Abstract:
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.
Key words:optimal control, Caputo derivative, diffusion-wave equation, $l$-problem of moments.
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