Event‐triggered global leader‐following consensus of a group of neutrally stable linear systems subject to input saturation

Abstract

This paper studies the global leader-following consensus problem for a multiagent system using event-triggered linear feedback control laws. The leader agent is described by a neutrally stable linear system and the follower agents are also described by a neutrally stable linear system but with saturating input. Both the state-feedback case and the output-feedback case are considered. In each case, an event-triggered control law is constructed for each follower agent and an event-triggering strategy is designed for updating these control laws. These event-triggered control laws are shown to achieve global leader-following consensus when the communication topology among the follower agents is strongly connected and detailed balanced and the leader is a neighbor of at least one follower agent. The Zeno behavior is excluded. The theoretical results are illustrated by simulation.KEYWORDS event-triggered control, input saturation, leader-following consensus, multi-agent systems, output feedback INTRODUCTIONRecent years have witnessed an increasing number of works on event-triggered control, which evolves from traditional sampled-data control. In traditional sampled-data control, signals are sampled periodically. Later, aperiodic sampling is developed to deal with the case that the sampling intervals are uncertain or vary with time. There are many results on sampled-data control (see, for example, other works 1-3 ) and aperiodic sampling (see, for example, related works 4-6 ). Event-triggered control has the property of aperiodic sampling, where the state is sampled only when required, eg, the sampled error exceeding a threshold value. Event-triggered control has the advantages of reducing the unnecessary sampling and requiring fewer control updates than traditional sampled-data control. Much attention has been paid to event-triggered control and fruitful results have been obtained (see, for example, other works 7-11 ) Event-triggered control design for multi-agent systems has aroused much interest. Cooperative control of multi-agent systems (see, for example, related works 12-14 ) requires frequent updates of control input, which poses a great challenge to the controller design for systems with limited resources. Yang et al 15 proposed a decentralized event-triggered consensus controller for each agent to achieve consensus, where each agent has its own triggering instants. The Zeno behavior, infinitely many triggers in a finite time, is also excluded in the aforementioned work. 15 In the work of Fan et al, 16 distributed event-triggered voltage control strategy is developed for the reactive power sharing of a microgrid, which can significantly reduce the amount of communication for the microgrid.As one of the most common physical constraints in practical control systems, actuator saturation has drawn much attention over the past few decades. Many problems have been solved for systems with actuator saturation such as 3376

Cooperative robust output regulation of linear uncertain multi‐agent systems: A dynamic event‐triggered approach

“…[15][16][17][18][19][20][21][22] Later, the event-triggered control approach is introduced to solve some consensus problems of multi-agent systems. [23][24][25][26] Recently, the event-triggered cooperative output regulation problem begins to receive more and more attention. [27][28][29][30][31][32] To be precise, the cooperative output regulation problem of heterogeneous linear multi-agent systems is studied in Reference 27 by event-triggered control.…”

“…Then, various event‐triggered control problems of linear and nonlinear systems are considered 15‐22 . Later, the event‐triggered control approach is introduced to solve some consensus problems of multi‐agent systems 23‐26 . Recently, the event‐triggered cooperative output regulation problem begins to receive more and more attention 27‐32 .…”

Fully distributed event‐triggered asymptotic attitude coordination of multiple spacecraft systems with disturbances

“…Over the last decade, a rich body of distributed event-triggered cooperative control schemes have been developed to reach average consensus for a group of integrators, 17 to solve the cooperative output regulation problem for certain or uncertain linear systems, [18][19][20][21][22] and to achieve the leader-following consensus of multiple neutrally stable linear systems subjected to actuator saturation. 23 To remove the requirement of the global knowledge of the network topology and make the control scheme fully distributed, the dynamic coupling gain technique has been applied in recent studies on the event-triggered consensus and containment control problems. [24][25][26][27] Moreover, the fully distributed event-triggered control for multiple linear systems with quantizers was studied in Reference 28 to further reduce communication burdens of digital channels.…”

“…The idea of event‐triggered control was then widely applied to the cooperative control of multi‐agent systems (MASs) to alleviate communication burden. Over the last decade, a rich body of distributed event‐triggered cooperative control schemes have been developed to reach average consensus for a group of integrators, 17 to solve the cooperative output regulation problem for certain or uncertain linear systems, 18‐22 and to achieve the leader‐following consensus of multiple neutrally stable linear systems subjected to actuator saturation 23 . To remove the requirement of the global knowledge of the network topology and make the control scheme fully distributed, the dynamic coupling gain technique has been applied in recent studies on the event‐triggered consensus and containment control problems 24‐27 .…”

“…Despite the extensive studies of event‐triggered distributed control of MASs, the relevant results are rather limited as to the attitude coordination of multiple spacecraft under communication constraint. Nonlinearity in both the kinematics and dynamics hinders the direct application of the results in References 18‐28. Very recently, the event‐triggered attitude coordination problem for multiple spacecraft has been investigated in a few works 29‐31 .…”