Periodic event‐triggered consensus control for multi‐agent systems with switching jointly connected topologies

Abstract

The consensus problem for a class of multi-agent systems with switching jointly connected topologies via periodic event-triggered control is studied. The distinguishing feature of such system is that the eigenvalues of system matrix can contain positive real parts. Due to the coexistence of unstable system matrix and disconnected topologies, the agents can diverge from each other across some periods even if the control input is imposed on them. To overcome this difficulty, a periodic-sampling time unit (PSTU) approach is introduced to analyse the local convergence or divergence property within each sampling time unit based on the periodic event-triggering control. Then the stabilisation property of switching behaviours is utilised to compensate the divergence within each switching interval via the dwell time technique. It is interesting to see that each switching period is considered to consist of finite number of PSTUs. Then by confining a pair of lower and upper bounds on the dwell time, the overall consensus can be reached. Further, a novel class of event-dependent discretised Lyapunov functions are utilised to describe the error characteristics and computable conditions for the overall consensus can be derived. Finally, the effectiveness of the proposed result is illustrated by a numerical example.

Consensus of piecewise time-varying multi-agent systems with switching topologies

“…Most of the existing results on multi-agent systems under switching topologies utilize the multiple time-invariant Lyapunov function method (Savino et al (2016), Sun et al, 2020a, 2020b; Sun and Wang, 2020b; Valcher and Zorzan, 2017; Wen et al, 2014, 2015). However, the multiple time-invariant Lyapunov function method is not applicable in this paper because it is difficult or even impossible to construct time-invariant Lyapunov functions for the time-varying system (2) within different time periods.…”

“…However, the topologies may be switching in many practical cases due to communication constraints or failures in communication channels. Recently, numerous results have explored the consensus problems with switching topologies (Savino et al, 2016; Sun et al, 2020a, 2020b; Sun and Wang, 2020b; Valcher and Zorzan, 2017; Wen et al, 2014, 2015). Wen et al (2014) investigate the consensus control problem of multi-agent systems under switching topologies, in which the communication topology is modeled by the Markov jumps with uncertain rates of transitions.…”

“…However, there are a few results on the time-varying multi-agent systems with switching topologies. The results in Wen et al (2014), Savino et al (2016), Wen et al (2015), Sun et al (2020b), Sun and Wang (2020b), Sun et al (2020a) and Valcher and Zorzan (2017) are not applicable in this problem due to the piecewise characteristics of the system matrix. The consensus control of time-varying multi-agent systems under switching topologies needs investigation.…”

Dynamic event‐triggered control for leader‐following consensus of multiagent systems with the estimator

“…Much effort has been made to look for an effective control scheme to solve the above shortcomings. In this case, event-triggered control (ETC) has attracted the attention of researchers [15][16][17]. Using this control method, each agent only exchanges information with the neighbours when the control protocol is violated.…”

“…Compared with refs. [15,19], it only needs the states of the neighbours at the triggering instants instead of continuous measurement. 2) An event-triggered protocol is proposed, and an auxiliary variable is designed to dynamically adjust the triggering threshold.…”