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Optimal control over a system with distributed parameters. (Russian) Zbl 0648.49005

The paper discusses an optimal control problem for a linear (with respect to the state and the control) parabolic system with one spatial variable and quadratic cost functional. The author proposes analytical formulas for optimal control by means of an expansion in Fourier series. Convergence of the series is not investigated. This causes some inaccuracies in the paper, e.g., the proposition on the existence of an optimal control in the case where the cost functional does not depend on the control is not correct.
Reviewer: U.Raitums

MSC:

49J20 Existence theories for optimal control problems involving partial differential equations
42A16 Fourier coefficients, Fourier series of functions with special properties, special Fourier series
93C20 Control/observation systems governed by partial differential equations
35B37 PDE in connection with control problems (MSC2000)
35K40 Second-order parabolic systems
93C05 Linear systems in control theory
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