This thesis investigates the distributed event-triggered control problem in multi-agent systems. In particular, we emphasise on the event-triggered consensus and distributed optimisation problems. We consider a multi-agent system where each agent is a single integrator with actuator disturbance, and only local information is accessible while each agent broadcasts its own state to its neighbourhood when a certain condition is met based on the local information available. We propose a novel distributed stochastic event-triggering law for the consensus problem to significantly reduce the communication among agents by harnessing stochasticity based on existing deterministic event-triggering laws. We first analyse the consensus performance for the multi-agent system under the propose...[ Read more ]

This thesis investigates the distributed event-triggered control problem in multi-agent systems. In particular, we emphasise on the event-triggered consensus and distributed optimisation problems. We consider a multi-agent system where each agent is a single integrator with actuator disturbance, and only local information is accessible while each agent broadcasts its own state to its neighbourhood when a certain condition is met based on the local information available. We propose a novel distributed stochastic event-triggering law for the consensus problem to significantly reduce the communication among agents by harnessing stochasticity based on existing deterministic event-triggering laws. We first analyse the consensus performance for the multi-agent system under the proposed event-triggering law, and prove that the system can reach practical consensus with the error bound linearly proportional to the disturbance and an arbitrarily small parameter. In other words, the multi-agent system reaches arbitrarily small consensus error provided that the actuation disturbance is absent. Furthermore, we show that the system does not exhibit Zeno behaviour by deriving a strictly positive lower bound on the inter-communication time for any agent in the system. Numerical examples are provided to illustrate the effectiveness of the proposed event-triggering law in comparison with the deterministic triggering law, and to demonstrate its application. Built on the analysis from the consensus problem, we propose the adoption of the proposed stochastic event-triggering law to the distributed optimisation problem. We first illustrate that the distributed optimisation problem is in fact a generalisation of the aforementioned consensus problem. We then prove that the multi-agent system is capable of solving the optimisation problem to an arbitrary residual error. Similar to the consensus problem, we also provide a strictly positive lower bound on the inter-communication time to prove the non-existence of Zeno behaviour. Numerical simulations are provided to show the performance compared with existing event triggers.