Hamilton – Jacobi – Bellman equations in optimal control problems for systems with fractional-order derivatives

In this talk, optimal control problems in which a motion of a dynamical system is described by differential equations with Caputo fractional derivatives will be considered. Results on the study of characteristic (nonlocal and infinitesimal) properties of the functional of optimal result of control (the value functional) and the development of methods for constructing optimal feedback control strategies will be presented. The focus will be on issues related to the application of the dynamic programming principle to the problems under consideration, the formalism of the corresponding Hamilton – Jacobi – Bellman equations, and the development of the theory of generalized (minimax, viscosity) solutions of such equations.