相关论文: The turnpike property for mean-field optimal contr…
Control theory of dynamical systems offers a powerful framework for tackling challenges in deep neural networks and other machine learning architectures. We show that concepts such as simultaneous and ensemble controllability offer new…
In this paper we consider a mean field optimal control problem with an aggregation-diffusion constraint, where agents interact through a potential, in the presence of a Gaussian noise term. Our analysis focuses on a PDE system coupling a…
We prove a general existence result in stochastic optimal control in discrete time where controls take values in conditional metric spaces, and depend on the current state and the information of past decisions through the evolution of a…
Recent results in the literature have provided connections between the so-called turnpike property, near optimality of closed-loop solutions, and strict dissipativity. Motivated by applications in economics, optimal control problems with…
This article is concerned with stochastic control problems for backward doubly stochastic differential equations of mean-field type, where the coefficient functions depend on the joint distribution of the state process and the control…
This paper provides necessary conditions of optimality for optimal control problems with time delays in both state and control variables. Different versions of the necessary conditions cover fixed end-time problems and, under additional…
This paper is devoted to analysing the explicit slow decay rate and turnpike in the infinite-horizon linear quadratic optimal control problems for hyperbolic systems. Assume that some weak observability or controllability are satisfied, by…
The paper addresses an existence problem for infinite horizon optimal control when the system under control is exponentially stabilizable or stable. Classes of nonlinear control systems for which infinite horizon optimal controls exist are…
We study a high-dimensional stochastic optimization problem which features both control and stopping. In particular, a central planner steers a large population of particles, and can also remove particles at any time by paying a penalty. In…
We derive a framework to compute optimal controls for problems with states in the space of probability measures. Since many optimal control problems constrained by a system of ordinary differential equations (ODE) modelling interacting…
We study Mean Field stochastic control problems where the cost function and the state dynamics depend upon the joint distribution of the controlled state and the control process. We prove suitable versions of the Pontryagin stochastic…
We establish existence of nearly-optimal controls, conditions for existence of an optimal control and a saddle-point for respectively a control problem and zero-sum differential game associated with payoff functionals of mean-field type,…
Considering a general nonlinear dissipative finite dimensional optimal control problem in fixed time horizon T , we establish a two-term asymptotic expansion of the value function as $T\rightarrow+\infty$. The dominating term is T times the…
We derive a Maximum Principle for optimal control problems with constraints given by the coupling of a system of ODEs and a PDE of Vlasov-type. Such problems arise naturally as ${\Gamma}$-limits of optimal control problems subject to ODE…
We consider a vibrating string that is fixed at one end with Neumann control action at the other end. We investigate the optimal control problem of steering this system from given initial data to rest, in time T , by minimizing an objective…
In this article, we establish exponential turnpike theorems for a class of nonlinear deterministic meanfield optimal control problems. We carry out our analysis simultaneously in the so-called Lagrangian and Eulerian frameworks. In the…
We consider the problem of minimizing the entropy, energy, or exergy production for state transitions of irreversible port-Hamiltonian systems subject to control constraints. Via a dissipativity-based analysis we show that optimal solutions…
We study the problem of mean-field control when the state dynamics are given by general systems of forward-backward stochastic differential equations (FBSDEs) with heterogeneous mean-field interactions. Firstly, we introduce a novel…
We study optimal control for mean-field forward backward stochastic differential equations with payoff functionals of mean-field type. Sufficient and necessary optimality conditions in terms of a stochastic maximum principle are derived. As…
In this article, we propose a new unifying framework for the investigation of multi-agent control problems in the mean-field setting. Our approach is based on a new definition of differential inclusions for continuity equations formulated…