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arXiv · 1811.07421

Periodic switching strategies for an isoperimetric control problem with application to nonlinear chemical reactions

P. Benner·A. Seidel-Morgenstern·A. Zuyev
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Abstract

This paper deals with an isoperimetric optimal control problem for nonlinear control-affine systems with periodic boundary conditions. As it was shown previously, the candidates for optimal controls for this problem can be obtained within the class of bang-bang input functions. We consider a parametrization of these inputs in terms of switching times. The control-affine system under consideration is transformed into a driftless system by assuming that the controls possess properties of a partition of unity. Then the problem of constructing periodic trajectories is studied analytically by applying the Fliess series expansion over a small time horizon. We propose analytical results concerning the relation between the boundary conditions and switching parameters for an arbitrary number of switchings. These analytical results are applied to a mathematical model of non-isothermal chemical reactions. It is shown that the proposed control strategies can be exploited to improve the reaction performance in comparison to the steady-state operation mode.

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P. Benner, A. Seidel-Morgenstern, A. Zuyev. 2018-11-18. Periodic switching strategies for an isoperimetric control problem with application to nonlinear chemical reactions. https://doi.org/10.1016/j.apm.2018.12.005

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