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We study the asymptotic behavior of solutions to linear-quadratic mean field stochastic optimal control problems. By formulating an ergodic control framework, we characterize the convergence between the finite time horizon control problem…
In this work we derive an interval turnpike result for adjoints of finite- and infinite-dimensional nonlinear optimal control problems under the assumption of an interval turnpike on states and controls. We consider stabilizable dynamics…
This article is concerned with the asymptotic behavior of the two-dimensional inviscid Boussinesq equations with a damping term in the velocity equation. Precisely, we provide the time-decay rates of the smooth solutions to that system. The…
This survey reviews portfolio selection problem for long-term horizon. We consider two objectives: (i) maximize the probability for outperforming a target growth rate of wealth process (ii) minimize the probability of falling below a target…
We consider an optimal control problem for an abstract nonlinear dissipative evolution equation. The differential constraint is penalized by augmenting the target functional by a nonnegative global-in-time functional which is null-minimized…
We derive an explicit expression for the leading term in the late-time, large-distance asymptotic expansion of a transverse dynamical two-point function of the XX chain in the spacelike regime. This expression is valid for all non-zero…
We consider a class of exit--time control problems for nonlinear systems with a nonnegative vanishing Lagrangian. In general, the associated PDE may have multiple solutions, and known regularity and stability properties do not hold. In this…
We consider the control problem with \textit{exit time}. Unlike the Bolza and Mayer problems, in this problem the terminal time of the trajectories is not fixed, but it is the first time at which they reach a given closed subset -…
We consider averages convergence as the time-horizon goes to infinity of optimal solutions of time-dependent optimal control problems to optimal solutions of the corresponding stationary optimal control problems. Control problems play a key…
We aim at characterizing the asymptotic behavior of value functions in the control of piece-wise deterministic Markov processes (PDMP) of switch type under nonexpansive assumptions. For a particular class of processes inspired by temperate…
We consider a nonlinear control system with vector-valued measures as controls and with dynamics depending on time delayed states. First, we introduce a notion of discontinuous, bounded variation solution associated with this system and…
The paper proposes first steps towards the formalization and characterization of time-varying turnpikes in optimal control of mechanical systems. We propose the concepts of velocity steady states, which can be considered as partial steady…
In this article, we study the classical finite-horizon optimal stopping problem for multidimensional diffusions through an approach that differs from what is typically found in the literature. More specifically, we first prove a key…
We establish a polynomial turnpike estimate for an optimal control problem consisting of a system of infinitely many controlled oscillators, considered as an abstract differential equation in a Hilbert space, with a quadratic cost. Our…
An optimal control problem related to the probability of transition between stable states for a thermally driven Ginzburg-Landau equation is considered. The value function for the optimal control problem with a spatial discretization is…
We consider irreversible and coupled reversible-irreversible nonlinear port-Hamiltonian systems and the respective sets of thermodynamic equilibria. In particular, we are concerned with optimal state transitions and output stabilization on…
In this paper, we develop several necessary conditions of turnpike property for generalizaid linear-quadratic (LQ) optimal control problem in infinite dimensional setting. The term 'generalized' here means that both quadratic and linear…
In this manuscript, we study the turnpike property in stochastic discrete-time optimal control problems for interacting agents. Extending previous deterministic results, we show that the turnpike effect persists in the presence of noise…
In this paper, we introduce turnpike arguments in the context of optimal state estimation. In particular, we show that the optimal solution of the state estimation problem involving all available past data serves as turnpike for the…
This paper deals with the long time behavior of the optimal solution of stochastic backward linear-quadratic optimal control problem over the finite time horizon. Both weak and strong turnpike properties are established under appropriate…