperative stabilization algorithm, trading off with the exponential convergence to a neighborhood around the origin, we further show that a practical event triggering mechanism can be developed to better deal with the effect of modeling mismatch on the number of triggering events. We also prove the proposed event triggering mechanisms do not exhibit Zeno behavior to ensure the feasibility of the proposed ideas in the sense of reduced communication load and, thereby, energy consumption.