Distributed cooperative output regulation of heterogeneous linear multi-agent systems based on event- and self-triggered control with undirected topology

Event\self‐triggered leader‐following consensus of multi‐agent systems with general dynamics

“…Before giving the main results, we give necessary lemmas, assumptions, and definitions as follows: Lemma 1 In the linear system ( A,B,C ), if the pair ( A,B ) is stabilisable and the pair ( C,A ) is observable [7], then there exists a unique solution to the following algebraic Riccati equation: Assumption 1 The information exchanging graph G among agents in the system consisting of (1) and (2) is connected. Assumption 2 ( A,B ) is stabilisable and are system matrices. Remark 1 Assumptions 1 and 2 are standard in solving the leader–follower consensus problem in multi‐agent systems, such as [15, 29, 33], and so on. Definition 1 The system composed of (1) and (2) is said to get leader‐following consensus [29], if there exists control input so that for any initial conditions the closed‐loop system composed of (1), (2), and satisfies …”

“…In the leader‐following systems, the state of the leader does not depend on any other agents' states, and it can only send messages to the only part of followers, which are the neighbours of the leader. It is worth mentioning that the output regulation problem [13–15] can be regarded as a leader‐following consensus problem in a sense. It was found that the leader‐following systems had great advantages in energy saving and strengthening communication in multi‐agent systems [16].…”

Fully distributed bipartite leader‐following consensus for uncertain linear multi‐agent systems with event‐triggered mechanism

“…Thus, the amount of transmission data and the communication cost will be largely reduced. Some pioneering works on event‐triggered control have been extensively investigated 21‐30 . For instance, the event‐triggered control technology was proposed in Reference 24 to address the consensus issue.…”

“…Due to this limitation, the novel triggering condition with time‐dependent threshold or state‐independent threshold was put forward 25‐27 . Since the time‐dependent threshold decouples the network evolution of system dynamics and the state‐dependent threshold causes too many unnecessary triggers, the combination threshold was then proposed 28‐30 …”

“…It can achieve the intermittent communication between neighbors; suppress the effect of uncertainty; and solve the problem of antagonistic communication between neighbor agents. The fully distributed adaptive bipartite event‐triggered leader‐following consensus problem for MASs with uncertainties is ignored by the existing control schemes but is settled by the proposed controller in this paper. In addition to the advantages of static controller, the fully distribute adaptive controller also has the advantage of not relying on the global information of the communication topology. The event‐triggered control of conventional consensus problems has been intensively investigated in the literatures 24‐30,32‐35 . In this paper, the points including uncertain MASs, bipartite control, event‐triggered control, and adaptive control are taken into account at the same time.…”