© The Institution of Engineering and Technology
In this study, the stochastic sampled-data approach is developed to deal with the H ∞ control problem for a class of linear multi-agent systems. For each agent, signals should be transmitted to the control input, including not only its own measurements, but also the output information received from the neighbour agents. The relationships of information communications between the whole multi-agents are totally reflected by a weighted directed graph with a fixed topology structure. To the addressed problem, the author's focus is to design an output feedback controller for each agent such that, for the external energy bounded disturbances, the exponential stability in the mean square sense and interference rejection ability under consideration can be guaranteed. By assuming that the sampling period of each agent switches between two values in a probabilistic way, the stochastic sampling phenomenon is well characterised in every sampling tasks. In virtue of Lyapunov theory and semi-definite programming method, sufficient conditions are derived to ensure the exponential stability as well as H ∞ performance, and the feedback controllers are also designed by solving some certain matrix inequalities. Finally, a numerical simulation is given to demonstrate the validness of the proposed control strategy.
References
-
-
1)
-
20. Fridman, E., Seuret, A., Richard, J.P.: ‘Robust sampled-data stabilization of linear systems: An input delay approach’, Automatica, 2004, 40, (8), pp. 1441–1446 (doi: 10.1016/j.automatica.2004.03.003).
-
2)
-
3. Yu, W.W., Chen, G.R., Cao, M.: ‘Some necessary and sufficient conditions for second-order consensus in multi-agent dynamical systems’, Automatica, 2010, 46, (6), pp. 1089–1095 (doi: 10.1016/j.automatica.2010.03.006).
-
3)
-
22. Wei, G.L., Wang, Z.D., Shen, B.: ‘Probability-dependent gain-scheduled control for discrete stochastic delayed systems with randomly occurring nonlinearities’, Int. J. Robust Nonlinear, 2013, 23, (7), pp. 815–826 (doi: 10.1002/rnc.2788).
-
4)
-
8. Qin, J.H., Gao, H.J., Yu, C.B.: ‘On discrete-time convergence for general linear multi-agent systems under dynamic topology’, IEEE Trans. Autom. Control, 2014, 59, (4), pp. 1054–1059 (doi: 10.1109/TAC.2013.2285777).
-
5)
-
6. Qin, J.H., Gao, H.J.: ‘A sufficient condition for convergence of sampled-data consensus for double-integrator dynamics with nonuniform and time-varying communication delays’, IEEE Trans. Autom. Control, 2012, 57, (9), pp. 2417–2422 (doi: 10.1109/TAC.2012.2188425).
-
6)
-
21. Gao, H.J., Wu, J.L., Shi, P.: ‘Robust sampled-data H∞ control with stochastic sampling’, Automatica, 2009, 45, (7), pp. 1729–1736 (doi: 10.1016/j.automatica.2009.03.004).
-
7)
-
16. Shen, B., Wang, Z.D., Liang, J.L., Liu, X.H.: ‘Sampled-data H∞ filtering for stochastic genetic regulatory networks’, Int. J. Robust Nonlinear, 2011, 21, (5), pp. 1759–1777 (doi: 10.1002/rnc.1703).
-
8)
-
4. Kar, S., Moura, J.M.F.: ‘Distributed consensus algorithms in sensor networks: quantized sata and random link failures’, IEEE Trans. Autom. Control, 2010, 58, (3), pp. 1383–1400.
-
9)
-
1. Liu, Y.R., Ho, D.W.C., Wang, Z.D.: ‘A new framework for consensus for discrete-time directed networks of multi-agents with distributed delays’, Int. J. Control, 2012, 85, (11), pp. 1755–1765 (doi: 10.1080/00207179.2012.703331).
-
10)
-
5. Wang, Z.D., Ding, D.R., Dong, H.L., Shu, H.S.: ‘H∞ consensus control for multi-agent systems with missing measurements: the finite-horizon case’, Syst. Control. Lett., 2013, 62, (10), pp. 827–836 (doi: 10.1016/j.sysconle.2013.06.004).
-
11)
-
2. Shi, J.T., He, X., Wang, Z.D., Zhou, D.H.: ‘Iterative consensus for a class of second-order multi-agent systems’, J. Intell. Robot. Syst., 2014, 73, (1–4), pp. 655–664 (doi: 10.1007/s10846-013-9996-2).
-
12)
-
9. Shen, B., Wang, Z., Liu, X.: ‘A stochastic sampled-data approach to distributed ℋ∞ filtering in sensor networks’, IEEE Trans. Circuits Syst. I, 2011, 58, (9), pp. 2237–2246 (doi: 10.1109/TCSI.2011.2112594).
-
13)
-
15. Shen, B., Wang, Z.D., Liu, X.H.: ‘Sampled-data synchronization control of dynamical networks with stochastic sampling’, IEEE Trans. Autom. Control, 2012, 57, (10), pp. 2644–2650 (doi: 10.1109/TAC.2012.2190179).
-
14)
-
10. Ding, D.R., Wang, Z.D., Shen, B., Dong, H.L.: ‘Envelope-constrained H∞ filtering with fading measurements and randomly occurring nonlinearities: the finite horizon case’, Automatica, 2015, 55, (), pp. 37–45 (doi: 10.1016/j.automatica.2015.02.024).
-
15)
-
17. Zhang, W.A., Dong, H., Guo, G., Yu, L.: ‘Distributed sampled-data H∞ filtering for sensor networks with nonuniform sampling periods’, IEEE Trans. Ind. Inf., 2014, 10, (2), pp. 871–881 (doi: 10.1109/TII.2014.2299897).
-
16)
-
12. Luo, Y.Q., Wei, G.L., Liu, Y.R., Ding, X.M.: ‘Reliable H∞ state estimation for 2-D discrete systems with infinite distributed delays and incomplete observations’, Int. J. Gen. Syst., 2015, 44, (2), pp. 155–168 (doi: 10.1080/03081079.2014.973729).
-
17)
-
11. Ding, D.R., Wang, Z.D., Lam, J., Shen, B.: ‘Finite-Horizon H∞ control for discrete time-varying systems with randomly occurring nonlinearities and fading measurements’, IEEE Trans. Autom. Control, .
-
18)
-
23. Qin, J., Yu, C., Gao, H.: ‘Coordination for linear multiagent systems with dynamic interaction topology in the leader-following framework’, IEEE Trans. Ind. Electron., 2014, 61, (5), pp. 2412–2422 (doi: 10.1109/TIE.2013.2273480).
-
19)
-
13. Yu, W.W., Zhou, L., Yu, X.H., Lu, J.H., Lu, R.Q.: ‘Consensus in multi-agent systems with second-order dynamics and sampled data’, IEEE Trans. Ind. Inf., 2013, 9, (4), pp. 2137–2146 (doi: 10.1109/TII.2012.2235074).
-
20)
-
18. Chen, T.W., Francis, B.A.: ‘H∞ optimal sampled-data control: computation and design’, Automatica, 1996, 32, (2), pp. 223–228 (doi: 10.1016/0005-1098(96)85551-8).
-
21)
-
1. Olfati-Saber, R., Murray, R.M.: ‘Consensus problems in networks of agents with switching topology and time-delays’, IEEE Trans. Autom. Control, 2004, 49, (9), pp. 1520–1533 (doi: 10.1109/TAC.2004.834113).
-
22)
-
23. Yang, F.W., Wang, Z.D., Hung, Y.S., Gani, M.: ‘H∞ control for networked systems with random communication delays’, IEEE Trans. Autom. Control, 2006, 51, (3), pp. 511–518 (doi: 10.1109/TAC.2005.864207).
-
23)
-
19. Fridman, E., Shaked, U., Suplin, V.: ‘Input/output delay approach to robust sampled-data H∞ control’, Syst. Control Lett., 2005, 54, (3), pp. 271–282 (doi: 10.1016/j.sysconle.2004.08.012).
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cta.2014.1087
Related content
content/journals/10.1049/iet-cta.2014.1087
pub_keyword,iet_inspecKeyword,pub_concept
6
6