Fields of extremals and sensitivity analysis for multi-input bilinear optimal control problems

Heinz Schättler; Urszula Ledzewicz

doi:10.3934/dcds.2015.35.4611

Article Contents

2015, Volume 35, Issue 9: 4611-4638. Doi: 10.3934/dcds.2015.35.4611

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Fields of extremals and sensitivity analysis for multi-input bilinear optimal control problems

Heinz Schättler^1, and
Urszula Ledzewicz^2,

1.
Dept. of Electrical and Systems Engineering, Washington University, St. Louis, Missouri, 63130-4899
2.
Dept. of Mathematics and Statistics, Southern Illinois University Edwardsville, Edwardsville, Illinois, 62026-1653

Received: May 2014

Revised: October 2014

Published: May 2017

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Abstract

Optimal control problems with fixed terminal time are considered for multi-input bilinear systems with the control set given by a compact interval and the objective function affine in the controls. Systems of this type have been widely used in the modeling of cell-cycle specific cancer chemotherapy over a prescribed therapy horizon for both homogeneous and heterogeneous tumor populations. Necessary conditions for optimality lead to concatenations of bang and singular controls as prime candidates for optimality. In this paper, the method of characteristics will be formulated as a general procedure to embed such a controlled reference extremal into a field of broken extremals. Sufficient conditions for the strong local optimality of a controlled reference bang-bang trajectory will be formulated in terms of solutions to associated sensitivity equations. These results will be applied to a model for cell cycle specific cancer chemotherapy with cytotoxic and cytostatic agents.

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Mathematics Subject Classification: Primary: 49K15; Secondary: 92C50, 93C95.

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References

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