Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Bücher
Zeitschriften
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
SLX-Digitalkonferenz: Zukunftswerkstatt 2024

Mehr Umsatz mit Top-Kontakten

Am 7. Mai erfahren Sie, wie Vertriebsteams Leadgenerierung, Leadnurturing und Leadstrategien effizient steuern können.
Erweiterte Suche
Anmelden
nach oben
Autonomous Robots
Erschienen in: Autonomous Robots 8/2018

13.02.2018

A distributed control and parameter estimation protocol with prescribed performance for homogeneous lagrangian multi-agent systems

verfasst von: Charalampos P. Bechlioulis, Michael A. Demetriou, Kostas J. Kyriakopoulos

Erschienen in: Autonomous Robots | Ausgabe 8/2018

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

In this paper, we consider the formation control problem for uncertain homogeneous Lagrangian nonlinear multi-agent systems in a leader-follower scheme under a directed communication protocol. A distributed adaptive control protocol of minimal complexity is proposed that achieves prescribed, arbitrarily fast and accurate formation establishment as well as synchronization of the parameter estimates of all followers. The estimation and control laws are distributed in the sense that the control signal and the update laws are calculated based solely on local relative state information. Moreover, provided that the communication graph is strongly connected and contrary to the related works on multi-agent systems, the controller-imposed transient and steady state performance bounds are fully decoupled from: (i) the underlying graph topology, (ii) the control gains selection and (iii) the agents’ model uncertainties. Finally, extensive simulation studies on the attitude control of flying spacecrafts clarify and verify the approach.
Vorheriger Artikel Guest editorial: Special issue on distributed robotics—from fundamentals to applications
Nächster Artikel ALAN: adaptive learning for multi-agent navigation

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Jetzt informieren
Fußnoten
1
Several other works have been proposed for the coordinated tracking control problem in multi-agent systems, that however have assumed that all followers have access to the leader state, leading inevitably in centralized approaches.
 
2
Our recent results (Bechlioulis et al. 2016) on the distributed control and parameter estimation of unknown Lagrangian multi-agent systems are extended here by considering a significantly more generic directed communication protocol as well as by verifying the theoretical findings via extensive comparative simulation studies.
 
3
Apparently, when no relative offsets are required (i.e., all \(c_{ij}=0\), \(i=1,\dots ,N\)), we consider the synchronization/consensus problem, where a common response, dictated by the leader node, is required for all following agents.
 
4
An \(\mathcal {M}\)-matrix is a square matrix having its off-diagonal entries non-positive and all principle minors non-negative.
 
5
The desired command/reference trajectory information \(x_{0}\) is only pinned to a subgroup of the N following agents.
 
6
Notice that the right product of a matrix \(\mathcal {A}\) with a positive definite and diagonal matrix \(\mathcal {D}\) corresponds to the multiplication of each column of \(\mathcal {A}\) with the corresponding diagonal element of \(\mathcal {D}\). Thus, if \(\mathcal {A}\) is an \(\mathcal {M}\)-matrix, which is equivalent to all its principal minors being positive, then \(\mathcal {AD}\) is also an \(\mathcal {M} \)-matrix since the signs of its principal minors are the same with those of \(\mathcal {A}\), owing to the positive definiteness of \(\mathcal {D}\).
 
7
The symmetric part of the Laplacian matrix of a strongly connected and balanced graph is a positive semi-definite matrix (Wu 2005).
 
8
Notice that from the proposed control scheme (7a)–(7d), we can select the control gains \(K_{p_{i}}\), \(K_{v_{i}}\) such that \(\tau _{i}\) are retained within certain bounds.
 
9
Notice that the proposed methodology does not explicitly take into account any specifications in the input (magnitude or slew rate). Such research direction is an open issue for future investigation and would increase significantly the applicability of the proposed scheme.
 
10
The attitude synchronization of multiple spacecrafts plays an important role in aerospace engineering since it increases the coverage of the earth surface during such missions. Apparently, the synchronization control problem is a subclass of generic formation control problems where no relative offsets are required (i.e., all \(c_{ij}=0\), \(i=1,\ldots ,N\)).
 
Literatur
Bechlioulis, C. P., & Kyriakopoulos, K. J. (2014). Robust model-free formation control with prescribed performance and connectivity maintenance for nonlinear multi-agent systems. In Proceedings of the IEEE conference on decision and control, pp. 4509–4514.
Bechlioulis, C. P., & Kyriakopoulos, K. J. (2015). Robust model-free formation control with prescribed performance for nonlinear multi-agent systems. In Proceedings of IEEE international conference on robotics and automation, pp. 1268–1273.
Bechlioulis, C. P., Demetriou, M. A., & Kyriakopoulos, K. J. (2016). Distributed control and parameter estimation for homogeneous lagrangian multi-agent systems. In Proceedings of the IEEE conference on decision and control.
Bechlioulis, C. P., & Rovithakis, G. A. (2008). Robust adaptive control of feedback linearizable mimo nonlinear systems with prescribed performance. IEEE Transactions on Automatic Control, 53(9), 2090–2099.MathSciNetCrossRef
Bechlioulis, C. P., & Rovithakis, G. A. (2010). Prescribed performance adaptive control for multi-input multi-output affine in the control nonlinear systems. IEEE Transactions on Automatic Control, 55(5), 1220–1226.MathSciNetCrossRef
Bechlioulis, C. P., & Rovithakis, G. A. (2014). A low-complexity global approximation-free control scheme with prescribed performance for unknown pure feedback systems. Automatica, 50(4), 1217–1226.MathSciNetCrossRef
Cao, Y., & Ren, W. (2012). Distributed coordinated tracking with reduced interaction via a variable structure approach. IEEE Transactions on Automatic Control, 57(1), 33–48.MathSciNetCrossRef
Chen, G., & Lewis, F. L. (2011). Distributed adaptive tracking control for synchronization of unknown networked lagrangian systems. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, 41(3), 805–816.CrossRef
Cheng, L., Hou, Z., Tan, M., Lin, Y., & Zhang, W. (2010). Neural-network-based adaptive leader-following control for multiagent systems with uncertainties. IEEE Transactions on Neural Networks, 21(8), 1351–1358.CrossRef
Chung, S.-J., Ahsun, U., & Slotine, J.-J. E. (2009). Application of synchronization to formation flying spacecraft: Lagrangian approach. Journal of Guidance, Control, and Dynamics, 32(2), 512–526.CrossRef
Das, A., & Lewis, F. L. (2010). Distributed adaptive control for synchronization of unknown nonlinear networked systems. Automatica, 46(12), 2014–2021.MathSciNetCrossRef
Dimarogonas, D. V., & Kyriakopoulos, K. J. (2008). A connection between formation infeasibility and velocity alignment in kinematic multi-agent systems. Automatica, 44(10), 2648–2654.MathSciNetCrossRef
Dong, W. (2011). On consensus algorithms of multiple uncertain mechanical systems with a reference trajectory. Automatica, 47(9), 2023–2028.MathSciNetCrossRef
El-Ferik, S., Qureshi, A., & Lewis, F. L. (2014). Neuro-adaptive cooperative tracking control of unknown higher-order affine nonlinear systems. Automatica, 50(3), 798–808.MathSciNetCrossRef
Fax, J. A., & Murray, R. M. (2004). Information flow and cooperative control of vehicle formations. IEEE Transactions on Automatic Control, 49(9), 1465–1476.MathSciNetCrossRef
Hong, Y. P., & Pan, C. T. (1992). A lower bound for the smallest singular value. Linear Algebra and its Applications, 172, 27–32.MathSciNetCrossRef
Hou, Z., Cheng, L., & Tan, M. (2009). Decentralized robust adaptive control for the multiagent system consensus problem using neural networks. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, 39(3), 636–647.CrossRef
Jadbabaie, A., Lin, J., & Morse, A. S. (2003). Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Transactions on Automatic Control, 48(6), 988–1001.MathSciNetCrossRef
Karayiannidis, Y., Dimarogonas, D. V., & Kragic, D. (2012). Multi-agent average consensus control with prescribed performance guarantees. In Proceedings of the IEEE conference on decision and control, pp. 2219–2225.
Khalil, H. (1992). Nonlinear Systems. New York: Macmillan Inc.MATH
Liu, Y., & Lunze, J. (2014). Leader-follower synchronisation of autonomous agents with external disturbances. International Journal of Control, 87(9), 1914–1925.MathSciNetCrossRef
Liu, Y., Min, H., Wang, S., Liu, Z., & Liao, S. (2014). Distributed adaptive consensus for multiple mechanical systems with switching topologies and time-varying delay. Systems and Control Letters, 64(1), 119–126.MathSciNetCrossRef
Markley, F. L., & Crassidis, J. L. (2014). Fundamentals of spacecraft attitude determination and control, 1st ed., ser. Space Technology Library 33. New York: Springer.MATH
Mei, J., Ren, W., & Ma, G. (2011). Distributed coordinated tracking with a dynamic leader for multiple euler-lagrange systems. IEEE Transactions on Automatic Control, 56(6), 1415–1421.MathSciNetCrossRef
Nestinger, S. S., & Demetriou, M. A. (2012). Adaptive collaborative estimation of multi-agent mobile robotic systems. In Proceedings of IEEE international conference on robotics and automation, pp. 1856–1861.
Olfati-Saber, R., & Murray, R. M. (2004). Consensus problems in networks of agents with switching topology and time-delays. IEEE Transactions on Automatic Control, 49(9), 1520–1533.MathSciNetCrossRef
Peymani, E., Grip, H. F., & Saberi, A. (2015). Homogeneous networks of non-introspective agents under external disturbances–\(H_{\infty }\) almost synchronization. Automatica, 52, 363–372.MathSciNetCrossRef
Priolo, A., Gasparri, A., Montijano, E., & Sagues, C. (2013). A decentralized algorithm for balancing a strongly connected weighted digraph. In Proceedings of the American control conference, pp. 6547–6552.
Qu, Z. (2009). Cooperative control of dynamical systems: Applications to autonomous vehicles. New York: Springer.MATH
Ren, W., & Beard, R. W. (2005). Consensus seeking in multiagent systems under dynamically changing interaction topologies. IEEE Transactions on Automatic Control, 50(5), 655–661.MathSciNetCrossRef
Sadikhov, T., Demetriou, M. A., Haddad, W. M., & Yucelen, T. (2014). Adaptive estimation using multiagent network identifiers with undirected and directed graph topologies. Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME, 136(2), 021018.CrossRef
Seyboth, G. S., Dimarogonas, D. V., Johansson, K. H., Frasca, P., & Allgwer, F. (2015). On robust synchronization of heterogeneous linear multi-agent systems with static couplings. Automatica, 53, 392–399.MathSciNetCrossRef
Shen, Q., & Shi, P. (2015). Distributed command filtered backstepping consensus tracking control of nonlinear multiple-agent systems in strict-feedback form. Automatica, 53, 120–124.MathSciNetCrossRef
Shivakumar, P. N., & Chew, K. H. (1974). A sufficient condition for nonvanishing of determinants. Proceedings of the American Mathematical Society, 43(1), 63–66.MathSciNetCrossRef
Shuster, M. D. (1993). Survey of attitude representations. Journal of the Astronautical Sciences, 41(4), 439–517.MathSciNet
Song, Q., Cao, J., & Yu, W. (2010). Second-order leader-following consensus of nonlinear multi-agent systems via pinning control. Systems and Control Letters, 59(9), 553–562.MathSciNetCrossRef
Su, Y., & Huang, J. (2014). Cooperative semi-global robust output regulation for a class of nonlinear uncertain multi-agent systems. Automatica, 50(4), 1053–1065.MathSciNetCrossRef
Trentelman, H. L., Takaba, K., & Monshizadeh, N. (2013). Robust synchronization of uncertain linear multi-agent systems. IEEE Transactions on Automatic Control, 58(6), 1511–1523.MathSciNetCrossRef
Ugrinovskii, V. (2014). Gain-scheduled synchronization of parameter varying systems via relative \(H_{\infty }\) consensus with application to synchronization of uncertain bilinear systems. Automatica, 50(11), 2880–2887.MathSciNetCrossRef
Wieland, P., Sepulchre, R., & Allgower, F. (2011). An internal model principle is necessary and sufficient for linear output synchronization. Automatica, 47(5), 1068–1074.MathSciNetCrossRef
Wu, C. W. (2005). Algebraic connectivity of directed graphs. Linear and Multilinear Algebra, 53(3), 203–223.MathSciNetCrossRef
Xiang, J., Li, Y., & Wei, W. (2013). Synchronisation of linear high-order multi-agent systems: An internal model approach. IET Control Theory and Applications, 7(17), 2110–2116.MathSciNetCrossRef
Yang, D., Liu, X., Li, Z., & Guo, Y. (2013). Distributed adaptive sliding mode control for attitude tracking of multiple spacecraft. In Chinese control conference, CCC, pp. 6917–6922.
Yoo, S. J. (2013). Distributed adaptive consensus tracking of a class of networked non-linear systems with parametric uncertainties. IET Control Theory and Applications, 7(7), 1049–1057.MathSciNetCrossRef
Yu, W., Chen, G., & Cao, M. (2010). Distributed leader-follower flocking control for multi-agent dynamical systems with time-varying velocities. Systems and Control Letters, 59(9), 543–552.MathSciNetCrossRef
Yu, H., Shi, P., & Lim, C. (2016). Robot formation control in stealth mode with scalable team size. International Journal of Control, 89, 2155–2168.MathSciNetCrossRef
Yu, H., Shi, P., & Lim, C. (2017). Scalable formation control in stealth with limited sensing range. International Journal of Robust and Nonlinear Control, 27(3), 410–433.MathSciNetCrossRef
Zhang, K., & Demetriou, M. A. (2014). Adaptive attitude synchronization control of spacecraft formation with adaptive synchronization gains. Journal of Guidance, Control, and Dynamics, 37(5), 1644–1651.CrossRef
Zhang, K., & Demetriou, M. A. (2015). Adaptation and optimization of the synchronization gains in the adaptive spacecraft attitude synchronization. Aerospace Science and Technology, 46, 116–123.CrossRef
Zhang, H., & Lewis, F. L. (2012). Adaptive cooperative tracking control of higher-order nonlinear systems with unknown dynamics. Automatica, 48(7), 1432–1439.MathSciNetCrossRef
Metadaten
Titel
A distributed control and parameter estimation protocol with prescribed performance for homogeneous lagrangian multi-agent systems
verfasst von
Charalampos P. Bechlioulis
Michael A. Demetriou
Kostas J. Kyriakopoulos
Publikationsdatum
13.02.2018
Verlag
Springer US
Erschienen in
Autonomous Robots / Ausgabe 8/2018
Print ISSN: 0929-5593
Elektronische ISSN: 1573-7527
DOI
https://doi.org/10.1007/s10514-018-9700-2

Weitere Artikel der Ausgabe 8/2018

Autonomous Robots 8/2018 Zur Ausgabe

OriginalPaper

Distributed system of autonomous buoys for scalable deployment and monitoring of large waterbodies

OriginalPaper

Dynamic teams of robots as ad hoc distributed computers: reducing the complexity of multi-robot motion planning via subspace selection

OriginalPaper

Bound to help: cooperative manipulation of objects via compliant, unactuated tails

OriginalPaper

Distributed camouflage for swarm robotics and smart materials

OriginalPaper

Decentralized navigation method for a robotic swarm with nonhomogeneous abilities

OriginalPaper

Multi robot collision avoidance in a shared workspace

Neuer Inhalt

    Bildnachweise