Sliding mode control for consensus tracking of second-order nonlinear multi-agent systems driven by Brownian motion

Abstract

The consensus tracking problem of nonlinear stochastic multi-agent systems with directed topologies is investigated in this study. To solve the consensus tracking problem, first, an innovative concept of sub-reachability is introduced, and then, the specified sliding hyperplane is designed. A novel consensus tracking protocol is then proposed by using sliding mode techniques. With the help of Itô integral techniques and stochastic Lyapunov method, the sub-reachability of sliding motion and consensus tracking are proved; that is, the sliding mode variable structure control protocol steers the consensus errors to the given sliding surface in a finite time, and the sliding motion is exponentially stable in the sense of mean square. The efficacy of the proposed method is tested by a numerical case.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 61573154, 61573156), and partly supported by Science and Technology Project of Guangdong Province (Grant Nos. 2015A010106003, 2014A020217015).

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Correspondence to Yunjian Peng.

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Zhao, B., Peng, Y., Song, Y. et al. Sliding mode control for consensus tracking of second-order nonlinear multi-agent systems driven by Brownian motion. Sci. China Inf. Sci. 61, 70216 (2018). https://doi.org/10.1007/s11432-017-9407-6

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Keywords

  • stochastic nonlinear multi-agent systems
  • sub-reachability
  • sliding hyperplane
  • sliding mode variable structure control protocol
  • itô integral techniques
  • consensus tracking errors