Abstract
A decentralized control scheme is proposed for linear systems composed of overlapping subsystems. By expanding the state space of the system, a higher-dimensional space is formed where the subsystems appear as disjoint. In the expanded space, standard optimization techniques can be used to formulate a suboptimal decentralized control law for the overall system. A suitable contraction of the obtained control law, which is compatible with the information constraints imposed by the overlapping subsystems, can be implemented in the original system. The application of the proposed decentralized control scheme is illustrated using a 19th order model for load-frequency control of a two-area interconnected power system.
Similar content being viewed by others
References
Ho, Y. C., andChu, K. C.,Information Structure in Dynamic Multi-Person Control Problems, Automatica, Vol. 10, pp. 341–351, 1974.
Šiljak, D. D.,Large-Scale Dynamic Systems: Stability and Structure, North-Holland Publishing Company, New York, New York, 1978.
Athans, M., Levine, W. S., andLevis, A. H.,A System for the Optimal and Suboptimal Position and Velocity Control for a String of High-Speed Vehicles, Proceedings of the Fifth AICA Congress, Lausanne, Switzerland, 1967.
Isaksen, L., andPayne, H. J.,Suboptimal Control of Linear Systems by Augmentation with Application to Freeway Traffic Regulation, IEEE Transactions on Automatic Control, Vol. AC-18, pp. 210–219, 1973.
Ćalović, M., Djorović, M., andŠiljak, D. D.,Decentralized Approach to Automatic Generation Control of Interconnected Power Systems, Proceedings of the International Conference on Large High-Voltage Electric Systems (CIGRE), Paris, France, 1978.
Aoki, M.,On Decentralized Stabilization and Dynamic Assignment Problems, Journal of International Economics, Vol. 6, pp. 143–171, 1976.
Šiljak, D. D.,Reliable Control Using Multiple Control Systems, International Journal of Control, Vol. 31, pp. 303–329, 1980.
Ikeda, M., andŠiljak D. D.,Overlapping Decompositions, Expansions, and Contractions of Dynamic Systems, Large Scale Systems, Vol. 1, pp. 29–38, 1980.
Benveniste, A., Bernhard, P., andCohen, G.,On the Decomposition of Stochastic Control Problems, Proceedings of the IFAC Symposium on Large-Scale Systems, Theory and Applications (Supplement), Udine, Italy, 1976.
Krtolica, R., andSiljak, D. D.,Suboptimality of Decentralized Stochastic Control and Estimation, IEEE Transactions on Automatic Control, Vol. AC-25, pp. 76–83, 1980.
Kalman, R. E., andBertram, J. E.,Control System Analysis and Design via the Second Method of Lyapunov, Part 1, Continuous-Time Systems, Transactions of the ASME, Vol. 82, pp. 371–393, 1960.
Wonham, W. M.,On a Matrix Riccati Equation of Stochastic Control, SIAM Journal on Control, Vol. 6, pp. 681–697, 1968.
Kalman, R. E.,Contributions to the Theory of Optimal Control, Boletin de la Sociedad Matematica Mexicana, Vol. 5, pp. 102–119, 1960.
Anderson, B. D. O., andMoore, J. B.,Linear Optimal Control, Prentice Hall, Englewood Cliffs, New Jersey, 1971.
Author information
Authors and Affiliations
Additional information
Communicated by Y. C. Ho
The research reported herein was supported in part by the US Department of Energy, Electric Energy Division, under Contract No. EC-77-S-03-1493, and in part by the National Science Foundation under Grant No. ECS-8011210.
Rights and permissions
About this article
Cite this article
Ikeda, M., Šiljak, D.D. & White, D.E. Decentralized control with overlapping information sets. J Optim Theory Appl 34, 279–310 (1981). https://doi.org/10.1007/BF00935477
Issue Date:
DOI: https://doi.org/10.1007/BF00935477