Abstract
In this paper, a locally computed suboptimal control strategy for a class of interconnected systems is introduced. First, optimal statefeedback control equations are derived for a finite-horizon quadratic cost. Then, the control for each subsystem is separated into two portions. The first portion stabilizes the isolated subsystem, and the second portion corresponds to the interactions. To achieve a locally calculable control, an approximation to the optimal control equations is introduced, and two iterative suboptimal control algorithms are developed. In the first algorithm, the initial conditions of subsystems are assumed to be known; in the second algorithm, this information is replaced by statistical distributions. The orders of errors in the iterations of the algorithm and in the suboptimality are given in terms of interconnections. An example with comparisons is also included to show the performance of the approach.
Similar content being viewed by others
References
Jamshidi, M.,Large-Scale Systems, North-Holland, Amsterdam, Holland, 1983.
Šiljak, D. D.,Large-Scale Dynamic Systems, Stability and Structure, North-Holland, Amsterdam, Holland, 1978.
Khalil, H. K., andKokotovic, P. V.,Control Strategies for Decision Makers Using Different Models of the Same System, IEEE Transactions on Automatic Control, Vol. AC-23, pp. 289–297, 1978.
Özgüner, Ü.,Near-Optimal Control of Composite Systems: The Multi-Time-Scale Approach, IEEE Transactions on Automatic Control, Vol. AC-24, pp. 652–655, 1979.
Davison, E. J., andÖzgüner, Ü.,The Expending System Problem, Systems and Control Letters, Vol. 1, pp. 255–260, 1982.
Ikeda, M., Šiljak, D. D., andWhite, D. E.,Decentralized Control with Overlapping Information Sets, Journal of Optimization Theory and Applications, Vol. 34, pp. 279–310, 1981.
İftar, A., andÖzgüner, Ü.,A New Inclusion Concept and Optimal Control for Systems with Overlapping Information Sets, Proceedings of the 25th Annual Allerton Conference on Communications, Control, and Computing, Allerton House, Monticello, Illinois, pp. 1152–1161, 1987.
Bailey, F. N., andRamapriyan, H. K.,Bounds on Suboptimality in the Control of Linear Dynamic Systems, IEEE Transactions on Automatic Control, Vol. AC-18, pp. 532–534, 1973.
Özgüner, Ü., andPerkins, W. R.,Graph Theory in the Analysis of Large-Scale Composite Systems, Proceedings of the International Symposium on Circuits and Systems, pp. 121–123, 1975.
Ikeda, M., Šiljak, D. D., andYasuda, K.,Optimality of Decentralized Control for Large-Scale Systems, Automatica, Vol. 19, pp. 309–316, 1983.
Chong, C., andAthans, M.,On the Periodic Coordination of Linear Stochastic Systems, Automatica, Vol. 12, pp. 321–335, 1976.
Acar, L., andÖzgüner, Ü.,Distributed Computations of Optimal Control Strategies for a Class of Interconnected Systems, Proceedings of the 25th Annual Allerton Conference on Communications, Control, and Computing, Allerton House, Monticello, Illinois, pp. 1162–1171, 1987.
Friedlander, B.,Decentralized Design of Decentralized Controllers, Control and Dynamic Systems, Edited by C. T. Leondes, Academic Press, New York, New York, Vol. 22, pp. 165–194, 1985.
Al-Abbass, F., andÖzgüner, Ü.,Decentralized Model Reference Adaptive System Using a Variable Structure Control, Proceedings of the 24th Conference on Decision and Control, Fort Lauderdale, Florida, pp. 1473–1478, 1985.
Ioannou, P. A.,Decentralized Adaptive Control of Interconnected Systems, IEEE Transactions on Automatic Control, Vol. AC-31, pp. 291–298, 1986.
Morgan, R. G., andÖzgüner, Ü.,A Decentralized Variable Structure Control Algorithm for Robotic Manipulators, IEEE Journal of Robotics and Automation, Vol. RA-1, pp. 57–65, 1985.
Toivonen, H. T., andMakila, P. M.,A Descent Anderson-Moore Algorithm for the Optimal Decentralized Control, Automatica, Vol. 21, pp. 743–744, 1985.
Lasserre, J. B.,Detecting Planning Horizons in Deterministic Infinite-Horizon Optimal Control, IEEE Transactions on Automatic Control, Vol. AC-31, pp. 70–72, 1986.
Yanchevsky, A. E., andHirkonen, V. J.,Optimization of Feedback Systems with Constrained Information Flow, International Journal on Systems Sciences, Vol. 12, pp. 1459–1468, 1981.
Geromel, J. C., andBernussou, J.,Optimal Decentralized Control of Dynamic Systems, Automatica, Vol. 18, pp. 545–557, 1982.
Bellman, R.,Dynamic Programming, Princeton University Press, Princeton, New Jersey, 1957.
Boudarel, R., Delmas, J., andGuichet, P.,Dynamic Programming and Its Application to Optimal Control, Academic Press, New York, New York, 1971.
Chen, G., andMills, Jr., W. H.,Finite Elements and Terminal Penalization for Quadratic Cost Optimal Control Problems Governed by Ordinary Differential Equations, SIAM Journal on Control and Optimization, Vol. 19, pp. 744–764, 1981.
Hodžić, M., andŠiljak, D. D.,Iterative Methods for Parallel-Multirate Estimation, Preprints of the 4th IFAC/IFORS Symposium on Large-Scale Systems: Theory and Applications, Zürich, Switzerland, pp. 169–175, 1986.
Acar, L.,Local Control Strategies for a Class of Interconnected and Knowledge-Rich Hierarchical Systems, Ohio State University, PhD Thesis, 1988.
Author information
Authors and Affiliations
Additional information
Communicated by M. Simaan
Rights and permissions
About this article
Cite this article
Acar, L., Özgüner, Ü. A locally computed suboptimal control strategy for a class of interconnected systems. J Optim Theory Appl 62, 189–210 (1989). https://doi.org/10.1007/BF00941053
Issue Date:
DOI: https://doi.org/10.1007/BF00941053