Abstract
The problem of controlling a linear dynamic plant in real time given its nondeterministic model and imperfect measurements of the inputs and outputs is considered. The concepts of current distributions of the initial state and disturbance parameters are introduced. The method for the implementation of disclosable loop using the separation principle is described. The optimal control problem under uncertainty conditions is reduced to the problems of optimal observation, optimal identification, and optimal control of the deterministic system. To extend the domain where a solution to the optimal control problem under uncertainty exists, a two-stage optimal control method is proposed. Results are illustrated using a dynamic plant of the fourth order.
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References
Control and Dynamic Systems: Advances in Theory and Applications, Ed. by C. T. Leondes (Academic, New York, 1973; Mir, Moscow, 1980).
R. Gabasov, F. M. Kirillova, and A. I. Tyatyushkin, Constructive Optimization Techniques, Vol. 1: Control Problems (Universitetskoe, Minsk, 1984) [in Russian].
R. Gabasov, F. M. Kirillova, and N. S. Pavlenok, “Optimal control of a dynamic system using perfect measurements of its states,” Dokl. Math. 86, 436–440 (2012).
R. Gabasov, F. M. Kirillova, and Vo Thi Thanh Ha, “Optimal real-time control of multidimensional dynamic plant,” Autom. Remote Control 76, 98–110 (2015).
R. Gabasov, F. M. Kirillova, and Vo Thi Thanh Ha, “Observation of linear systems using the disclosable loop principle,” Problemy Fiz. Mat. Tekhn., No. 4(21), 60–69 (2014).
L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko, The Mathematical Theory of Optimal Processes (Nauka, Moscow, 1976; Gordon and Breach, New York, 1986).
R. Bellman, Dynamic Programming (Princeton Univ. Press, Princeton, 1957; Inostrannaya Literatura, Moscow, 1960).
R. Gabasov, N. M. Dmitruk, and F. M. Kirillova, “Optimal Control of Multidimensuional Systems by Inaccurate Measurements of Their Outputs,” Tr. Inst. Matematiki i mekhaniki Ural’skoe Otd. Ross. Akad. Nauk (Yekaterinburg, 2004), Vol. 10, No. 2, pp. 35–37 [in Russian].
R. Gabasov, F. M. Kirillova, and A. I. Tyatyushkin, Constructive Optimization Techniques, Vol. 1: Linear Problems (Universitetskoe, Minsk, 1984) [in Russian].
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Original Russian Text © R. Gabasov, F.M. Kirillova, Vo Thi Thanh Ha, 2016, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2016, Vol. 56, No. 3, pp. 394–408.
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Gabasov, R., Kirillova, F.M. & Ha, V.T.T. Application of linear programming techniques for controlling linear dynamic plants in real time. Comput. Math. and Math. Phys. 56, 382–395 (2016). https://doi.org/10.1134/S0965542516030064
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DOI: https://doi.org/10.1134/S0965542516030064