Abstract
System design often explores optimality of performance. What is optimal is, however, often not predefined or static in most cases, because it is affected by the context of operation, such as the environment or external system inputs. In this paper, we formulate the maintenance of optimality of performance in dynamical systems in terms of the standard notion of stabilization. For systems with observable external inputs and computable optimality, stabilization may be achieved by adding a stabilizing input estimator to the system. But environments and external inputs are often unobservable. To overcome this difficulty, we present two alternative methods, one based on a game-theoretic MinMax strategy that leads to Nash equilibrium, and the other based on a feedback control mechanism that adds a stabilizing output transformer to the system. We exemplify these two approaches with a pursuit-evasion application and a MAC layer duty cycle adaptation protocol, respectively.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Manna, Z., Pnueli, A.: Models for reactivity. Informatica, 609–678 (1993)
Gouda, M.G., Herman, T.: Adaptive programming. IEEE Transaction of Software Engineering 17(9), 911–921 (1991)
Arora, A., Gouda, M.: Closure and convergence: A foundation of fault-tolerant computing. IEEE Transactions on Software Engineering 19(10), 1015–1027 (1993)
Kutten, S., Patt-Shamir, B.: Adaptive stabilization of reactive protocols. In: Lodaya, K., Mahajan, M. (eds.) FSTTCS 2004. LNCS, vol. 3328, pp. 396–407. Springer, Heidelberg (2004)
Arora, A., Nesterenko, M.: Unifying stabilization and termination in message-passing systems. Distributed Computing 17(3), 279–290 (2005)
Burman, J., Kutten, S., Herman, T., Patt-Shamir, B.: Asynchronous and fully self-Stabilizing time-adaptive majority consensus. In: Anderson, J.H., Prencipe, G., Wattenhofer, R. (eds.) OPODIS 2005. LNCS, vol. 3974, Springer, Heidelberg (2006)
Beauquier, J., Genolini, C., Kutten, S.: Optimal reactive k-stabilization: the case of mutual exclusion. In: PODC. Proceedings of the 18th ACM Symposium on Principles of Distributed Computing, pp. 209–218 (1999)
Theel, O.: Exploitation of Lyapunov Theory for Verifying Self-Stabilizing Algorithms. In: Herlihy, M.P. (ed.) DISC 2000. LNCS, vol. 1914, Springer, Heidelberg (2000)
Dhama, A., Oehlerking, J., Theel, O.: Verification of Orbitally Self-stabilizing Distributed Algorithms using Lyapunov Functions and Poincaré Maps. In: Proceedings of the 12th International Conference on Parallel and Distributed Systems (2006)
Anceaume, E., Défago, X., Gradinariu, M., Roy, M.: Towards a Theory of Self-organization. In: Anderson, J.H., Prencipe, G., Wattenhofer, R. (eds.) OPODIS 2005. LNCS, vol. 3974, Springer, Heidelberg (2006)
Dolev, S., Tzachar, N.: Empire of Colonies: Self-stabilizing and Self-organizing Distributed Algorithms. In: Shvartsman, A.A. (ed.) OPODIS 2006. LNCS, vol. 4305, Springer, Heidelberg (2006)
Dasgupta, A., Ghosh, S., Tixeuil, S.: Selfish stabilization. In: Datta, A.K., Gradinariu, M. (eds.) SSS 2006. LNCS, vol. 4280, pp. 231–243. Springer, Heidelberg (2006)
Arora, A., Ramnath, R., Ertin, E., Bapat, S., Naik, V., Cao, H., et al.: ExScal: Elements of an extreme wireless sensor network. In: Proceedings of the 11th International Conference on Embedded and Real-Time Computing Systems and Applications (2005)
Cao, H., Ertin, E., Kulathumani, V., Sridharan, M., Arora, A.: Differential Games in Large Scale Sensor Actuator Networks. In: IPSN. Proceedings of the 5th International Conference on Information Processing in Sensor Networks (2006)
Cao, H., Ertin, E., Arora, A.: MiniMax Equilibrium of Networked Differential Games, Technical Report OSU-CISRC-4/07 (2007)
Verdu, S., Poor, H.: On minimax robustness: A general approach and applications. IEEE Transactions on Information Theory IT-30, 328–340 (1984)
Cao, H., Parker, K.W., Arora, A.: O-MAC: a receiver centric power management protocol. In: ICNP. Proceedings of the 14th IEEE International Conference on Network Protocols, IEEE Computer Society Press, Los Alamitos (2006)
Cao, H., Arora, A., Parker, K.W., Lai, T.H.: Continuous asynchronous discovery with efficient synchronous communication for mobile networks, Technical Report OSU-CISRC-4/07 (2007)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Cao, H., Arora, A. (2007). Stabilization in Dynamic Systems with Varying Equilibrium. In: Masuzawa, T., Tixeuil, S. (eds) Stabilization, Safety, and Security of Distributed Systems. SSS 2007. Lecture Notes in Computer Science, vol 4838. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-76627-8_8
Download citation
DOI: https://doi.org/10.1007/978-3-540-76627-8_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-76626-1
Online ISBN: 978-3-540-76627-8
eBook Packages: Computer ScienceComputer Science (R0)