
Mathematical Biosciences and Engineering, 2018, 15(5): 11371154. doi: 10.3934/mbe.2018051.
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Optimal control problems with time delays: Two case studies in biomedicine
1. Münster University of Applied Sciences, Department of Mechanical Engineering, Stegerwaldstr. 39, 48565 Steinfurt, Germany
2. University of Münster, Applied Mathematics: Institute of Analysis and Numerics, Einsteinstr. 62, 49143 Münster, Germany
Received: , Accepted: , Published:
There exists an extensive literature on delay differential models in biology and biomedicine, but only a few papers study such models in the framework of optimal control theory. In this paper, we consider optimal control problems with multiple time delays in state and control variables and present two applications in biomedicine. After discussing the necessary optimality conditions for delayed optimal control problems with controlstate constraints, we propose discretization methods by which the delayed optimal control problem is transformed into a largescale nonlinear programming problem. The first case study is concerned with the delay differential model in [
Keywords: Optimal control; time delays; discretization methods; chemoimmunotherapy of cancer; control of Hepatitis B infection
Citation: Laurenz Göllmann, Helmut Maurer. Optimal control problems with time delays: Two case studies in biomedicine. Mathematical Biosciences and Engineering, 2018, 15(5): 11371154. doi: 10.3934/mbe.2018051
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This article has been cited by:
 1. F.A. Rihan, S. Lakshmanan, H. Maurer, Optimal control of tumourimmune model with timedelay and immunochemotherapy, Applied Mathematics and Computation, 2019, 353, 147, 10.1016/j.amc.2019.02.002
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