@inbook{e168bf836a4d42f285369a935f5cb194,
title = "Dynamic programming viscosity solution approach and its applications to optimal control problems",
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.",
keywords = "Convergence, Dynamic programming approach, Numerical solution, Optimal feedback control, Viscosity solution",
author = "Bing Sun and Tao, {Zhen Zhen} and Wang, {Yang Yang}",
note = "Publisher Copyright: {\textcopyright} 2019, Springer Nature Switzerland AG.",
year = "2019",
doi = "10.1007/978-3-030-12232-4_12",
language = "English",
series = "Studies in Systems, Decision and Control",
publisher = "Springer International Publishing",
pages = "363--420",
booktitle = "Studies in Systems, Decision and Control",
address = "Switzerland",
}