Related papers: Optimal control in Bombieri's and Tammi's conjectu…
We deal with the convergence of the value function of an approximate control problem with uncertain dynamics to the value function of a nonlinear optimal control problem. The assumptions on the dynamics and the costs are rather general and…
We consider control systems governed by nonlinear O.D.E.'s that are affine in the time-derivative du/dt of the control u. The latter is allowed to be an integrable, possibly of unbounded variation function, which gives the system an…
We study the convergence problem for mean field control, also known as optimal control of McKean-Vlasov dynamics. We assume that the data is smooth but not convex, and thus the limiting value function $\mathcal{U} :[0,T] \times…
In this work, we will investigate the question of optimal control for bilinear systems with constrained endpoint. The optimal control will be characterized through a set of unconstrained minimization problems that approximate the former.…
Mathematical Selection is a method in which we select a particular choice from a set of such. It have always been an interesting field of study for mathematicians. Combinatorial optimisation is the practice of selecting the best constituent…
We tackle a nonlinear optimal control problem for a stochastic differential equation in Euclidean space and its state-linear counterpart for the Fokker-Planck-Kolmogorov equation in the space of probabilities. Our approach is founded on a…
This paper concerns an optimal control problem $(P)$ related to a nonlinear Fokker-Planck equation. The problem is deeply related to a stochastic optimal control problem $(P_S)$ for a McKean-Vlasov equation. The existence of an optimal…
This paper studies a class of non$-$Markovian singular stochastic control problems, for which we provide a novel probabilistic representation. The solution of such control problem is proved to identify with the solution of a $Z-$constrained…
We consider the optimal control problem of stochastic evolution equations in a Hilbert space under a recursive utility, which is described as the solution of a backward stochastic differential equation (BSDE). A very general maximum…
We consider a linear stochastic differential equation with stochastic drift and multiplicative noise. We study the problem of approximating its solution with the process that solves the equation where the possibly stochastic drift is…
We study a family of optimal control problems in which one aims at minimizing a cost that mixes a quadratic control penalization and the variance of the system, both for finitely many agents and for the mean-field dynamics as their number…
The aim of this paper is to derive a maximum principle for a control problem governed by a stochastic partial differential equation (SPDE) with locally monotone coefficients. In particular, necessary conditions for optimality for this…
In this paper we study a class of combined regular and singular stochastic control problems that can be expressed as constrained BSDEs. In the Markovian case, this reduces to a characterization through a PDE with gradient constraint. But…
Numerically computing global policies to optimal control problems for complex dynamical systems is mostly intractable. In consequence, a number of approximation methods have been developed. However, none of the current methods can quantify…
We study the problem of empirical minimization for variance-type functionals over functional classes. Sharp non-asymptotic bounds for the excess variance are derived under mild conditions. In particular, it is shown that under some…
The purpose of this paper is to review and highlight some connections between the problem of nonlinear smoothing and optimal control of the Liouville equation. The latter has been an active area of recent research interest owing to work in…
This paper develops a unified methodology for probabilistic analysis and optimal control design for jump diffusion processes defined by polynomials. For such systems, the evolution of the moments of the state can be described via a system…
We study the problem of maximizing a non-negative monotone $k$-submodular function $f$ under a knapsack constraint, where a $k$-submodular function is a natural generalization of a submodular function to $k$ dimensions. We present a…
The optimal control of problems that are constrained by partial differential equations with uncertainties and with uncertain controls is addressed. The Lagrangian that defines the problem is postulated in terms of stochastic functions, with…
We study a stochastic optimal control problem for jump-diffusion systems whose drift coefficient is piecewise Lipschitz continuous and exhibits threshold-induced discontinuities. Such dynamics naturally arise in applications with…