Optimal Control over Moving Sources in the Heat Equation
- 41 Downloads
We study the problem of optimal control over the processes described by the heat equation and a system of ordinary differential equations. For the problem of optimal control, we prove the existence and uniqueness of solutions, establish sufficient conditions for the Fréchet differentiability of the purpose functional, deduce the expression for its gradient, and obtain necessary conditions of optimality in the form of an integral maximum principle.
KeywordsHeat Equation Admissible Control Reflexive Banach Space Pontryagin Function Unique Generalize Solution
Unable to display preview. Download preview PDF.
- 1.A. G. Butkovskii, Methods of Control over Systems with Distributed Parameters [in Russian], Nauka, Moscow (1965).Google Scholar
- 2.A. G. Butkovskii and L. M. Pustyl’nikov, Theory of Moving Control over Systems with Distributed Parameters [in Russian], Nauka, Moscow (1980).Google Scholar
- 4.S. I. Lyashko, Generalized Control over Linear Systems [in Russian], Naukova Dumka, Kiev (1998).Google Scholar
- 10.R. A. Teimurov, “On the problem of optimal control over moving sources for heat equations,” Izv. Vyssh. Uchebn. Zaved., Severo-Kavkaz. Region, Ser. Estestven. Nauk., No. 4, 17–20 (2012).Google Scholar
- 11.R. A. Teimurov, “On the control problem by moving sources for systems with distributed parameters,” Vestn. Tomsk. Gos. Univ., Ser. Mat. Mekh., No. 1(21), 24–33 (2013).Google Scholar
- 12.F. P. Vasil’ev, Methods for the Solution of Extremal Problems [in Russian], Nauka, Moscow (1981).Google Scholar
- 13.O. A. Ladyzhenskaya, V. A. Solonnikov, and N. N. Ural’tseva, Linear and Quasilinear Equations of Parabolic Type [in Russian], Nauka, Moscow (1976).Google Scholar
- 14.J.-L. Lions and E. Magenes, Problèmes aux Limites non Homogènes et Applications [Russian translation], Mir, Moscow (1971).Google Scholar
- 15.A. N. Tikhonov and V. Ya. Arsenin, Methods for the Solution of Ill-Posed Problems [in Russian], Nauka, Moscow (1974).Google Scholar
- 16.O. A. Ladyzhenskaya, Boundary-Value Problems of Mathematical Physics [in Russian], Nauka, Moscow (1973).Google Scholar
- 17.V. P. Mikhailov, Partial Differential Equations [in Russian], Nauka, Moscow (1983).Google Scholar