Solving Optimal Feedback Control of Chinese Population Dynamics by Viscosity Solution Approach
| Authors: | Sun Bing, Academy of Mathematics and System Sciences, Academia Sinica, China
Guo Bao-Zhu, University of the Witwatersrand, South Africa and Academy of Mathematics and System Sciences, Academia Sinica, China |
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| Topic: | 2.4 Optimal Control |
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| Session: | Specific Problems in Optimal Control |
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| Keywords: | Numerical solutions, Finite difference, Optimal control, Feedbackcontrol, Dynamic programming, Distributed-parameter systems, Optimality. |
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Abstract
In this paper, the optimal birth feedback control of a McKendricktype age-structured population dynamic system based on the Chinese populationdynamics is considered. Adopt the dynamic programming approach, to obtainthe Hamilton-Jacobi-Bellman equation and prove that the value function is itsviscosity solution. By the derived classical verification theorem, the optimal birthfeedback control is found explicitly. A finite difference scheme is designed to solvingnumerically the optimal birth feedback control. Under the same constraint, bycomparing with different controls, the validity of the optimality of the obtainedcontrol is verified numerically.
