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Optimal Control Problem for Systems Modelled by Diffusion-Wave Equation
Postnov, S. S.
Vladikavkaz Mathematical Journal 2022. Vol. 24. Issue 3.
This paper deals with an optimal control problem for a model system defined by a one-dimensional non-homogeneous diffusion-wave equation with a time derivative of fractional-order. 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 time-optimal control at given restriction on control norm. The study is based on the use of an exact solution of the diffusion-wave equation, with the help of which the optimal control problem is reduced to an infinite-dimensional \(l\)-moment problem. We also consider a finite-dimensional \(l\)-moment problem obtained in a similar way using an approximate solution of the diffusion-wave equation. Correctness and solvability are analyzed for this problem. Finally, an example of boundary control calculation using a finite-dimensional \(l\)-moment problem is considered.
Keywords: optimal control, Caputo derivative, diffusion-wave equation, \(l\)-problem of moments
Language: Russian Download the full text
For citation: Postnov, S. S. Optimal Control Problem for Systems Modelled by Diffusion-Wave Equation, Vladikavkaz Math. J., 2022, vol. 24, no. 3, pp. 108-119 (in Russian). DOI 10.46698/s3949-8806-8270-n
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