Consensus protocol for multiple delta operator systems. (English) Zbl 1376.93003
Summary: This paper considers the consensus problem for multiple delta operator systems. The delta operator system is used for describing continuous time processes at rapid rate sampling. Moreover, it has been known to have a better model description than that of shift-operator-based approach. In this work, the consensus problem is first solved for multiple delta operator systems by using a distributed protocol. To achieve consensus, several important sufficient conditions are proposed for the fast sampling systems based on the parameters of sampling period and consensus strength. In addition, two distributed consensus protocols are constructed for both leaderless multiple delta operator systems and leader-follower multiple delta operator systems. Finally, the effectiveness of the theoretical analysis is illustrated by applying distributed consensus protocol to multi-agent systems.
MSC:
| 93A14 | Decentralized systems |
| 93C57 | Sampled-data control/observation systems |
| 68T42 | Agent technology and artificial intelligence |
References:
| [1] | Jadbabaie, A.; Lin, J.; Morse, A., Coordination of groups of mobile autonomous agents using nearest neighbor rules, IEEE Trans. Automat. Control, 48, 6, 988-1001 (2003) · Zbl 1364.93514 |
| [2] | Olfati-Saber, R.; Murray, R., Consensus problems in networks of agents with switching topology and time-delays, IEEE Trans. Automat. Control, 49, 9, 1520-1533 (2004) · Zbl 1365.93301 |
| [3] | Ren, W.; Beard, R. W., Consensus seeking in multiagent systems under dynamically changing interaction topologies, IEEE Trans. Automat. Control, 50, 5, 655-661 (2005) · Zbl 1365.93302 |
| [4] | Yu, W.; Chen, G.; Cao, M., Some necessary and sufficient conditions for second-order consensus in multi-agent dynamical systems, Automatica, 46, 6, 1089-1095 (2010) · Zbl 1192.93019 |
| [5] | Huang, C.; Ho, D. W.C.; Lu, J., Partial information based distributed filtering in two-targets tracking sensor networks, IEEE Trans. Circuits Syst. I. Regul. Pap., 59, 4, 820-832 (2012) · Zbl 1468.93168 |
| [6] | Li, L.; Ho, D. W.C.; Lu, J., A unified approach to practical consensus with quantized data and time delay, IEEE Trans. Circuits Syst. I. Regul. Pap., 60, 10, 2668-2678 (2013) |
| [7] | Song, Q.; Liu, F.; Cao, J.; Yu, W., M-matrix strategies for pinning-controlled leader-following consensus in multiagent systems with nonlinear dynamics, IEEE Trans. Cybern., 43, 6, 1688-1697 (2013) |
| [8] | Wang, H., Consensus of networked mechanical systems with communication delays: a unified framework, IEEE Trans. Automat. Control, 59, 6, 1571-1576 (2014) · Zbl 1360.93058 |
| [9] | Xiong, W.; Yu, W.; Lu, J.; Yu, X., Fuzzy modelling and consensus of nonlinear multiagent systems with variable structure, IEEE Trans. Circuits Syst. I. Regul. Pap., 61, 4, 1183-1191 (2014) |
| [10] | Dong, H.; Wang, Z.; Lam, J.; Gao, H., Distributed filtering in sensor networks with randomly occurring saturations and successive packet dropouts, Internat. J. Robust Nonlinear Control, 24, 12, 1743-1759 (2014) · Zbl 1301.93159 |
| [11] | Tang, Y.; Gao, H.; Kurths, J., Distributed robust synchronization of dynamical networks with stochastic coupling, IEEE Trans. Circuits Syst. I. Regul. Pap., 61, 5, 1508-1519 (2014) · Zbl 1468.93188 |
| [12] | Chen, S.; Ho, D. W.C.; Li, L.; Liu, M., Fault-tolerant consensus of multi-agent system with distributed adaptive protocol, IEEE Trans. Cybern., 45, 10, 2142-2155 (2015) |
| [13] | Yang, H.; Xia, Y.; Shi, P.; Zhao, L., (Analysis and Synthesis of Delta Operator Systems. Analysis and Synthesis of Delta Operator Systems, Lecture Notes in Control and Information Sciences, vol. 430 (2012)) |
| [14] | Xia, Y.; Fu, M.; Yang, H.; Liu, G.-P., Robust sliding-mode control for uncertain time-delay systems based on delta operator, IEEE Trans. Ind. Electron., 56, 9, 3646-3655 (2009) |
| [15] | Goodwin, G. C.; Leal, R. L.; Mayne, D. Q.; Middleton, R. H., Rapprochement between continuous and discrete model reference adaptive control, Automatica, 22, 2, 199-207 (1986) · Zbl 0614.93039 |
| [16] | Qiu, J.; Xia, Y.; Yang, H.; Zhang, J., Robust stabilisation for a class of discrete-time systems with time-varying delays via delta operators, IET Control Theory Appl., 2, 1, 87-93 (2008) |
| [17] | Yang, H.; Xia, Y.; Fu, M.; Shi, P., Robust adaptive sliding mode control for uncertain delta operator systems, Internat. J. Adapt. Control Signal Process., 24, 8, 623-632 (2010) · Zbl 1204.93057 |
| [18] | Yang, H.; Xia, Y.; Qiu, J.; Zhang, J., Filtering for a class of discrete-time systems with time-delays via delta operator approach, Int. J. Syst. Sci., 41, 4, 423-433 (2010) · Zbl 1301.93163 |
| [19] | Li, H.; Sun, F.; Yang, H.; Xia, Y., Gain scheduling control of delta operator system using network-based measurements, IEEE Trans. Instrum. Meas., 63, 3, 538-547 (2014) |
| [20] | Li, Z.; Gao, H.; Karimi, H. R., Stability analysis and controller synthesis of discrete-time switched systems with time delay, Systems Control Lett., 66, 85-93 (2014) · Zbl 1288.93072 |
| [21] | Yang, H.; Xia, Y.; Shi, P.; Fu, M., A novel delta operator kalman filter design and convergence analysis, IEEE Trans. Circuits Syst. I. Regul. Pap., 58, 10, 2458-2468 (2011) · Zbl 1468.93180 |
| [22] | Yang, H.; Li, Z.; Shi, P.; Hua, C., Control of periodic sampling systems subject to actuator saturation, Internat. J. Robust Nonlinear Control, 25, 18, 3661-3678 (2015) · Zbl 1336.93104 |
| [23] | Chen, W.; Xu, S.; Zou, Y., Stabilization of hybrid neutral stochastic differential delay equations by delay feedback control, Systems Control Lett., 88, 1-13 (2016) · Zbl 1336.93163 |
| [24] | Yang, H.; Xia, Y., Low frequency positive real control for delta operator systems, Automatica, 48, 8, 1791-1795 (2012) · Zbl 1267.93063 |
| [25] | Horn, R. A.; Johnson, C. R., Matrix Analysis (1985), Cambridge University Press: Cambridge University Press Cambridge [Cambridgeshire]; New York · Zbl 0576.15001 |
| [26] | You, K.; Xie, L., Network topology and communication data rate for consensusability of discrete-time multi-agent systems, IEEE Trans. Automat. Control, 56, 10, 2262-2275 (2011) · Zbl 1368.93014 |
| [28] | Zhang, H.; Lewis, F.; Das, A., Optimal design for synchronization of cooperative systems: State feedback, observer and output feedback, IEEE Trans. Automat. Control, 56, 8, 1948-1952 (2011) · Zbl 1368.93265 |
| [29] | Suchomski, P., Numerically robust delta-domain solutions to discrete-time Lyapunov equations, Systems Control Lett., 47, 4, 319-326 (2002) · Zbl 1106.65314 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
