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We establish the existence of martingale solutions to a class of stochastic conservation equations. The underlying models correspond to random perturbations of kinetic models for collective motion such as the Cucker-Smale and Motsch-Tadmor…
It is a longstanding unsolved problem to characterize the optimal feedback controls for general linear quadratic optimal control problem of stochastic evolution equation with random coefficients. A solution to this problem is given in [21]…
In this paper, we study the following nonlinear backward stochastic integral partial differential equation with jumps \begin{equation*} \left\{ \begin{split} -d V(t,x) =&\displaystyle\inf_{u\in U}\bigg\{H(t,x,u, DV(t,x),D \Phi(t,x), D^2…
We consider a Bayesian adaptive optimal stochastic control problem where a hidden static signal has a non-separable influence on the drift of a noisy observation. Being allowed to control the specific form of this dependence, we aim at…
This article investigates the exact controllability of three-dimensional stochastic Maxwell equations, a coupled system comprising two stochastic partial differential equations. The research establishes the observability inequality for the…
We here consider optimal control problems governed by nonlinear stochastic equations on a Hilbert space H with nonconvex payoff, which is rewritten as a deterministic optimal control problem governed by a Kolmogorov equation in H. We prove…
This paper considers the problem of partially observed optimal control for forward stochastic systems which are driven by Brownian motions and an independent Poisson random measure with a feature that the cost functional is of mean-field…
This paper investigates an optimal control problem associated with a two-dimensional multi-species Cahn-Hilliard-Keller-Segel tumor growth model, which incorporates complex biological processes such as species diffusion, chemotaxis,…
We prove a version of the maximum principle, in the sense of Pontryagin, for the optimal control of a stochastic partial differential equation driven by a finite dimensional Wiener process. The equation is formulated in a semi-abstract form…
The aim of this notes is to give a concise introduction to control theory for systems governed by stochastic partial differential equations. We shall mainly focus on controllability and optimal control problems for these systems. For the…
Optimal control of stochastic nonlinear dynamical systems is a major challenge in the domain of robot learning. Given the intractability of the global control problem, state-of-the-art algorithms focus on approximate sequential optimization…
We address the generalized variational problem of Herglotz from an optimal control point of view. Using the theory of optimal control, we derive a generalized Euler-Lagrange equation, a transversality condition, a DuBois-Reymond necessary…
We consider a stochastic control problem where the set of controls is not necessarily convex and the system is governed by a nonlinear backward stochastic differential equation. We establish necessary as well as sufficient conditions of…
In this manuscript we consider a class optimal control problem for stochastic differential delay equations. First, we rewrite the problem in a suitable infinite-dimensional Hilbert space. Then, using the dynamic programming approach, we…
In this paper, we study the stochastic optimal control problem for control system with time-varying delay. The corresponding stochastic differential equation is a kind of stochastic differential delay equation. We prove the existence and…
Optimal Dirichlet boundary control for a fractional/normal evolution with a final observation is considered. The unique existence of the solution and the first-order optimality condition of the optimal control problem are derived. The…
The optimal control problem of stochastic systems is commonly solved via robust or scenario-based optimization methods, which are both challenging to scale to long optimization horizons. We cast the optimal control problem of a stochastic…
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…
We consider the control problem of the stochastic Navier-Stokes equations in multidimensional domains introduced in \cite{ocpc} restricted to noise terms defined by Q-Wiener processes. Using a stochastic maximum principle, we derive a…
We develop a mathematical model for sailboat navigation that can play the same role that the Black and Scholes model plays in mathematical finance: it captures essential features of sailboat navigation, it can provide insights that might…