Consensus of multi-agent system with distributed control on time scales. (English) Zbl 1410.93061
Summary: In this paper, we investigate consensus problem of multi-agent system with distributed control on time scales, which simultaneously includes discrete time delays. Due to Lyapunov stability method and theory of calculus on time scales, sufficient conditions are derived for reaching the globally exponential consensus of the considered system. Finally, simulation examples are given to illustrate the effectiveness of our theoretical results.
MSC:
| 93C23 | Control/observation systems governed by functional-differential equations |
| 34D06 | Synchronization of solutions to ordinary differential equations |
| 34N05 | Dynamic equations on time scales or measure chains |
| 93A14 | Decentralized systems |
References:
| [1] | Yu, W.; Chen, G.; Cao, M., Distributed leader-follower flocking control for multi-agent dynamical systems with time-varying velocities, Syst. Control Lett., 59, 543-552 (2010) · Zbl 1207.37054 |
| [2] | Fan, M.; Zhang, H.; Wang, M., Bipartite flocking for multi-agent systems, Commun. Nonlinear Sci. Numer. Simul., 19, 3313-3322 (2014) · Zbl 1510.93006 |
| [3] | Sun, Y., Stability analysis of flocking for multi-agent dynamic systems, Nonlinear Anal. Real World Appl., 14, 1075-1081 (2013) · Zbl 1281.34082 |
| [4] | Dong, R.; Geng, Z., Consensus based formation control laws for systems on lie groups, Syst. Control Lett., 62, 014-111 (2013) · Zbl 1259.93004 |
| [5] | Wang, W.; Huang, J., Distributed adaptive control for consensus tracking with application to formation control of nonholonomic mobile robots, Automatica, 50, 1254-1263 (2014) · Zbl 1298.93212 |
| [6] | Lei, D.; Guo, G., Distributed event-triggered \(h_∞\) consensus filtering in sensor networks, Signal Process., 108, 365-375 (2015) |
| [7] | Yang, R.; Liu, G., Predictive output feedback control for networked control systems, IEEE Trans. Ind. Electron., 61, 512-520 (2014) |
| [8] | Cao, Y.; Ren, W., Multi-agent consensus using both current and outdated states with fixed and undirected interaction, J. Intell. Robot. Syst., 58, 95-106 (2010) · Zbl 1203.68291 |
| [9] | Liu, Y.; Liu, X., Synchronization and state estimation for discrete-time complex networks with distributed delays, IEEE Trans. Syst. Man Cybern. Part B, 38, 1314-1325 (2008) |
| [10] | Lei, D.; Han, Q.; Guo, G., Network-based leader-following consensus for distributed multi-agent systems, Automatica, 49, 2281-2286 (2013) · Zbl 1364.93014 |
| [11] | Chao, H.; Ye, X., Pairwise synchronization of multi-agent systems with nonuniform information exchange, Syst. Control Lett., 74, 58-63 (2014) · Zbl 1300.93015 |
| [12] | Yu, Z.; Jiang, H.; Hu, C., Leader-following consensus of fractional-order multi-agent systems under fixed topology, Neurocomputing, 149, 613-620 (2015) |
| [13] | Hengster-Movric, K.; You, K., Synchronization of discrete-time multi-agent systems on graphs using Riccati design, Automatica, 49, 414-423 (2013) · Zbl 1259.93005 |
| [14] | Xu, X.; Chen, S., Leader-following consensus of discrete-time multi-agent systems with observer-based protocols, Neurocomputing, 118, 334-341 (2013) |
| [15] | Fanti, M.; Mangini, A., A new class of consensus protocols for agent networks with discrete time dynamics, Automatica, 54, 1-7 (2015) · Zbl 1318.93003 |
| [16] | Chen, X.; Song, Q., Global stability of complex-valued neural networks with both leakage time delay and discrete time delay on time scales, Neurocomputing, 121, 254-264 (2013) |
| [17] | Li, Y.; Zhao, K., Robust stability of delayed reaction-diffusion recurrent neural networks with Dirichlet boundary conditions on time scales, Neurocomputing, 74, 1632-1637 (2011) |
| [18] | Zhou, B.; Song, Q.; Wang, H., Global exponential stability of neural networks with discrete and distributed delays and general activation function on time scales, Neurocomputing, 74, 3142-3150 (2011) · Zbl 1419.62066 |
| [19] | Cheng, Q.; Cao, J., Synchronization of complex dynamical networks with discrete time delays on time scales, Neurocomputing, 151, 729-736 (2015) |
| [20] | Shen, J.; Cao, J., Consensus of multi-agent systems on time scales, IMA J. Math. Control Inf., 29, 507-517 (2012) · Zbl 1256.93068 |
| [21] | Liu, J.; Guo, L., Distributed delay control of multi-agent system with nonlinear dynamics: stochastic disturbance, Neurocomputing, 152, 164-169 (2015) |
| [22] | Bohner, M.; Peterson, A., Dynamic Equations on Time Scales: An Introduction with Applications (2001), BirkhWauser: BirkhWauser Boston · Zbl 0978.39001 |
| [23] | Langville, A.; Stewart, W., The Kronecker product and stochastic automata networks, J. Comput. Appl. Math, 167, 2, 429-447 (2004) · Zbl 1104.68062 |
| [24] | Cheng, Q.; Cao, J., Global synchronization of complex networks with discrete time delays and stochastic disturbances, Neural Comput. Appl., 20, 8, 1167-1179 (2011) |
| [25] | Boyd, S.; Ghaoui, L., Linear Matrix Inequalities in Systems and Control Theory (1994), SIAM: SIAM Philadephia, PA, USA · Zbl 0816.93004 |
| [26] | Wen, G.; Duan, Z., Consensus of multi-agent systems with nonlinear dynamics and sampled-data information: a delayed-input approach, Int. J. Robust Nonlinear Control, 23, 602-619 (2013) · Zbl 1273.93012 |
| [28] | Chen, Y.; Lü, J.; Lin, Z., Consensus of discrete-time multi-agent systems with transmission nonlinearity, Automatica, 49, 1768-1775 (2013) · Zbl 1360.93019 |
| [29] | Liu, C.; Liu, F., Stationary consensus of heterogeneous multi-agent systems with bounded communication delays, Automatica, 47, 2130-2133 (2013) · Zbl 1227.93010 |
| [30] | Ren, W., Formation keeping and attitude alignment for multiple spacecraft through local interactions, J. Guid. Control Dyn., 30, 2, 173-180 (2007) |
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