In this article, we derive first-order necessary optimality conditions for a constrained optimal control problem formulated in the Wasserstein space of probability measures. To end, introduce new notion localised metric subdifferential compactly supported measures, and investigate intrinsic linearised Cauchy problems associated to non-local continuity equations. particular, show that when veloc...

We present a recently developed complete version of the Pontryagin maximum principle for a class of infinite-horizon optimal control problems arising in economics. The peculiarity of the result is that the adjoint variable is explicitly specified by a formula which resembles the Cauchy formula for solutions of linear differential systems. In certain situations this formula implies the “standard...

The paper studies discrete/finite-difference approximations of optimal control problems governed by continuous-time dynamical systems with endpoint constraints. Finitedifference systems, considered as parametric control problems with the decreasing step of discretization, occupy an intermediate position between continuous-time and discrete-time (with fixed steps) control processes and play a si...

Abstract. The paper concerns the study of the Pontryagin Maximum Principle for an infinite dimensional and infinite horizon boundary control problem for linear partial differential equations. The optimal control model has already been studied both in finite and infinite horizon with Dynamic Programming methods in a series of papers by the same author et al. [26, 27, 28, 29, 30]. Necessary and s...

An optimal control problem modeling the economic behavior of a representative household is studied. The existence its solution proved, necessary optimality conditions in form Pontryagin–Clarke maximum principle are obtained, and an synthesis constructed. model identified against Russian statistical data. used to analyze consumer crediting Russia influence on economy under COVID-19 pandemic cond...

Abstract A sequentialquadratic Hamiltonian schemefor solving open-loop differential Nash games is proposed and investigated. This method formulated in the framework of Pontryagin maximum principle represents an efficient robust extension successive approximations strategy for optimal control problems. Theoretical results are presented that prove well-posedness scheme, numerical experiments repo...

Analyzing one example of LC circuit in [8], show its Lagrange problem only have other type critical points except for minimum type and maximum type under many circumstances. One novel variational principle is established instead of Pontryagin maximum principle or other extremal principles to be suitable for all types of critical points in nonlinear LC circuits. The generalized Euler-Lagrange eq...