A leader-following consensus of multi-agent systems with actuator saturation and semi-Markov switching topologies

Jiangtao Dai; Ge Guo; Jiangtao Dai; Ge Guo

doi:10.3934/mbe.2024217

Mathematical Biosciences and Engineering

2024, Volume 21, Issue 4: 4908-4926. doi: 10.3934/mbe.2024217

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Theory article

A leader-following consensus of multi-agent systems with actuator saturation and semi-Markov switching topologies

Jiangtao Dai ^{1
,
,},
Ge Guo ²

1.
Department of Basic Courses, Tianjin Sino-German University of Applied Sciences, Tianjin 300350, China
2.
The State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang 110819, China

Academic Editor: Yang Kuang

Received: 24 December 2023 Revised: 18 February 2024 Accepted: 23 February 2024 Published: 01 March 2024

The leader-following consensus (LFC) issue is investigated in this paper for multi-agent systems (MASs) subject to actuator saturation with semi-Markov switching topologies (SMST). A new consensus protocol is proposed by using a semi-Markov process to model the switching of network topologies. Compared to the traditional Markov switching topologies, the SMST is more general and practical because the transition rates are time-varying. By using the local sector conditions and a suitable Lyapunov-Krasovskii functional, some sufficient conditions are proposed such that the leaderfollowing mean-square consensus is locally achieved. Based on the derived sufficient conditions, an optimization problem is analyzed to determine the consensus feedback gains and to find a maximal estimate of the domain of consensus attraction (DOCA) of a closed-loop model. At the end, a numerical case is presented to verify the performance of the design method.
- actuator saturation,
- domain of consensus attraction,
- leader-following consensus,
- multi-agent systems,
- semi-Markov switching topologies
Citation: Jiangtao Dai, Ge Guo. A leader-following consensus of multi-agent systems with actuator saturation and semi-Markov switching topologies[J]. Mathematical Biosciences and Engineering, 2024, 21(4): 4908-4926. doi: 10.3934/mbe.2024217

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Abstract

The leader-following consensus (LFC) issue is investigated in this paper for multi-agent systems (MASs) subject to actuator saturation with semi-Markov switching topologies (SMST). A new consensus protocol is proposed by using a semi-Markov process to model the switching of network topologies. Compared to the traditional Markov switching topologies, the SMST is more general and practical because the transition rates are time-varying. By using the local sector conditions and a suitable Lyapunov-Krasovskii functional, some sufficient conditions are proposed such that the leaderfollowing mean-square consensus is locally achieved. Based on the derived sufficient conditions, an optimization problem is analyzed to determine the consensus feedback gains and to find a maximal estimate of the domain of consensus attraction (DOCA) of a closed-loop model. At the end, a numerical case is presented to verify the performance of the design method.

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