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An optimal control problem by parabolic equation with boundary smooth control and an integral constraint
Institute of Mathematics, Economics and Computer Science, Irkutsk State University, Irkutsk, Russia |
In the paper, we consider an optimal control problem by differential boundary condition of parabolic equation. We study this problem in the class of smooth controls satisfying certain integral constraints. For the problem under consideration we obtain a necessary optimality condition and propose a method for improving admissible controls. For illustration, we solve one numerical example to show the effectiveness of the proposed method.
References:
| [1] |
A. Arguchintsev, Optimal Control by Hyperbolic Systems, Fizmatlit, Moscow, 2007. |
| [2] |
A. Arguchintsev,
Optimal Control by Initial Boundary Condition of Hyperbolic Systems, Irkutsk State University, Irkutsk, 2003. |
| [3] |
A. Butkovsky,
Theory of Optimal Control by Distributed Systems, Nauka, Moscow, 1965. |
| [4] |
A. Butkovsky,
Methods of Control by Systems with Distributed Parameters, Nauka, Moscow, 1975. |
| [5] |
N. Demidenko,
Modelling and Optimization by Systems with Distributed Parametres, Nauka, Novosibirsk, 2006. |
| [6] |
N. Demidenko,
Control Distributed Systems, Nauka, Novosibirsk, 1999. |
| [7] |
A. Egorov,
Optimal Control by Thermal Processes and Diffusion, Nauka, Moscow, 1978. |
| [8] |
J.-L. Lions,
Optimal Control by Systems Described by Partial Differential ations, Mir, Moscow, 1972. |
| [9] |
J.-L. Lions,
Control by Singular Distributed Systems, Nauka, Moscow, 1987. |
| [10] |
P. Neittaanmaki,
Optimal Control of Nonlinear Parabolic Systems, Marcel Dekker Inc, New York - Basel - Hong Kong, 1994. |
| [11] |
A. Tikhonov,
Equations of Mathematical Physics, Nauka, Moscow, 1977. |
| [12] |
F. Vasiliev,
Methods of Optimization, Factorial Press, Moscow, 2002. |
show all references
References:
| [1] |
A. Arguchintsev, Optimal Control by Hyperbolic Systems, Fizmatlit, Moscow, 2007. |
| [2] |
A. Arguchintsev,
Optimal Control by Initial Boundary Condition of Hyperbolic Systems, Irkutsk State University, Irkutsk, 2003. |
| [3] |
A. Butkovsky,
Theory of Optimal Control by Distributed Systems, Nauka, Moscow, 1965. |
| [4] |
A. Butkovsky,
Methods of Control by Systems with Distributed Parameters, Nauka, Moscow, 1975. |
| [5] |
N. Demidenko,
Modelling and Optimization by Systems with Distributed Parametres, Nauka, Novosibirsk, 2006. |
| [6] |
N. Demidenko,
Control Distributed Systems, Nauka, Novosibirsk, 1999. |
| [7] |
A. Egorov,
Optimal Control by Thermal Processes and Diffusion, Nauka, Moscow, 1978. |
| [8] |
J.-L. Lions,
Optimal Control by Systems Described by Partial Differential ations, Mir, Moscow, 1972. |
| [9] |
J.-L. Lions,
Control by Singular Distributed Systems, Nauka, Moscow, 1987. |
| [10] |
P. Neittaanmaki,
Optimal Control of Nonlinear Parabolic Systems, Marcel Dekker Inc, New York - Basel - Hong Kong, 1994. |
| [11] |
A. Tikhonov,
Equations of Mathematical Physics, Nauka, Moscow, 1977. |
| [12] |
F. Vasiliev,
Methods of Optimization, Factorial Press, Moscow, 2002. |
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