Related papers: On optimal mean-field type control problems of sto…
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…
In this paper, we consider the stochastic optimal control problem for the interacting particle system. We obtain the stochastic maximum principle of the optimal control system by introducing a generalized backward stochastic differential…
We study optimal control of stochastic Volterra integral equations (SVIE) with jumps by using Hida-Malliavin calculus. - We give conditions under which there exists unique solutions of such equations. - Then we prove both a sufficient…
Recent work linking deep neural networks and dynamical systems opened up new avenues to analyze deep learning. In particular, it is observed that new insights can be obtained by recasting deep learning as an optimal control problem on…
In this study, we consider an optimal control problem driven by a stochastic differential equation with state constraints. Here, the state constraints mean the constraints about the path of state. In order to show the maximum principe for…
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…
The effectiveness of collective navigation of biological or artificial agents requires to accommodate for contrasting requirements, such as staying in a group while avoiding close encounters and at the same time limiting the energy…
This paper is concerned with stochastic impulse control problems in which the running cost changes depending on the impulse control. Because of such a dependence, it brings several difficulties when the usual dynamic programming principle…
In this paper, we study an optimal control problem of linear backward stochastic differential equation (BSDE) with quadratic cost functional under partial information. This problem is solved completely and explicitly by using a stochastic…
This article (I) considers the known optimal control model of a quantum information transfer along a spin chain with controlled external parabolic magnetic field, with an arbitrary length. The article adds certain lower and upper pointwise…
We are interested in the optimal control problem associated with certain quadratic cost functionals depending on the solution $X=X^\alpha$ of the stochastic mean-field type evolution equation in $\mathbb R^d$ $dX_t=b(t,X_t,\mathcal…
In this paper, we consider the mixed optimal control of a linear stochastic system with a quadratic cost functional, with two controllers-one can choose only deterministic time functions, called the deterministic controller, while the other…
We study a stochastic optimal control problem for fully coupled forward-backward stochastic control systems with a nonempty control domain. For our problem, the first-order and second-order variational equations are fully coupled linear…
This work puts forward a novel numerical approach for solving the stochastic optimal control problem (SOCP) and the mean field control (MFC) problem using projection algorithm inspired by the stochastic maximum principle (SMP) which is also…
Stochastic optimal control problems have a long tradition in applied probability, with the questions addressed being of high relevance in a multitude of fields. Even though theoretical solutions are well understood in many scenarios, their…
This paper introduces a new type of second order stochastic backward Hamilton-Jacobi-Bellman (HJB) equations for optimal stochastic control problems with a currently observable but non-predicable parameter process, in addition to the…
A Cahn-Hilliard equation with stochastic multiplicative noise and a random convection term is considered. The model describes isothermal phase-separation occurring in a moving fluid, and accounts for the randomness appearing at the…
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…
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…
This paper studies a class of mean-field control (MFC) problems with singular controls under general dynamic state-control-law constraints. We first propose a customized relaxed control formulation to cope with the dynamic mixed constraints…