Skip to main content
SpringerLink
Log in

Graph process specifications for hybrid networked systems

  • Published:
Discrete Event Dynamic Systems Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  • 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 558–563

  • 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, Citeseer

  • Attia S, Alamir M, de Wit C (2005) Sub optimal control of switched nonlinear systems under location and switching constraints. In: IFAC world congress

  • 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):167–186

    Article  MathSciNet  MATH  Google Scholar 

  • Bamieh B, Paganini F, Dahleh M (2002) Distributed control of spatially invariant systems. IEEE Trans Automat Contr 47(7):1091–1107

    Article  MathSciNet  Google Scholar 

  • 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 1190–1194

  • Branicky M, Borkar V, Mitter S (1998) A unified framework for hybrid control: model and optimal control theory. IEEE Trans Automat Contr 43(1):31–45

    Article  MathSciNet  MATH  Google Scholar 

  • Brockett R (1988) On the computer control of movement. In: Proceedings of IEEE international conference on robotics and automation, vol 1, pp 534–540

  • 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):139

    Article  Google Scholar 

  • Egerstedt M, Wardi Y, Axelsson H (2006) Transition-time optimization for switched-mode dynamical systems. IEEE Trans Automat Contr 51(1):110–115

    Article  MathSciNet  Google Scholar 

  • 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 2966–2971

  • 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 3972–3977

  • Jadbabaie A, Lin J, Morse A (2003) Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Trans Automat Contr 48(6):988–1001

    Article  MathSciNet  Google Scholar 

  • Ji M, Egerstedt M (2007) Distributed coordination control of multiagent systems while preserving connectedness. IEEE Trans Robot 23(4):693–703

    Article  Google Scholar 

  • Johansson K, Egerstedt M, Lygeros J, Sastry S (1999) On the regularization of Zeno hybrid automata. Syst Control Lett 38(3):141–150

    Article  MathSciNet  MATH  Google Scholar 

  • Kloetzer M, Belta C (2007) Temporal logic planning and control of robotic swarms by hierarchical abstractions. IEEE Trans Robot 23(2):320–330

    Article  Google Scholar 

  • Koutsoukos X, Antsaklis P, Stiver J, Lemmon M (2000) Supervisory control of hybrid systems. Proc IEEE 88(7):1026–1049

    Article  Google Scholar 

  • Lin Z, Broucke M, Francis B (2004) Local control strategies for groups of mobile autonomous agents. IEEE Trans Automat Contr 49(4):622–629

    Article  MathSciNet  Google Scholar 

  • Liu Y, Passino K, Polycarpou M (2003) Stability analysis of one-dimensional asynchronous swarms. IEEE Trans Automat Contr 48(10):1848–1854

    Article  MathSciNet  Google Scholar 

  • Lynch N (1996) Distributed algorithms. Morgan Kaufmann

  • Manikonda V, Krishnaprasad PS, Hendler J (1998) Languages, behaviors, hybrid architectures and motion control. In: Willems J, Baillieul J (eds) Mathematical control theory, Springer-Verlag

  • 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 Control

  • 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 6080–6087

  • Mesbahi M, Egerstedt M (2010) Graph theoretic methods for multiagent networks. Princeton University Press, Princeton, NJ

    Google Scholar 

  • Morse A (1997) Control using logic-based switching. Citeseer

  • Motee N, Jadbabaie A (2008) Optimal control of spatially distributed systems. IEEE Trans Automat Contr 53(7):1616–1629

    Article  MathSciNet  Google Scholar 

  • Muhammad A, Egerstedt M (2005) Connectivity graphs as models of local interactions. Appl Math Comput 168(1):243–269

    Article  MathSciNet  MATH  Google Scholar 

  • Olfati-Saber R, Murray R (2004) Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans Automat Contr 49(9):1520–1533

    Article  MathSciNet  Google Scholar 

  • Olfati-Saber R, Fax J, Murray R (2007) Consensus and cooperation in networked multi-agent systems. Proc IEEE 95(1):215–233

    Article  Google Scholar 

  • Rantzer A (2007) A separation principle for distributed control. In: Proceedings of the 45th IEEE Conference on Decision and Control, 2006. IEEE, pp 3609–3613

  • Ren W, Beard R (2005) Consensus seeking in multiagent systems under dynamically changing interaction topologies. IEEE Trans Automat Contr 50(5):655–661

    Article  MathSciNet  Google Scholar 

  • Rotkowitz M, Lall S (2006) A characterization of convex problems in decentralized control. IEEE Trans Automat Contr 51(2):274–286

    Article  MathSciNet  Google Scholar 

  • 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 1997–1998

  • 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 466–481

  • Shaikh M, Caines P (2007) On the hybrid optimal control problem: theory and algorithms. IEEE Trans Automatic Control 52(9):1587–1603

    Article  MathSciNet  Google Scholar 

  • Smith B, Howard A, McNew J, Wang J, Egerstedt M (2009) Multi-robot deployment and coordination with embedded graph grammars. Auton Robots 26(1):79–98

    Article  Google Scholar 

  • Tanner H, Pappas G, Kumar V (2004) Leader-to-formation stability. IEEE Trans Robot Autom 20(3):443–455

    Article  Google Scholar 

  • Tanner H, Jadbabaie A, Pappas G (2007) Flocking in fixed and switching networks. IEEE Trans Automat Contr 52(5):863–868

    Article  MathSciNet  Google Scholar 

  • Twu P, Egerstedt M (2010) Optimal decentralization of multi-agent motions. In: Proceedings of the American Control Conference, 2010. IEEE, pp 2326–2331

  • Twu P, Martin P, Egerstedt M (2010) Graph process specifications for hybrid networked systems. In: Proceedings of 10th international workshop on discrete event systems

  • 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 168–176

  • 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 4401–4406

  • 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):1406–1426

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

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.

Author information

Authors and Affiliations

  1. Department of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA, 30332, USA

    Philip Y. Twu & Magnus B. Egerstedt

  2. York College of Pennsylvania, York, PA, 17403, USA

    Patrick Martin

Authors
  1. Philip Y. Twu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Patrick Martin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Magnus B. Egerstedt
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Philip Y. Twu.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Twu, P.Y., Martin, P. & Egerstedt, M.B. Graph process specifications for hybrid networked systems. Discrete Event Dyn Syst 22, 541–577 (2012). https://doi.org/10.1007/s10626-012-0134-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10626-012-0134-2

Keywords

Search

Navigation