Abstract
This chapter is concerned with optimal control problems of dynamical systems described by partial differential equations (PDEs). Firstly, using the Dubovitskii-Milyutin approach, we obtain the necessary condition of optimality, i.e., the Pontryagin maximum principle for optimal control problem of an age-structured population dynamics for spread of universally fatal diseases. Secondly, for an optimal birth control problem of a McKendrick type age-structured population dynamics, we establish the optimal feedback control laws by the dynamic programming viscosity solution (DPVS) approach. Finally, for a well-adapted upwind finite-difference numerical scheme for the HJB equation arising in optimal control, we prove its convergence and show that the solution from this finite-difference scheme converges to the value function of the associated optimal control problem.
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