Solving optimal feedback control of Chinese population dynamics by viscosity solution approach

in this paper, the optimal birth feedback control of a McKendrick type age-structured population dynamic system based on the Chinese population dynamics is considered. Adopt the dynamic programming approach, to obtain the Hamilton-Jacobi-Bellman equation and prove that the value function is its viscosity solution. By the derived classical verification theorem, the optimal birth feedback control is found explicitly. A finite difference scheme is designed to solving numerically the optimal birth feedback control. Under the same constraint, by comparing with different controls, the validity of the optimality of the obtained control is verified numerically.