Abstract
In this paper, a bearing-based containment control problem of multi-agent systems with disturbances is studied. The nonlinearity of the bearing results in the existence of nonlinear time-varying parameters in the closed-loop system. When the leaders are stationary, under the sufficient conditions on the disturbances and the connectivity of the directed sensing graph, the boundedness of the nonlinear time-varying parameters is rigorously proved, with which it is shown that the containment error converges to zero asymptotically. When the leaders are moving, by using the properties of the bearing and the projection, it is proved that the containment error is uniformly ultimately bounded and can be reduced by adjusting the edge weight. Numerical examples illustrate the effectiveness of the proposed controller.
This work was supported in part by the National Natural Science Foundation of China under Grants 62103277, 62025305, and in part by the Oceanic Interdisciplinary Program of Shanghai Jiao Tong University under Grant SL2022MS008.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Ji, M., Ferrari-Trecate, G., Egerstedt, M., Buffa, A.: Containment control in mobile networks. IEEE Trans. Autom. Control 53(8), 1972–1975 (2008)
Notarstefano, G., Egerstedt, M., Haque, M.: Containment in leader-follower networks with switching communication topologies. Automatica 47(5), 1035–1040 (2011)
Cao, Y., Ren, W., Egerstedt, M.: Distributed containment control with multiple stationary or dynamic leaders in fixed and switching directed networks. Automatica 48(8), 1586–1597 (2012)
Shi, G., Hong, Y., Johansson, K.H.: Connectivity and set tracking of multi-agent systems guided by multiple moving leaders. IEEE Trans. Autom. Control 57(3), 663–675 (2012)
Cao, Y., Stuart, D., Ren, W., Meng, Z.: Distributed containment control for multiple autonomous vehicles with double-integrator dynamics: algorithms and experiments. IEEE Trans. Control Syst. Technol. 19(4), 929–938 (2011)
Li, J., Ren, W., Xu, S.: Distributed containment control with multiple dynamic leaders for double-integrator dynamics using only position measurements. IEEE Trans. Autom. Control 57(6), 1553–1559 (2012)
Yang, C., Duan, M., Lin, P., Ren, W., Gui, W.: Distributed containment control of continuous-time multi-agent systems with nonconvex control input constraints. IEEE Trans. Ind. Electron. 66(10), 7927–7934 (2019)
Huang, Y., Duan, M., Mo, L.: Multi-agent containment control with nonconvex states constraints, nonuniform time-delays and switching directed networks. IEEE Trans. Neural Netw. Learn. Syst. 31(11), 5021–5028 (2020)
Wang, Q., Fu, J., Wang, J.: Fully distributed containment control of high-order multi-agent systems with nonlinear dynamics. Syst. Control Lett. 99, 33–39 (2017)
Liu, K., **e, G., Wang, L.: Containment control for second-order multiagent systems with time-varying delays. Syst. Control Lett. 67(7), 24–31 (2014)
Wang, D., Wang, D., Wang, W.: Necessary and sufficient conditions for containment control of multi-agent systems with time delay. Automatica 103, 418–423 (2019)
Lü, H., He, W., Han, Q.L., Ge, X., Peng, C.: Finite-time containment control for nonlinear multi-agent systems with external disturbances. Inf. Sci. 512, 338–351 (2020)
Zhao, Y., Tang, F., Zong, G., Zhao, X., Xu, N.: Event-based adaptive containment control for nonlinear multiagent systems with periodic disturbances. IEEE Trans. Circuits Syst. II Express Briefs 69(12), 5049–5053 (2022)
Farina, A.: Target tracking with bearings only measurements. Signal Process. 78(1), 61–78 (1999)
Santilli, M., Franceschelli, M., Gasparri, A.: Robust containment control in multi-agent systems with common coordinate frames and bearing angle measurements. In: IEEE Conference on Decision and Control, pp. 3710–3717 (2019)
Santilli, M., Franceschelli, M., Gasparri, A.: Dynamic resilient containment control in multirobot systems. IEEE Trans. Rob. 38(1), 57–70 (2022)
Zheng, R., Sun, D.: Rendezvous of unicycles: a bearings-only and perimeter shortening approach. Syst. Control Lett. 62(5), 401–407 (2013)
Zhao, S., Zheng, R.: Flexible bearing-only rendezvous control of mobile robots. In: Chinese Control Conference, pp. 8051–8056 (2017)
Karimian, A., Tron, R.: Bearing-only consensus and formation control under directed topologies. In: American Control Conference, pp. 3503–3510 (2020)
Yang, Z., Zhu, S., Chen, C., Feng, G., Guan, X.: Entrap** a target in an arbitrarily shaped orbit by a single robot using bearing measurements. Automatica 113, 108805 (2020)
Yang, Z., Chen, C., Zhu, S., Guan, X., Feng, G.: Distributed entrap** control of multiagent systems using bearing measurements. IEEE Trans. Autom. Control 66(12), 5696–5710 (2021)
Zhao, S., Li, Z., Ding, Z.: Bearing-only formation tracking control of multiagent systems. IEEE Trans. Autom. Control 64(11), 4541–4554 (2019)
Duan, M., Yang, Z., Zhu, S., Chen, C.: Bearing-only containment control of multi-agent systems. Int. J. Robust Nonlinear Control 33, 11335–11350 (2023). https://doi.org/10.1002/rnc.6948
Godsil, C., Royle, G.: Algebraic Graph Theory. Springer-Verlag, New York (2001). https://doi.org/10.1007/978-1-4613-0163-9
Hiriart-Urruty, J.-B., Lemar\(\acute{\rm e}\)chal, C.: Convex Analysis and Minimization Algorithms I. Springer-Verlag, Heidelberg (1993). https://doi.org/10.1007/978-3-662-02796-7
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2024 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Duan, M., Yang, Z., Zhu, S., Chen, C. (2024). Bearing-Based Containment Control of Multi-agent Systems with Disturbances. In: Jiang, GP., Wang, M., Ren, Z. (eds) Proceedings of 2023 7th Chinese Conference on Swarm Intelligence and Cooperative Control. CCSICC 2023. Lecture Notes in Electrical Engineering, vol 1204. Springer, Singapore. https://doi.org/10.1007/978-981-97-3340-8_27
Download citation
DOI: https://doi.org/10.1007/978-981-97-3340-8_27
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-97-3339-2
Online ISBN: 978-981-97-3340-8
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)