Abstract
In the paper a nonlinear boundary optimal control problem is investigated for thermal process described by Volterra integro-differential equation. Sufficient conditions are established for unique solvability of a nonlinear optimization problem. An algorithm is developed for constructing a complete solution of the nonlinear optimization problem.
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V. Volterra, Functional Theory, Integral and Integro-Differential Equations (in Russian). (Nauka, Moscow, 1984)
V.S. Vladimirov, Mathematical problems of the uniform-speed particle transport theory of transport (in Russian). Proc. Steklov Inst. Math. 61, 3–158 (1961)
A.I. Egorov, Optimal Control of Thermal and Diffusion Processes (in Russian). (Nauka, Moscow, 1978)
E.W. Sachs, A.K. Strauss, Efficient solution of a partial integro-differential equation in finance. Appl. Numer. Math. 58, 1687–1703 (2008)
A. Kowalewski, Optimal control of an infinite order hyperbolic system with multiple time-varying lags. Automatyka 15, 53–65 (2011)
J. Thorwe, S. Bhalekar, Solving partial integro-differential equations using Laplace transform method. Am. J. Comput. Appl. Math. 2(3), 101–104 (2012)
A.Z. Khurshudyan, On optimal boundary and distributed control of partial integro-differential equations. Arch. Contol. Sci. 24(60), 525–526 (2014)
M.V. Krasnov, Integral Equations (in Russian). (Nauka, Moscow, 1975)
A. Kerimbekov, Nonlinear Optimal Control of the Linear Systems with Distributed Parameters. Texts and Monographs in Physical and Mathematical Sciences (in Russian). (Ilim, Bishkek, 2003)
A. Kerimbekov, E. Abdyldaeva, On the solvability of a nonlinear tracking problem under boundary control for the elastic oscillations described by Fredholm integro-differential equations, in 27th IFIP TC 7 Conference, CSMO 2015, Sophia Antipolis, France, June 29–July 3, 2015 Revised Selected Papers. System Modeling and Optimization (2017), pp. 312–321
A. Kerimbekov, E. Abdyldaeva, U. Duyshenalieva, Generalized solution of a boundary value problem under point exposure of external forces. J. Pure Appl. Math. 113(4), 609–623 (2017)
A. Kerimbekov, E. Abdyldaeva, U. Duyshenalieva, E. Seidakmat Kyzy, On solvability of optimization problem for elastic oscillations with multipoint sources of control. J. AIP Conf. Proc. 1880, 060009 (2017). https://doi.org/10.1063/1.5000663
L.A. Lusternik, V.I. Sobolev, Elements of Functional Analysis (in Russian). (Nauka, Moscow, 1965)
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Kyzy, E.S., Kerimbekov, A. (2019). On Solvability of Tracking Problem Under Nonlinear Boundary Control. In: Lindahl, K., Lindström, T., Rodino, L., Toft, J., Wahlberg, P. (eds) Analysis, Probability, Applications, and Computation. Trends in Mathematics(). Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-04459-6_20
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DOI: https://doi.org/10.1007/978-3-030-04459-6_20
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