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2016 | OriginalPaper | Buchkapitel

14. Synthesis of Distributed Control Laws for Multi-agent Systems Using Delayed Relative Information with LQR Performance

verfasst von : Paresh Deshpande, Prathyush P. Menon, Christopher Edwards

Erschienen in: Delays and Networked Control Systems

Verlag: Springer International Publishing

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Abstract

In this chapter, a multiagent system composed of linear identical dynamical agents is considered. The agents are assumed to share relative state information over a communication network. This exchange of relative information is assumed to be subject to delays. New methods to synthesize distributed state feedback control laws for the multiagent system, using delayed relative information along with local state information with guaranteed LQR performance, are presented in this chapter. Two types of delays are considered in the relative information exchange: fixed and time-varying. Existing delay-dependent stability criteria are modified to incorporate LQR performance guarantees while retaining convex LMI representations to facilitate the synthesis of the control gains.

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Fußnoten
1
Another research area involving the stabilization of time-delay systems is networked control systems [15, 40]. This is not the class of problems considered in this chapter.
 
Literatur
1.
Zurück zum Zitat B. Bamieh, F. Paganini, M.A. Dahleh, Distributed control of spatially invariant systems. IEEE Trans. Autom. Control 47(7), 1091–1107 (2002)MathSciNetCrossRef B. Bamieh, F. Paganini, M.A. Dahleh, Distributed control of spatially invariant systems. IEEE Trans. Autom. Control 47(7), 1091–1107 (2002)MathSciNetCrossRef
2.
Zurück zum Zitat F. Borrelli, T. Keviczky, Distributed LQR design for identical dynamically decoupled systems. IEEE Trans. Autom. Control 53(8), 1901–1912 (2008)MathSciNetCrossRef F. Borrelli, T. Keviczky, Distributed LQR design for identical dynamically decoupled systems. IEEE Trans. Autom. Control 53(8), 1901–1912 (2008)MathSciNetCrossRef
3.
Zurück zum Zitat R. Cepeda-Gomez, N. Olgac, Consensus analysis with large and multiple communication delays using spectral delay space concept. Int. J. Control 84(12), 1996–2007 (2011)MathSciNetCrossRefMATH R. Cepeda-Gomez, N. Olgac, Consensus analysis with large and multiple communication delays using spectral delay space concept. Int. J. Control 84(12), 1996–2007 (2011)MathSciNetCrossRefMATH
4.
Zurück zum Zitat Y. Cao, W. Ren, LQR-based optimal linear consensus algorithms, in IEEE American Control Conference (ACC) (2009) Y. Cao, W. Ren, LQR-based optimal linear consensus algorithms, in IEEE American Control Conference (ACC) (2009)
5.
Zurück zum Zitat J.C. Delvenne, R. Carli, S. Zampieri, Optimal strategies in the average consensus problem, in IEEE Conference on Decision and Control (CDC) (2007) J.C. Delvenne, R. Carli, S. Zampieri, Optimal strategies in the average consensus problem, in IEEE Conference on Decision and Control (CDC) (2007)
6.
Zurück zum Zitat J.A. Fax, R.M. Murray, Information flow and cooperative control of vehicle formations. IEEE Trans. Autom. Control 49(9), 1465–1476 (2004)MathSciNetCrossRef J.A. Fax, R.M. Murray, Information flow and cooperative control of vehicle formations. IEEE Trans. Autom. Control 49(9), 1465–1476 (2004)MathSciNetCrossRef
7.
Zurück zum Zitat E. Fridman, U. Shaked, An improved stabilization method for linear time-delay systems. IEEE Trans. Autom. Control 47(11), 1931–1937 (2002)MathSciNetCrossRef E. Fridman, U. Shaked, An improved stabilization method for linear time-delay systems. IEEE Trans. Autom. Control 47(11), 1931–1937 (2002)MathSciNetCrossRef
8.
Zurück zum Zitat E. Fridman, U. Shaked, Delay-dependent stability and \(\fancyscript {H}^{\inf }\) control: constant and time-varying delays. Int. J. Control 76(1), 48–60 (2003)MathSciNetCrossRefMATH E. Fridman, U. Shaked, Delay-dependent stability and \(\fancyscript {H}^{\inf }\) control: constant and time-varying delays. Int. J. Control 76(1), 48–60 (2003)MathSciNetCrossRefMATH
9.
Zurück zum Zitat E. Fridman, U. Shaked, K. Liu, New conditions for delay-derivative-dependent stability. Automatica 45(11), 2723–2727 (2009)MathSciNetCrossRefMATH E. Fridman, U. Shaked, K. Liu, New conditions for delay-derivative-dependent stability. Automatica 45(11), 2723–2727 (2009)MathSciNetCrossRefMATH
10.
Zurück zum Zitat P. Gahinet, A. Nemirovski, A.J. Laub, M. Chilali, LMI Control ToolBox (The MathWorks Inc., 1995) P. Gahinet, A. Nemirovski, A.J. Laub, M. Chilali, LMI Control ToolBox (The MathWorks Inc., 1995)
11.
Zurück zum Zitat C. Godsil, G. Royle, Algebraic Graph Theory (Springer, 2001) C. Godsil, G. Royle, Algebraic Graph Theory (Springer, 2001)
12.
Zurück zum Zitat F. Gouaisbaut, D. Peaucelle, Delay-dependent stability analysis of linear time delay systems, in IFAC Workshop on Time Delay Systems (TDS) (2006) F. Gouaisbaut, D. Peaucelle, Delay-dependent stability analysis of linear time delay systems, in IFAC Workshop on Time Delay Systems (TDS) (2006)
13.
Zurück zum Zitat K. Gu, V.L. Kharitonov, J. Chen, Stability of Time-Delay Systems (Birkhauser, 2003) K. Gu, V.L. Kharitonov, J. Chen, Stability of Time-Delay Systems (Birkhauser, 2003)
14.
Zurück zum Zitat Y. He, Q. Wang, C. Lin, M. Wu, Delay-range-dependent stability for systems with time-varying delay. Automatica 43(2), 371–376 (2007)MathSciNetCrossRefMATH Y. He, Q. Wang, C. Lin, M. Wu, Delay-range-dependent stability for systems with time-varying delay. Automatica 43(2), 371–376 (2007)MathSciNetCrossRefMATH
15.
Zurück zum Zitat S. Hirche, T. Matiakis, M. Buss, A distributed controller approach for delay-independent stability of networked control systems. Automatica 45(8), 828–1836 (2009)MathSciNetCrossRefMATH S. Hirche, T. Matiakis, M. Buss, A distributed controller approach for delay-independent stability of networked control systems. Automatica 45(8), 828–1836 (2009)MathSciNetCrossRefMATH
16.
Zurück zum Zitat A. Jadbabaie, J. Lin, A.S. Morse, Coordination of groups of mobile autonomous agents using nearest neighbour rules, in IEEE Conference on Decision and Control (CDC) (2002) A. Jadbabaie, J. Lin, A.S. Morse, Coordination of groups of mobile autonomous agents using nearest neighbour rules, in IEEE Conference on Decision and Control (CDC) (2002)
17.
Zurück zum Zitat T. Keviczky, F. Borrelli, K. Fregene, D. Godbole, G. Balas, Decentralized receding horizon control and coordination of autonomous vehicle formations. IEEE Trans. Autom. Control 16(1), 19–33 (2008) T. Keviczky, F. Borrelli, K. Fregene, D. Godbole, G. Balas, Decentralized receding horizon control and coordination of autonomous vehicle formations. IEEE Trans. Autom. Control 16(1), 19–33 (2008)
18.
Zurück zum Zitat Y.S. Kim, M. Mesbahi, On maximizing the second smallest eigenvalue of a state-dependent graph Laplacian. IEEE Trans. Autom. Control 51(1), 116–120 (2006)MathSciNetCrossRef Y.S. Kim, M. Mesbahi, On maximizing the second smallest eigenvalue of a state-dependent graph Laplacian. IEEE Trans. Autom. Control 51(1), 116–120 (2006)MathSciNetCrossRef
19.
Zurück zum Zitat C. Langbort, V. Gupta, Minimal interconnection topology in distributed control design. SIAM J. Control Optim. 48(1), 397–413 (2009)MathSciNetCrossRefMATH C. Langbort, V. Gupta, Minimal interconnection topology in distributed control design. SIAM J. Control Optim. 48(1), 397–413 (2009)MathSciNetCrossRefMATH
20.
Zurück zum Zitat C. Langbort, R.S. Chandra, R. D’Andrea, Distributed control design for systems interconnected over an arbitrary graph. IEEE Trans. Autom. Control 49(9),1502–1519 (2004) C. Langbort, R.S. Chandra, R. D’Andrea, Distributed control design for systems interconnected over an arbitrary graph. IEEE Trans. Autom. Control 49(9),1502–1519 (2004)
21.
Zurück zum Zitat Z. Lin, B. Francis, M. Maggiore, State agreement for continuous time coupled nonlinear systems. SIAM J. Control Optim. 46(1), 288–307 (2007)MathSciNetCrossRefMATH Z. Lin, B. Francis, M. Maggiore, State agreement for continuous time coupled nonlinear systems. SIAM J. Control Optim. 46(1), 288–307 (2007)MathSciNetCrossRefMATH
22.
Zurück zum Zitat Y. Liu, Y. Jia, Robust \(\fancyscript {H}_{\infty }\) consensus control of uncertain multi-agent systems with time-delays. Int. J. Control Autom. Syst. 9(6), 1086–1094 (2011)MathSciNetCrossRef Y. Liu, Y. Jia, Robust \(\fancyscript {H}_{\infty }\) consensus control of uncertain multi-agent systems with time-delays. Int. J. Control Autom. Syst. 9(6), 1086–1094 (2011)MathSciNetCrossRef
23.
Zurück zum Zitat P. Massioni, M. Verhagen, Distributed control for identical dynamically coupled systems: A decomposition approach. IEEE Trans. Autom. Control 54(1), 124–135 (2009)MathSciNetCrossRef P. Massioni, M. Verhagen, Distributed control for identical dynamically coupled systems: A decomposition approach. IEEE Trans. Autom. Control 54(1), 124–135 (2009)MathSciNetCrossRef
24.
Zurück zum Zitat P.P. Menon, C. Edwards, Static output feedback stabilisation and synchronisation of complex networks with H2 performance. Int. J. Robust Nonlinear Control 20(6), 703–718 (2010)MathSciNetMATH P.P. Menon, C. Edwards, Static output feedback stabilisation and synchronisation of complex networks with H2 performance. Int. J. Robust Nonlinear Control 20(6), 703–718 (2010)MathSciNetMATH
25.
Zurück zum Zitat M. Mesbahi, State-dependent graphs, in IEEE Conference on Decision and Control (CDC) (2003) M. Mesbahi, State-dependent graphs, in IEEE Conference on Decision and Control (CDC) (2003)
26.
Zurück zum Zitat L. Moreau, Stability of multiagent systems with time dependent communication links. IEEE Trans. Autom. Control 50(2), 169–182 (2005)MathSciNetCrossRef L. Moreau, Stability of multiagent systems with time dependent communication links. IEEE Trans. Autom. Control 50(2), 169–182 (2005)MathSciNetCrossRef
27.
Zurück zum Zitat Y.S. Moon, P. Park, W.H. Kwon, Y.S. Lee, Delay-dependent robust stabilization of uncertain state-delayed systems. Int. J. Control 74(14), 1447–1455 (2001)MathSciNetCrossRefMATH Y.S. Moon, P. Park, W.H. Kwon, Y.S. Lee, Delay-dependent robust stabilization of uncertain state-delayed systems. Int. J. Control 74(14), 1447–1455 (2001)MathSciNetCrossRefMATH
28.
Zurück zum Zitat N. Motee, A. Jadbabaie, Approximation method and spatial interpolation in distributed control systems, in IEEE American Control Conference (ACC) (2009) N. Motee, A. Jadbabaie, Approximation method and spatial interpolation in distributed control systems, in IEEE American Control Conference (ACC) (2009)
29.
Zurück zum Zitat U. M\(\ddot{u}\)nz, A. Papachristodoulou, F. Allg\(\ddot{o}\)wer, Delay-dependent rendezvous and flocking of large scale multi-agent systems with communication delays, in IEEE Conference on Decision and Control (CDC) (2008) U. M\(\ddot{u}\)nz, A. Papachristodoulou, F. Allg\(\ddot{o}\)wer, Delay-dependent rendezvous and flocking of large scale multi-agent systems with communication delays, in IEEE Conference on Decision and Control (CDC) (2008)
30.
Zurück zum Zitat U. M\(\ddot{u}\)nz, A. Papachristodoulou, F. Allg\(\ddot{o}\)wer, Delay robustness in consensus problems. Automatica 46(8), 1252–1265 (2010) U. M\(\ddot{u}\)nz, A. Papachristodoulou, F. Allg\(\ddot{o}\)wer, Delay robustness in consensus problems. Automatica 46(8), 1252–1265 (2010)
31.
Zurück zum Zitat R. Olfati-Saber, R.M. Murray, Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans. Autom. Control 49(9), 1520–1533 (2004)MathSciNetCrossRef R. Olfati-Saber, R.M. Murray, Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans. Autom. Control 49(9), 1520–1533 (2004)MathSciNetCrossRef
32.
Zurück zum Zitat R. Olfati-Saber, J.A. Fax, R.M. Murray, Consensus and cooperation in networked multi-agent systems. Proc. IEEE 95(1), 215–133 (2007)CrossRef R. Olfati-Saber, J.A. Fax, R.M. Murray, Consensus and cooperation in networked multi-agent systems. Proc. IEEE 95(1), 215–133 (2007)CrossRef
33.
Zurück zum Zitat A. Papachristodoulou, A. Jadbabaie, U. M\(\ddot{u}\)nz, Effects of delay in multi-agent consensus and oscillator synchronization. IEEE Trans. Atuom. Control 55(6), 1471–1477 (2010) A. Papachristodoulou, A. Jadbabaie, U. M\(\ddot{u}\)nz, Effects of delay in multi-agent consensus and oscillator synchronization. IEEE Trans. Atuom. Control 55(6), 1471–1477 (2010)
34.
Zurück zum Zitat P. Park, J.W. Ko, Stability and robust stability for systems with a time-varying delay. Automatica 43(10), 1855–1858 (2007)MathSciNetCrossRefMATH P. Park, J.W. Ko, Stability and robust stability for systems with a time-varying delay. Automatica 43(10), 1855–1858 (2007)MathSciNetCrossRefMATH
35.
Zurück zum Zitat J. Qin, H. Gao, W.X. Zheng, Second order consensus for multi-agent systems with switching topology and communication delay. Syst. Control Lett. 60(6), 390–397 (2011)MathSciNetCrossRefMATH J. Qin, H. Gao, W.X. Zheng, Second order consensus for multi-agent systems with switching topology and communication delay. Syst. Control Lett. 60(6), 390–397 (2011)MathSciNetCrossRefMATH
36.
Zurück zum Zitat J.P. Richard, Time-delay systems: an overview of some recent advances and open problems. Automatica 39(10), 1667–1694 (2003)MathSciNetCrossRefMATH J.P. Richard, Time-delay systems: an overview of some recent advances and open problems. Automatica 39(10), 1667–1694 (2003)MathSciNetCrossRefMATH
37.
Zurück zum Zitat W. Ren, E.M. Atkins, Distributed multi-vehicle coordinated control via local information exchange. Int. J. Robust Nonlinear Control 17(10–11), 1002–1033 (2007)MathSciNetCrossRefMATH W. Ren, E.M. Atkins, Distributed multi-vehicle coordinated control via local information exchange. Int. J. Robust Nonlinear Control 17(10–11), 1002–1033 (2007)MathSciNetCrossRefMATH
38.
Zurück zum Zitat A. Seuret, D.V. Dimarogonas, K.H. Johanson, Consensus under communication delays, in IEEE Conference on Decision and Control (CDC) (2008) A. Seuret, D.V. Dimarogonas, K.H. Johanson, Consensus under communication delays, in IEEE Conference on Decision and Control (CDC) (2008)
39.
Zurück zum Zitat J. Sun, G.P. Liu, J. Chen, D. Rees, Improved delay-range-dependent stability criteria for linear systems with time-varying delays. Automatica 46(2), 466–470 (2009)MathSciNetCrossRefMATH J. Sun, G.P. Liu, J. Chen, D. Rees, Improved delay-range-dependent stability criteria for linear systems with time-varying delays. Automatica 46(2), 466–470 (2009)MathSciNetCrossRefMATH
40.
Zurück zum Zitat E. Tian, D. Yue, Z. Gu, Robust \({\fancyscript {H}}_{\infty }\) control for nonlinear system over a network: A piecewise analysis method. Fuzzy Sets Syst. 161(21), 2731–2745 (2010)MathSciNetCrossRefMATH E. Tian, D. Yue, Z. Gu, Robust \({\fancyscript {H}}_{\infty }\) control for nonlinear system over a network: A piecewise analysis method. Fuzzy Sets Syst. 161(21), 2731–2745 (2010)MathSciNetCrossRefMATH
42.
Zurück zum Zitat W. Yang, A.L. Bertozzi, X.F. Wang, Stability of a second order consensus algorithm with time delay, in IEEE Conference on Decision and Control (CDC) (2008) W. Yang, A.L. Bertozzi, X.F. Wang, Stability of a second order consensus algorithm with time delay, in IEEE Conference on Decision and Control (CDC) (2008)
Metadaten
Titel
Synthesis of Distributed Control Laws for Multi-agent Systems Using Delayed Relative Information with LQR Performance
verfasst von
Paresh Deshpande
Prathyush P. Menon
Christopher Edwards
Copyright-Jahr
2016
DOI
https://doi.org/10.1007/978-3-319-32372-5_14

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