Discrete Event Dynamic Systems

, Volume 22, Issue 4, pp 541–577 | Cite as

Graph process specifications for hybrid networked systems

  • Philip Y. TwuEmail author
  • Patrick Martin
  • Magnus B. Egerstedt


Many large-scale multi-agent missions consist of a sequence of subtasks, each of which can be accomplished separately by having agents execute appropriate decentralized controllers. However, many decentralized controllers have network topological prerequisites that must be satisfied in order to achieve the desired effect on a system. Therefore, one cannot always hope to accomplish the original mission by having agents naively switch through executing the controllers for each subtask. This paper extends the Graph Process Specification (GPS) framework, which was presented in previous work as a way to script decentralized control sequences for agents, while ensuring that network topological requirements are satisfied when each controller in the sequence is executed. Atoms, the fundamental building blocks in GPS, each explicitly state a network topological transition. Moreover, they specify the means to make that transition occur by providing a multi-agent controller, as well as a way to locally detect the transition. Scripting a control sequence in GPS therefore reduces to selecting a sequence of atoms from a library to satisfy network topological requirements, and specifying interrupt conditions for switching. As an example of how to construct an atom library, the optimal decentralization algorithm is used to generate atoms for agents to track desired multi-agent motions with when the network topology is static. The paper concludes with a simulation of agents performing a drumline-inspired dance using decentralized controllers generated by optimal decentralization and scripted using GPS.


Decentralized control Formal specification Graph theoretic models Hybrid systems Network topologies 



This work was sponsored by the US National Science Foundation through Grant # CCF 0820004, and ONR through MURI HUNT. The authors would also like to thank Prof. Christopher Moore for discussions about the Georgia Tech drumline.


  1. Alamir M, Attia S (2004) On solving optimal control problems for switched hybrid nonlinear systems by strong variations algorithms. In: Proceedings of 6th IFAC symposium on nonlinear control systems, pp 558–563Google Scholar
  2. Antsaklis P (2000) A brief introduction to the theory and applications of hybrid systems. In: Proc IEEE, special issue on hybrid systems: theory and applications, CiteseerGoogle Scholar
  3. Attia S, Alamir M, de Wit C (2005) Sub optimal control of switched nonlinear systems under location and switching constraints. In: IFAC world congressGoogle Scholar
  4. Axelsson H, Wardi Y, Egerstedt M, Verriest E (2008) Gradient descent approach to optimal mode scheduling in hybrid dynamical systems. J Optim Theory Appl 136(2):167–186MathSciNetzbMATHCrossRefGoogle Scholar
  5. Bamieh B, Paganini F, Dahleh M (2002) Distributed control of spatially invariant systems. IEEE Trans Automat Contr 47(7):1091–1107MathSciNetCrossRefGoogle Scholar
  6. Bemporad A, Borrelli F, Morari M (2000) Piecewise linear optimal controllers for hybrid systems. In: Proceedings of the American Control Conference, 2000. IEEE, vol 2, pp 1190–1194Google Scholar
  7. Branicky M, Borkar V, Mitter S (1998) A unified framework for hybrid control: model and optimal control theory. IEEE Trans Automat Contr 43(1):31–45MathSciNetzbMATHCrossRefGoogle Scholar
  8. Brockett R (1988) On the computer control of movement. In: Proceedings of IEEE international conference on robotics and automation, vol 1, pp 534–540Google Scholar
  9. Couzin I, Franks N (2003) Self-organized lane formation and optimized traffic flow in army ants. Proc R Soc Lond, B Biol Sci 270(1511):139CrossRefGoogle Scholar
  10. Egerstedt M, Wardi Y, Axelsson H (2006) Transition-time optimization for switched-mode dynamical systems. IEEE Trans Automat Contr 51(1):110–115MathSciNetCrossRefGoogle Scholar
  11. Eren T, Whiteley W, Anderson B, Morse A, Belhumeur P (2005) Information structures to secure control of rigid formations with leader-follower architecture. In: Proceedings of the American Control Conference, 2005. IEEE, pp 2966–2971Google Scholar
  12. Hedlund S, Rantzer A (1999) Optimal control of hybrid systems. In: Proceedings of the 38th IEEE Conference on Decision and Control, 1999. IEEE, vol 4, pp 3972–3977Google Scholar
  13. Jadbabaie A, Lin J, Morse A (2003) Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Trans Automat Contr 48(6):988–1001MathSciNetCrossRefGoogle Scholar
  14. Ji M, Egerstedt M (2007) Distributed coordination control of multiagent systems while preserving connectedness. IEEE Trans Robot 23(4):693–703CrossRefGoogle Scholar
  15. Johansson K, Egerstedt M, Lygeros J, Sastry S (1999) On the regularization of Zeno hybrid automata. Syst Control Lett 38(3):141–150MathSciNetzbMATHCrossRefGoogle Scholar
  16. Kloetzer M, Belta C (2007) Temporal logic planning and control of robotic swarms by hierarchical abstractions. IEEE Trans Robot 23(2):320–330CrossRefGoogle Scholar
  17. Koutsoukos X, Antsaklis P, Stiver J, Lemmon M (2000) Supervisory control of hybrid systems. Proc IEEE 88(7):1026–1049CrossRefGoogle Scholar
  18. Lin Z, Broucke M, Francis B (2004) Local control strategies for groups of mobile autonomous agents. IEEE Trans Automat Contr 49(4):622–629MathSciNetCrossRefGoogle Scholar
  19. Liu Y, Passino K, Polycarpou M (2003) Stability analysis of one-dimensional asynchronous swarms. IEEE Trans Automat Contr 48(10):1848–1854MathSciNetCrossRefGoogle Scholar
  20. Lynch N (1996) Distributed algorithms. Morgan KaufmannGoogle Scholar
  21. Manikonda V, Krishnaprasad PS, Hendler J (1998) Languages, behaviors, hybrid architectures and motion control. In: Willems J, Baillieul J (eds) Mathematical control theory, Springer-VerlagGoogle Scholar
  22. Martin P, de la Croix J, Egerstedt M (2008) MDLn: a motion description language for networked systems. In: Proceedings of 47th IEEE Conference on Decision and ControlGoogle Scholar
  23. McNew J, Klavins E (2006) Locally interacting hybrid systems with embedded graph grammars. In: Proceedings of the 45th IEEE Conference on Decision and Control, 2006. pp 6080–6087Google Scholar
  24. Mesbahi M, Egerstedt M (2010) Graph theoretic methods for multiagent networks. Princeton University Press, Princeton, NJGoogle Scholar
  25. Morse A (1997) Control using logic-based switching. CiteseerGoogle Scholar
  26. Motee N, Jadbabaie A (2008) Optimal control of spatially distributed systems. IEEE Trans Automat Contr 53(7):1616–1629MathSciNetCrossRefGoogle Scholar
  27. Muhammad A, Egerstedt M (2005) Connectivity graphs as models of local interactions. Appl Math Comput 168(1):243–269MathSciNetzbMATHCrossRefGoogle Scholar
  28. Olfati-Saber R, Murray R (2004) Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans Automat Contr 49(9):1520–1533MathSciNetCrossRefGoogle Scholar
  29. Olfati-Saber R, Fax J, Murray R (2007) Consensus and cooperation in networked multi-agent systems. Proc IEEE 95(1):215–233CrossRefGoogle Scholar
  30. Rantzer A (2007) A separation principle for distributed control. In: Proceedings of the 45th IEEE Conference on Decision and Control, 2006. IEEE, pp 3609–3613Google Scholar
  31. Ren W, Beard R (2005) Consensus seeking in multiagent systems under dynamically changing interaction topologies. IEEE Trans Automat Contr 50(5):655–661MathSciNetCrossRefGoogle Scholar
  32. Rotkowitz M, Lall S (2006) A characterization of convex problems in decentralized control. IEEE Trans Automat Contr 51(2):274–286MathSciNetCrossRefGoogle Scholar
  33. Shaikh M, Caines P (2002) On trajectory optimization for hybrid systems: theory and algorithms for fixed schedules. In: Proceedings of the 37th IEEE Conference on Decision and Control, 1998. IEEE, vol 2, pp 1997–1998Google Scholar
  34. Shaikh M, Caines P (2003) On the optimal control of hybrid systems: optimization of trajectories, switching times, and location schedules. In: Proceedings of the 6th international conference on Hybrid systems: computation and control, Springer-Verlag, pp 466–481Google Scholar
  35. Shaikh M, Caines P (2007) On the hybrid optimal control problem: theory and algorithms. IEEE Trans Automatic Control 52(9):1587–1603MathSciNetCrossRefGoogle Scholar
  36. Smith B, Howard A, McNew J, Wang J, Egerstedt M (2009) Multi-robot deployment and coordination with embedded graph grammars. Auton Robots 26(1):79–98CrossRefGoogle Scholar
  37. Tanner H, Pappas G, Kumar V (2004) Leader-to-formation stability. IEEE Trans Robot Autom 20(3):443–455CrossRefGoogle Scholar
  38. Tanner H, Jadbabaie A, Pappas G (2007) Flocking in fixed and switching networks. IEEE Trans Automat Contr 52(5):863–868MathSciNetCrossRefGoogle Scholar
  39. Twu P, Egerstedt M (2010) Optimal decentralization of multi-agent motions. In: Proceedings of the American Control Conference, 2010. IEEE, pp 2326–2331Google Scholar
  40. Twu P, Martin P, Egerstedt M (2010) Graph process specifications for hybrid networked systems. In: Proceedings of 10th international workshop on discrete event systemsGoogle Scholar
  41. Xiao L, Boyd S, Lall S (2006) A space-time diffusion scheme for peer-to-peer least-squares estimation. In: Proceedings of the 5th international conference on information processing in sensor networks, ACM, pp 168–176Google Scholar
  42. Xu X, Antsaklis P (2002a) Optimal control of switched autonomous systems. In: Proceedings of the 41st IEEE Conference on Decision and Control, 2002. IEEE, vol 4, pp 4401–4406Google Scholar
  43. Xu X, Antsaklis P (2002b) Optimal control of switched systems via non-linear optimization based on direct differentiations of value functions. Int J Control 75 16(17):1406–1426MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Philip Y. Twu
    • 1
    Email author
  • Patrick Martin
    • 2
  • Magnus B. Egerstedt
    • 1
  1. 1.Department of Electrical and Computer EngineeringGeorgia Institute of TechnologyAtlantaUSA
  2. 2.York College of PennsylvaniaYorkUSA

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