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Singular perturbations in optimal control problems

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Abstract

One presents a survey of the works on the theory of optimal control by deterministic objects, described by systems of ordinary differential or difference equations, where the investigation is carried out with the aid of the methods of the theory of singular perturbations. One analyzes the possibility of the application of the theory of singular perturbations to the investigation of control problems with large amplification coefficient in the feedback circuit, to the description of sliding regimes in systems with variable structure, and to the construction of effective numerical algorithms for the solution of optimization problems.

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Translated from Itogi Nauki i Tekhniki, Seriya Matematicheskii Analiz, Vol. 20, pp. 3–77, 1982.

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Vasil'eva, A.B., Dmitriev, M.G. Singular perturbations in optimal control problems. J Math Sci 34, 1579–1629 (1986). https://doi.org/10.1007/BF01262406

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