Consensus of Linear Multi-agent Systems with Persistent Disturbances
This paper focuses on the consensus problem of continuous-time multi-agent systems with persistent disturbances. A distributed protocol is designed, which consists of two parts, one is the traditional control protocol, the other one is the estimation of d
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Abstract This paper focuses on the consensus problem of continuous-time multiagent systems with persistent disturbances. A distributed protocol is designed, which consists of two parts, one is the traditional control protocol, the other one is the estimation of disturbances. Then, using the method of matrix analysis, the sufficient conditions for achieving consensus of the closed-loop systems are found out. Finally, simulations are provided to demonstrate the effectiveness of the proposed algorithm. Keywords Multi-agent system ⋅ Consensus ⋅ Disturbances ⋅ Control protocol
1 Introduction Multi-agent systems have the characteristic of autonomy, distribution, and coordination, and have the ability of self-organization, learning, and reasoning. Multi-agent systems are efficient to deal with the practical systems, such as the formation flight of the UAV, multi-robot systems, and so on [1, 2]. More and more attentions have been paid on cooperative control of multi-agent systems in recent years. The consensus problem of multi-agent systems is one of the most fundamental issues. Starting from the Vicsek model [3], a broad spectrum of scholars are much more kindly to study the consensus problems of multi-agent [6] systems with different characteristics. For example, the consensus problems of discrete-time were investigated in [4, 5]. For the continuous-time multi-agent systems, consensus problems were discussed in [6, 7]. It is shown that the consensus of first-order systems can be achieved if and only if the network topology contains a directed spanning tree. And then these results were extended to stochastic switching systems [6], some average consensus conditions were obtained. All of these results were given for the firstorder multi-agent systems. In practical systems, the control objects may be accelerated velocity rather than velocity and the methods can not be applied to second-order S. Guo ⋅ L. Mo (✉) ⋅ T. Pan School of Science, Beijing Technology and Business University, Beijing 100048, China e-mail: [email protected] © Springer Science+Business Media Singapore 2016 Y. Jia et al. (eds.), Proceedings of 2016 Chinese Intelligent Systems Conference, Lecture Notes in Electrical Engineering 405, DOI 10.1007/978-981-10-2335-4_10
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systems straightforward, so it is meaningful to investigate the consensus problems of second-order multi-agent systems. In [2], it shows that the second-order systems might not achieve consensus even if the network topology has a directed spanning tree. And a necessary and sufficient condition was given for the consensus of secondorder systems with directed topologies. Recently, the consensus problems of linear multi-agent systems were also considered. In [8], it was proved that the consensus can be reached if and only if all of the nonzero eigenvalues of the Laplacian matrix lie in the stable regions. In practical systems, it is inevitable that the system can be affected by external disturbances, so it is important to discuss the consensus problem of the multi-agent systems
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