Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
Introduction to Synchronization in Nature and Physics and Cooperative Control for Multi-Agent Systems on Graphs Read chapter Read first chapter

2014 | OriginalPaper | Chapter

6. Graphical Games: Distributed Multiplayer Games on Graphs

Authors : Frank L. Lewis, Hongwei Zhang, Kristian Hengster-Movric, Abhijit Das

Published in: Cooperative Control of Multi-Agent Systems

Publisher: Springer London

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

In this chapter, it is seen that distributed control protocols that both guarantee synchronization and are globally optimal for the multi-agent team always exist on any sufficiently connected communication graph if a different definition of optimality is used. To this end, we study the notion of Nash equilibrium for multiplayer games on graphs. This leads us to the idea of a new sort of differential game—graphical games. In graphical games, each agent has its own dynamics as well as its own local performance index. The dynamics and local performance indices of each agent are distributed; they depend on the state of the agent, the control of the agent, and the controls of the agent’s neighbors. We show how to compute distributed control protocols that guarantee global Nash equilibrium for multi-agent teams on any graph that has a spanning tree.

Dont have a licence yet? Then find out more about our products and how to get one now:

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!

inform now

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!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now
previous chapter Cooperative Globally Optimal Control for Multi-Agent Systems on Directed Graph Topologies
next chapter Graph Laplacian Potential and Lyapunov Functions for Multi-Agent Systems
Literature
1.
Abou-Kandil H, Freiling G, Ionescu V, Jank G (2003) Matrix Riccati Equations in Control and Systems Theory. Birkhäuser
2.
Abu-Khalaf M, Lewis FL (2005) Nearly optimal control laws for nonlinear systems with saturating actuators using a neural network HJB approach. Automatica 41(5):779–791
3.
Al-Tamimi A, Abu-Khalaf M, Lewis FL (2007) Adaptive critic designs for discrete-time zero-sum games with application to H-Infinity control. IEEE Trans Syst, Man, Cybern B 37(1):240–247
4.
Al-Tamimi A, Lewis FL, Abu-Khalaf M (2008) Discrete-time nonlinear HJB solution using approximate dynamic programming: convergence proof. IEEE Trans Syst, Man, Cybern B 38(4):943–949
5.
Başar T, Olsder GJ (1999) Dynamic Noncooperative Game Theory, 2nd edn. SIAM, Philadelphia
6.
Bertsekas DP, Tsitsiklis JN (1996) Neuro-Dynamic Programming. Athena Scientific, Belmont
7.
Brewer JW (1978) Kronecker products and matrix calculus in system theory. IEEE Trans Circuits Syst 25:772–781
8.
Busoniu L, Babuska R, De Schutter B (2008) A comprehensive survey of multi-agent reinforcement learning. IEEE Trans Syst, Man, Cybern C 38(2):156–172
9.
Dierks T, Jagannathan S (2010) Optimal control of affine nonlinear continuous-time systems using an online Hamilton–Jacobi–Isaacs formulation. In: Proc. IEEE Conf. Decision Control, Atlanta, GA, pp. 3048–3053
10.
Freiling G, Jank G, Abou-Kandil H (2002) On global existence of solutions to coupled matrix Riccati equations in closed loop Nash games. IEEE Trans Automat Contr 41(2):264–269
11.
Gajic Z, Li T-Y (1988) Simulation results for two new algorithms for solving coupled algebraic Riccati equations. Paper presented at 3rd international symposium on differential games, Sophia Antipolis, Nice, France
12.
Goldberg AV (1995) Scaling algorithms for the shortest paths problem. SIAM J Comput 24:494–504
13.
Ioannou P, Fidan B (2006) Adaptive Control Tutorial. SIAM, Philadelphia
14.
Johnson M, Hiramatsu T, Fitz-Coy N, Dixon WE (2010) Asymptotic stackelberg optimal control design for an uncertain euler lagrange system. In: Proc. IEEE Conf. Decision Control, Atlanta, GA, pp. 6686–6691
15.
Kakade S, Kearns M, Langford J, Ortiz L (2003) Correlated equilibria in graphical games. In: the 4th ACM conf. Electron. Commerce, San Diego, CA, pp. 42–47
16.
Kearns M, Littman M, Singh S (2001) Graphical models for game theory. In: Proc. Annual conf. Uncertainty in Artificial Intelligence, Seattle, WA, pp. 253–260
17.
Khoo S, Xie L, Man Z (2009) Robust finite-time consensus tracking algorithm for multirobot systems. IEEE Trans Mechatron 14:219–228
18.
Leake RJ, Liu R-W (1967) Construction of suboptimal control sequences. SIAM J Contr 5(1):54–63
19.
Lewis FL (1992) Applied Optimal Control and Estimation: Digital Design and Implementation. Prentice-Hall, Upper Saddle River
20.
Lewis FL, Vrabie D (2009) Reinforcement learning and adaptive dynamic programming for feedback control. IEEE Circuits & Systems Magazine (invited feature article), pp. 32–50, Third Quarter 2009
21.
Lewis FL, Jagannathan S, Yesildirek A (1999) Neural Network Control of Robot Manipulators and Nonlinear Systems. Taylor and Francis, London
22.
Lewis FL, Vrabie D, Syrmos VL (2012) Optimal control, 3rd edn. Wiley, Hoboken
23.
Lewis FL, Vrabie D, Vamvoudakis KG (2012) Reinforcement learning and feedback control. IEEE Control Systems Magazine, pp. 76–105
24.
Li X, Wang X, Chen G (2004) Pinning a complex dynamical network to its equilibrium. IEEE Trans Circuits Syst I, Reg Papers 51(10):2074–2087
25.
Littman ML (2001) Value-function reinforcement learning in Markov games. J Cogn Syst Res 2(1):55–66
26.
Marden JR, Young HP, Pao LY (2012) Achieving pareto optimality through distributed learning. In: Proc. IEEE Conf. Decision Control, Maui, HI, pp. 7419–7424
28.
Shinohara R (2010) Coalition proof equilibria in a voluntary participation game. Int J Game Theory 39(4):603–615
29.
Shoham Y, Leyton-Brown K (2009). Multiagent Systems: Algorithmic, Game-Theoretic, and Logical Foundations. Cambridge University Press, Cambridge
30.
Sutton RS, Barto AG (1998) Reinforcement learning—an introduction. MIT Press, Cambridge
31.
Tijs S (2003) Introduction to game theory. Hindustan Book Agency, New Delhi.
32.
Vamvoudakis KG, Lewis FL (2010). Online actor-critic algorithm to solve the continuous-time infinite horizon optimal control problem. Automatica 46(5):878–888
33.
Vamvoudakis KG, Lewis FL (2011). Multi-player non-zero sum games: online adaptive learning solution of coupled Hamilton–Jacobi equations. Automatica 47(8):1556–1569
34.
Vamvoudakis KG, Lewis FL, Hudas GR (2012) Multi-agent differential graphical games: online adaptive learning solution for synchronization with optimality. Automatica 48(8):1598–1611
35.
Vrabie D, Lewis FL (2009) Neural network approach to continuous-time direct adaptive optimal control for partially-unknown nonlinear systems. Neural Networks 2(3):237–246
36.
Vrabie D, Pastravanu O, Lewis FL, Abu-Khalaf M (2009). Adaptive optimal control for continuous-time linear systems based on policy iteration. Automatica 45(2):477–484
37.
Vrancx P, Verbeeck K, Nowe A (2008). Decentralized learning in Markov games. IEEE Tran Syst Man Cyber 38(4):976–981
38.
Wang F, Zhang H, Liu D (May 2009) Adaptive dynamic programming: an introduction. IEEE Comput Intell Mag 4(2):39–47
39.
Wang X, Chen G (2002). Pinning control of scale-free dynamical networks. Physica A 310(3–4):521–531
40.
Werbos PJ (1974) Beyond Regression: New Tools for Prediction and Analysis in the Behavior Sciences. Ph.D. Thesis, Harvard University
41.
Werbos PJ (1992) Approximate dynamic programming for real-time control and neural modeling. In: White DA, Sofge DA (eds) Handbook of Intelligent Control. Van Nostrand Reinhold, New York
42.
Zwick U (2002) All pairs shortest paths using bridging sets and rectangular matrix multiplication. J ACM 49(3):289-317.
Metadata
Title
Graphical Games: Distributed Multiplayer Games on Graphs
Authors
Frank L. Lewis
Hongwei Zhang
Kristian Hengster-Movric
Abhijit Das
Copyright Year
2014
Publisher
Springer London
Book
Cooperative Control of Multi-Agent Systems

Print ISBN: 978-1-4471-5573-7

Electronic ISBN: 978-1-4471-5574-4

Copyright Year: 2014

DOI
https://doi.org/10.1007/978-1-4471-5574-4_6