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Finite-Time Distributed Energy-to-Peak Control for Uncertain Multiagent Systems

DOI: 10.1155/2014/260201

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Abstract:

This paper investigates the finite-time distributed consensus control problem of multiagent systems with parameter uncertainties. The relative states of neighboring agents are used to construct the control law and some agents know their own states. By substituting the control input into multiagent systems, an augmented closed-loop system is obtained. Then, we analyze its finite-time boundedness (FTB) and finite-time performance. A sufficient condition for the existence of the designed controller is given with the form of linear matrix inequalities (LMIs). Finally, simulation results are described. 1. Introduction The coordination control problems of multiagent systems have attracted increasing attentions from various fields, such as formation flights [1, 2], multiple robots formation control [3, 4], air traffic control [5], and multivehicle systems cooperative control [6, 7]. For the reason that centralized control is too expensive or even infeasible to accomplish, the distributed control protocol has been studied extensively in recent years. The consensus problem for multiagent systems with switching communication topologies is studied in [8, 9], heterogeneous multiple agents are researched in [10], the distributed control problem for high-order multiagent systems is investigated in [11], the nonlinear uncertain multiagent systems are studied in [12], networked control problem for multiple agents with a leader is described in [13], multiagent systems with input time delays are investigated in [14], and, for the case that state information cannot be measured, a distributed output-feedback control for multiagent systems with Markov jumping is studied in [15]. However, to the best knowledge of the authors, there is no article investigating the finite-time energy-to-peak consensus problem for multiagent systems with parameter uncertainties. For the reason that the forms of external disturbances are not exactly known and the existence of parameter uncertainties in systems, the robust control method is proposed. There are mainly three robust control theories. The first one is energy-to-energy control, which is the well-known control [16–19], where the external disturbance can be any form but energy bounded. The second theory is peak-to-peak control, in which worse cases of performance variables are required to be minimized under the peak bounded external disturbances; it can be seen that the conservatism of peak-to-peak control is much less than the control. The last method is the energy-to-peak one, which is also called in discrete-time and in

References

[1]  W. Ren and R. W. Beard, “Decentralized scheme for spacecraft formation flying via the virtual structure approach,” Journal of Guidance, Control, and Dynamics, vol. 27, no. 1, pp. 73–82, 2004.
[2]  G. L. Slater, S. M. Byram, and T. W. Williams, “Collision avoidance for satellites in formation flight,” Journal of Guidance, Control, and Dynamics, vol. 29, no. 5, pp. 1140–1146, 2006.
[3]  W. Ren and N. Sorensen, “Distributed coordination architecture for multi-robot formation control,” Robotics and Autonomous Systems, vol. 56, no. 4, pp. 324–333, 2008.
[4]  T. Liu and Z. P. Jiang, “Distributed formation control of nonholonomic mobile robots without global position measurements,” Automatica, vol. 49, no. 2, pp. 592–600, 2013.
[5]  C. Tomlin, G. J. Pappas, and S. Sastry, “Conflict resolution for air traffic management: a study in multiagent hybrid systems,” IEEE Transactions on Automatic Control, vol. 43, no. 4, pp. 509–521, 1998.
[6]  W. Ren and E. Atkins, “Distributed multi-vehicle coordinated control via local information exchange,” International Journal of Robust and Nonlinear Control, vol. 17, no. 10-11, pp. 1002–1033, 2007.
[7]  J. Qin, W. X. Zheng, and H. Gao, “Consensus of multiple second-order vehicles with a time-varying reference signal under directed topology,” Automatica, vol. 47, no. 9, pp. 1983–1991, 2011.
[8]  Y. Su and J. Huang, “Cooperative output regulation with application to multi-agent consensus under switching network,” IEEE Transactions on Systems, Man, and Cybernetics B, vol. 42, no. 3, pp. 864–875, 2012.
[9]  P. Lin, Z. Li, Y. Jia, and M. Sun, “High-order multi-agent consensus with dynamically changing topologies and time-delays,” IET Control Theory & Applications, vol. 5, no. 8, pp. 976–981, 2011.
[10]  Y. Zheng, Y. Zhu, and L. Wang, “Consensus of heterogeneous multi-agent systems,” IET Control Theory & Applications, vol. 5, no. 16, pp. 1881–1888, 2011.
[11]  F. Xiao and L. Wang, “Consensus problems for high-dimensional multi-agent systems,” IET Control Theory & Applications, vol. 1, no. 3, pp. 830–837, 2007.
[12]  Y. Su and J. Huang, “Cooperative global output regulation of heterogeneous second-order nonlinear uncertain multi-agent systems,” Automatica, vol. 49, no. 11, pp. 3345–3350, 2013.
[13]  L. Ding, Q.-L. Han, and G. Guo, “Network-based leader-following consensus for distributed multi-agent systems,” Automatica, vol. 49, no. 7, pp. 2281–2286, 2013.
[14]  J. Xu, H. Zhang, and L. Xie, “Input delay margin for consensus ability of multi-agent systems,” Automatica, vol. 49, no. 6, pp. 1816–1820, 2013.
[15]  B. C. Wang and J. F. Zhang, “Distributed output feedback control of Markov jump multi-agent systems,” Automatica, vol. 49, no. 5, pp. 1397–1402, 2013.
[16]  H. Zhang, J. Wang, and Y. Shi, “Robust sliding-mode control for Markovian jump systems subject to intermittent observations and partially known transition probabilities,” Systems & Control Letters, vol. 62, no. 12, pp. 1114–1124, 2013.
[17]  H. Zhang, Y. Shi, and M. X. Liu, “ switched filtering for networked systems based on delay occurrence probabilities,” ASME Transactions, Journal of Dynamic Systems, Measurement, and Control, vol. 135, no. 6, Article ID 061002, 2013.
[18]  H. Zhang, Y. Shi, and M. X. Liu, “ step tracking control for networked discrete-time nonlinear systems with integral and predictive actions,” IEEE Transactions on Industrial Informatics, vol. 9, no. 1, pp. 337–345, 2013.
[19]  H. Zhang and Y. Shi, “Parameter-dependent filtering for linear time-varying systems,” ASME Transactions, Journal of Dynamic Systems, Measurement, and Control, vol. 135, no. 2, Article ID 021006, 2013.
[20]  H. Zhang, Y. Shi, and J. Wang, “On energy-to-peak filtering for nonuniformly sampled nonlinear systems: a Markovian jump system approach,” IEEE Transactions on Fuzzy Systems, 1 pages, 2013.
[21]  H. Zhang, Y. Shi, A. Saadat Mehr, and H. Huang, “Robust FIR equalization for time-varying communication channels with intermittent observations via an LMI approach,” Signal Processing, vol. 91, no. 7, pp. 1651–1658, 2011.
[22]  H. Zhang, A. S. Mehr, and Y. Shi, “Improved robust energy-to-peak filtering for uncertain linear systems,” Signal Processing, vol. 90, no. 9, pp. 2667–2675, 2010.
[23]  H. Zhang, Y. Shi, and A. Saadat Mehr, “Robust energy-to-peak filtering for networked systems with time-varying delays and randomly missing data,” IET Control Theory & Applications, vol. 4, no. 12, pp. 2921–2936, 2010.
[24]  X. Lin, H. Du, S. Li, and Y. Zou, “Finite-time stability and finite-time weighted -gain analysis for switched systems with time-varying delay,” IET Control Theory & Applications, vol. 7, no. 7, pp. 1058–1069, 2013.
[25]  F. Amato, G. Carannante, G. D. Tommasi, and A. Pironti, “Input-output finite-time stability of linear systems: necessary and sufficient conditions,” IEEE Transactions on Automatic Control, vol. 57, no. 12, pp. 3051–3063, 2012.
[26]  F. Amato, M. Ariola, and C. Cosentino, “Finite-time stability of linear time-varying systems: analysis and controller design,” IEEE Transactions on Automatic Control, vol. 55, no. 4, pp. 1003–1008, 2010.
[27]  J. Xu and J. Sun, “Finite-time stability of linear time-varying singular impulsive systems,” IET Control Theory & Applications, vol. 4, no. 10, pp. 2239–2244, 2010.
[28]  Z. Li, Z. Duan, L. Xie, and X. Liu, “Distributed robust control of linear multi-agent systems with parameter uncertainties,” International Journal of Control, vol. 85, no. 8, pp. 1039–1050, 2012.
[29]  Z. Li, Z. Duan, and G. Chen, “On and performance regions of multi-agent systems,” Automatica, vol. 47, no. 4, pp. 797–803, 2011.
[30]  S. He and C. Lin Liu, “Finite-time fuzzy control of nonlinear jump systems with time delays via dynamic observer-based state feedback,” IEEE Transactions on Fuzzy Systems, vol. 20, no. 4, pp. 605–614, 2012.
[31]  M. A. Rotea, “The generalized control problem,” Automatica, vol. 29, no. 2, pp. 373–385, 1993.
[32]  P. Shi, E.-K. Boukas, and R. K. Agarwal, “Control of Markovian jump discrete-time systems with norm bounded uncertainty and unknown delay,” IEEE Transactions on Automatic Control, vol. 44, no. 11, pp. 2139–2144, 1999.

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