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DOI: 10.46698/s394988068270n Optimal Control Problem for Systems Modelled by DiffusionWave Equation
Postnov, S. S.
Vladikavkaz Mathematical Journal 2022. Vol. 24. Issue 3.
Abstract:
This paper deals with an optimal control problem for a model system defined by a onedimensional nonhomogeneous diffusionwave equation with a time derivative of fractionalorder. In general case we consider both of boundary and distributed controls which are \(p\)integrable functions (including \(p=\infty\)). In this case two types of optimal control problem are posed and analyzed: the problem of control norm minimization at given control time and the problem of timeoptimal control at given restriction on control norm. The study is based on the use of an exact solution of the diffusionwave equation, with the help of which the optimal control problem is reduced to an infinitedimensional \(l\)moment problem. We also consider a finitedimensional \(l\)moment problem obtained in a similar way using an approximate solution of the diffusionwave equation. Correctness and solvability are analyzed for this problem. Finally, an example of boundary control calculation using a finitedimensional \(l\)moment problem is considered.
Keywords: optimal control, Caputo derivative, diffusionwave equation, \(l\)problem of moments
Language: Russian
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For citation: Postnov, S. S. Optimal Control Problem for Systems Modelled by DiffusionWave Equation,
Vladikavkaz Math. J., 2022, vol. 24, no. 3, pp. 108119 (in Russian).
DOI 10.46698/s394988068270n ← Contents of issue 
 

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