Abstract
The main objective of this paper is to consider linear constant systems composed of interconnected subsystems, and explore possibilities for locally optimal control strategies to become a globally optimal control law for the overall system. Modifications of performance indices and decentralized control laws are considered which result in centrally optimal systems having robust stability properties. A class of interconnected systems is specified in terms of the interconnection structure, which can always be optimized by decentralized feedback.
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References
R. E. Kalman, "When is a linear control system optimal?", Transactions of the ASME, 86, 1964, pp. 51–60.
Ü. Özgüner, "Local optimization in large scale composite dynamic systems", Proceedings of the 9th Asilomar Conference on Circuits, Systems, and Computers, Pacific Grove, California, 1975, pp. 87–91.
D. D. Šiljak, "Reliable control using multiple control systems", International Journal of Control, 31, 1980, pp. 303–329.
K. Yasuda, T. Hikata, and K. Hirai, "On decentrally optimizable interconnected systems", Proceedings of the 19th IEEE Conference on Decision and Control, Albuquerque, New Mexico, 1980, pp. 536–537.
M. E. Sezer and D. D. Šiljak, "Robustness of suboptimal control: Gain and phase margin", IEEE Transactions, AC-26, 1981, pp. 907–911.
M. Ikeda and D. D. Šiljak, "On decentrally stabilizable large-scale systems", Automatica, 16, 1980, pp. 331–334.
M. E. Sezer and D. D. Šiljak, "On decentralized stabilization and structure of linear large scale systems", Automatica, 17, 1981, pp. 641–644.
D. D. Šiljak, Large-Scale Dynamic Systems: Stability and Structure, North-Holland, New York, 1978.
R. E. Kalman, "Contributions to the theory of optimal control", Boletin de la Sociedad Matematica Mexicana, 5, 1960, pp. 102–119.
R. Krtolica and D. D. Šiljak, "Suboptimality of decentralized stochastic control and estimation", IEEE Transactions. AC-25, 1980, pp. 76–83.
M. Ikeda, D. D. Šiljak, and D. E. White, "Decentralized control with overlapping information sets", Journal of Optimization Theory and Applications, 34, 1981, pp. 279–310.
M. E. Sezer and D. D. Šiljak, "Sensitivity of large-scale systems", Journal of the Franklin Institute, 312, 1981, pp. 179–197.
V. Kučera, "A contribution to matrix quadratic equations", IEEE Transactions, AC-17, 1972, pp. 344–347.
W. M. Wonham, "On a matrix Riccati equation of stochastic control", SIAM Journal on Control, 6, 1968, pp. 681–697.
M. Araki, "Stability of large-scale nonlinear systems: Quadratic-order theory of composite systems method using M-matrices", IEEE Transactions, AC-23, 1978, 129–142.
V. Lakshmikantham and S. Leela, Differential and Integral Inequalities, Vols. I and II, Academic Press, New York, 1969.
L. Tartar, "A new characterization of M-matrices" (in French), Revue Française d'Automatique, Informatique et Recherche Opérationelle, 5, 1971, pp. 127–128.
M. Araki and B. Kondo, "Stability and transient behavior of composite nonlinear systems", IEEE Transactions, AC-17, 1972, pp. 537–541.
M. Ikeda, D. D. Šiljak, and K. Yasuda, "Optimality of decentralized control for large-scale systems", Automatica, (to appear).
M. Ikeda and D. D. Šiljak, "On optimality of decentralized control with overlapping information sets", Proceedings of the NCKU/AAS Symposium on Engineering Science and Mechanics, Tainan, Taiwan, 1981, pp. 51–65.
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© 1982 Springer-Verlag
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Ikeda, M., Šiljak, D.D. (1982). When is a linear decentralized control optimal?. In: Bensoussan, A., Lions, J.L. (eds) Analysis and Optimization of Systems. Lecture Notes in Control and Information Sciences, vol 44. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0044406
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DOI: https://doi.org/10.1007/BFb0044406
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