This paper addresses the event-triggered cooperative robust output regulation problem for multi-agent systems with uncertain exosystems. Existing distributed event-triggered observers rely on the accurate model of the exosystem, which cannot be applied to handle uncertain exosystems. To tackle this issue, a novel adaptive internal model-based observer is proposed. This observer estimates the exosystem’s output using event-triggered communication among agents. However, implementing this observer presents challenges in determining the decay rate of the observer error, which affects the prevention of Zeno behavior. To overcome these issues, two resettable and non-increasing dynamic variables are proposed to specify the event-triggering instants of each agent. With the dynamic variables, a positive minimum inter-event time can be provided with bounded MAS states, thus excluding Zeno behavior. Finally, the effectiveness of the proposed control protocol is verified through a simulation.

In this article, a fully distributed event-triggered protocol is proposed to solve the consensus problem of uncertain Euler-Lagrange (EL) multiagent systems (MASs) under jointly connected digraphs. First, distributed event-based reference generators are proposed to generate continuously differentiable reference signals via event-based communication under jointly connected digraphs. Unlike some existing works, only the states of agents rather than virtual internal reference variables need to be transmitted among agents. Second, adaptive controllers are exploited based on the reference generators so that each agent can track the reference signals. The uncertain parameters converge to their real values under an initially exciting (IE) assumption. It is proved that the uncertain EL MAS achieves state consensus asymptotically under the proposed event-triggered protocol composed of the reference generators and the adaptive controllers. A unique feature of the proposed event-triggered protocol is its fully distributed property: the protocol does not depend on global information about the jointly connected digraphs. Meanwhile, a minimum interevent time (MIET) is guaranteed. Finally, two simulations are conducted to show the validity of the proposed protocol.

This paper addresses the leader-following $H_{\infty}$ consensus of linear multi-agent systems via distributed dynamic event-triggered control protocols. Both multi-agent systems with homogeneous and heterogeneous linear dynamics are considered. A novel dynamic event-triggering mechanism based on a unified time-and event-triggering framework is proposed. The open-loop estimation method is adopted to avoid continuous communication between neighboring agents. As a comparison, a static event-triggering mechanism is also studied in this work. It is shown that the $H_{\infty}$ consensus problem can be handled by the control protocols with the dynamic or static event-triggering mechanisms. At last, effectiveness of the proposed event-triggered control protocols are verified by two numerical examples, which shows that the dynamic event-triggering mechanism can further enlarge inter-event times.

In this article, the cooperative output regulation problem of heterogeneous linear multiagent systems under jointly connected digraphs is addressed. The event-triggered control protocols based on state feedback and output feedback are proposed, respectively. It is shown that the output tracking errors of the resulting closed-loop control systems converge to 0 exponentially via the proposed protocols. One of the key advantages of the proposed event-triggering mechanism is that the information transmissions induced by event triggerings and topology switchings are independent, and data transmissions among agents are thus reduced. Furthermore, an explicit minimum interevent time is provided for all the agents so that the Zeno-behavior is excluded strictly. Finally, three numerical examples are provided to verify the effectiveness of the proposed protocols.

This article addresses the cooperative output regulation problem of heterogeneous linear multiagent systems with jointly connected digraphs under the assumption that the exosystem matrix is only known by the neighbors of the exosystem. First, a novel event-based adaptive distributed observer with time-dependent power functions as the event-triggering threshold is proposed to estimate the exosystem matrix and the exogenous signal simultaneously. A new analytical method based on the weighted mean-value theorem for integrals and Bellman–Gronwall lemma is developed to prove that the estimation errors converge to zero asymptotically. Second, a distributed dynamic control law is proposed based on the event-based adaptive observer, and it is shown that the tracking errors of the resulting closed-loop system converge to zero asymptotically. Two distinctive advantages of this work are that 1) the event-triggered control protocol is fully distributed, and 2) a positive minimum inter-event time is explicitly given so that Zeno behavior is strictly excluded. Finally, the effectiveness of the proposed fully distributed ETC protocol is illustrated by a numerical example.

This paper investigates the distributed continuous-time nonconvex optimization problem over unbalanced directed networks. The objective is to cooperatively drive all the agent states to an optimal solution that minimizes the sum of the local cost functions. Based on the topology balancing technique and adaptive control approach, a novel fully distributed algorithm is developed for each agent with neither prior global information concerning network connectivity nor convexity of local cost functions. By viewing the proposed algorithm as a perturbed system, its input-to-state stability with a vanishing perturbation is first established, and asymptotic convergence of the decision variables toward the optimal solution is then proved under the relaxed condition. A key feature of the algorithm design is that it removes the dependence on the smallest strong convexity constant of local cost functions, and the left eigenvector corresponding to the zero eigenvalue of the Laplacian matrix of unbalanced directed topologies. The effectiveness of the proposed fully distributed algorithm is illustrated with two examples.

This paper addresses the leader-following H ∞ output consensus problem of heterogeneous linear multi-agent systems (MASs) under directed graphs . Both state feedback and output feedback based event-triggered control (ETC) protocols are developed. First, to avoid continuous communication between neighboring agents, the open-loop estimation method is used in the proposed ETC protocols. Second, a unified time- and event-triggering mechanism with an explicit minimum inter-event time (MIET) is further developed based on the open-loop estimation method so that Zeno behavior can be excluded. It is shown that under the proposed ETC protocols, the controlled MAS can achieve H ∞ output consensus. Finally, two numerical examples are provided to verify effectiveness of the proposed ETC protocols.