Group consensus of discrete-time multi-agent systems with fixed and stochastic switching topologies
This paper investigates the group consensus problem for discrete-time multi-agent systems with a fixed topology and stochastic switching topologies. The stochastic switching topologies are assumed to be governed by a finite-time Markov chain. The group consensus problem of the multi-agent systems is converted into the stability problem of the error systems by a model transformation. Based on matrix theory and linear system theory, we obtain two necessary and sufficient conditions of couple-group consensus for the case of fixed topology, and one necessary and sufficient condition of mean-square couple-group consensus for the case of stochastic switching topologies. Algorithms are provided to design the feasible control gains. Then, the results are extended to the case of multi-group consensus. Finally, simulation examples are given to show the effectiveness of the proposed results.
KeywordsGroup consensus Multi-agent system Fixed topology Stochastic switching topology
The work of J.H. Park was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2013R1A1A2A10005201). Also, the work of H. Zhao was supported by the National Natural Science Foundation of China under Grants nos. 61203056, 61104007.
- 2.Yuan, D.M., Ma, Q., Wang, Z.: Dual averaging method for solving multi-agent saddle-point problems with quantized information. Trans. Inst Meas. Control 36(1), 38–46 (2014)Google Scholar
- 4.Qin, J.H., Gao, H.J., Zheng, W.X.: On average consensus in directed networks of agents with switching topology and time delay. Int. J. Syst. Sci. 42(12), 1947–1956 (2011)Google Scholar
- 10.Liu, S., Xie, L.H., Zhang, H.S.: Containment control of multi-agent systems by exploiting the control inputs of neighbors. Int. J. Robust Nonlinear Control. doi: 10.1002/rnc.3026
- 11.Cao, Y.C., Ren, W.: Finite-time consensus for second-order systems with unknown inherent nonlinear dynamics under an undirected switching grahp. In: American control conference, Montreal, pp. 26–31, 2012Google Scholar
- 12.Zhang, B., Jia, Y.M., Du, J.P., Zhang, J.: Finite-time consensus control for multiple manipulators with unmodeled dynamics. In: American control conference, Washington, DC. pp. 5400–5405, 2013 Google Scholar
- 13.Matei, I., Martins, N., Baras, J.S.: Consensus problems with directed Markovian communication patterns. In: Proceedings of American control conference, St. Louis, pp. 1298–1303 (2009)Google Scholar
- 14.Zhang, Y., Tian, Y.P.: Consentability and protocol design of multi-agent systems with stochastic switching topology. Automatica 45(5), 1195–1201 (2009)Google Scholar
- 17.Syed Ali, M., Marudai, M.: Stochastic stability of discrete-time uncertain recurrent neural networks with Markovian jumping and time-varying delays. Math. Comput. Model. 54(9–10), 1979–1988 (2011)Google Scholar
- 18.Ren, W., Atkins, E.: Distributed multi-vehicle coordinated control via local information exchange. Int. J. Robust Nonlinear Control 17, 1002–1033 (2007Google Scholar
- 19.Yu, J.Y., Wang, L.: Group consensus of multi-agent systems with undirected communication graphs. In: Proceedings of 7th Asian control conference, Hong Kong, pp. 05–110 (2009)Google Scholar
- 20.Yu, J.Y., Wang, L.: Group consensus in multi-agent systems with switching topologies. In: 48th IEEE conference on decision and conrol and 28th Chinese conrol conference, Shanghai, pp. 2652–2657 (2009)Google Scholar
- 22.Tan, C., Liu, G-P., Duan, G-R.: Couple-group consensus of multi-agent systems with directed and fixed topology. In: Proceedings of 30th Chinese control conference, Yantai, pp. 6515–6520 (2011)Google Scholar