Related papers: Mean field first order optimality condition under …
We address Newton-type problems of minimal resistance from an optimal control perspective. It is proven that for Newton-type problems the Pontryagin maximum principle is a necessary and sufficient condition. Solutions are then computed for…
We study the convergence problem of mean-field control theory in the presence of state constraints and non-degenerate idiosyncratic noise. Our main result is the convergence of the value functions associated to stochastic control problems…
In this paper we are interested in a new type of {\it mean-field}, non-Markovian stochastic control problems with partial observations. More precisely, we assume that the coefficients of the controlled dynamics depend not only on the paths…
We consider mean-field control problems in discrete time with discounted reward, infinite time horizon and compact state and action space. The existence of optimal policies is shown and the limiting mean-field problem is derived when the…
We derive a first order optimality condition for a class of agent-based systems, as well as for their mean-field counterpart. A relevant difficulty of our analysis is that the state equation is formulated on possibly infinite-dimensional…
We establish a geometric Pontryagin maximum principle for discrete time optimal control problems on finite dimensional smooth manifolds under the following three types of constraints: a) constraints on the states pointwise in time, b)…
We study the time-optimal robust control of a two-level quantum system subjected to field inhomogeneities. We apply the Pontryagin Maximum Principle and we introduce a reduced space onto which the optimal dynamics is projected down. This…
In this paper we consider mean-field optimal control problems with selective action of the control, where the constraint is a continuity equation involving a non-local term and diffusion. First order optimality conditions are formally…
This paper considers a mean field game model inspired by crowd motion where agents want to leave a given bounded domain through a part of its boundary in minimal time. Each agent is free to move in any direction, but their maximal speed is…
In this article, by using several new crucial {\it a priori} estimates which are still absent in the literature, we provide a comprehensive resolution of the first order generic mean field type control problems and also establish the…
The paper presents new sufficient conditions for the property of strong bi-metric regularity of the optimality map associated with an optimal control problem which is affine with respect to the control variable ({\em affine problem}). The…
In this paper, we investigate a mean-field singular stochastic optimal control problem for systems governed by mean-field regime-switching singular stochastic differential equations. The state process is assumed to depend on both a regular…
We study a constrained optimal control problem for an ensemble of control systems. Each sub-system (or plant) evolves on a matrix Lie group, and must satisfy given state and control action constraints pointwise in time. In addition, certain…
We present a Pontryagin maximum principle for discrete time optimal control problems with (a) pointwise constraints on the control actions and the states, (b) frequency constraints on the control and the state trajectories, and (c)…
The Pontryagin's Maximum Principle allows, in most cases, the design of optimal controls of affine nonlinear control systems by considering the sign of a smooth function. There are cases, although, where this function vanishes on a whole…
This paper focuses on the role of a government of a large population of interacting agents as a mean field optimal control problem derived from deterministic finite agent dynamics. The control problems are constrained by a PDE of…
In this work, we systematically investigate mean field games and mean field type control problems with multiple populations using a coupled system of forward-backward stochastic differential equations of McKean-Vlasov type stemming from…
We study the turnpike phenomenon for optimal control problems with mean field dynamics that are obtained as the limit $N\rightarrow \infty$ of systems governed by a large number $N$ of ordinary differential equations. We show that the…
Limited bandwidth and limited saturation in actuators are practical concerns in control systems. Mathematically, these limitations manifest as constraints being imposed on the control actions, their rates of change, and more generally, the…
Fractional optimal control problems via a wide class of fractional operators with a general analytic kernel are introduced. Necessary optimality conditions of Pontryagin type for the considered problem are obtained after proving a Gronwall…