Related papers: Optimal control of nonlinear stochastic differenti…
This paper studies a class of continuous-time scalar-state stochastic Linear-Quadratic (LQ) optimal control problem with the linear control constraints. Applying the state separation theorem induced from its special structure, we develop…
This paper investigates the $H_{2}/H_{\infty}$ control problem for linear stochastic differential systems under partial observation. Unlike existing studies that assume full state accessibility, we consider the scenario where the controller…
A class of optimal control problems governed by linear fractional diffusion equation with control constraint is considered. We first establish some results on the existence of strong solution to the state equation and the existence of…
Recent low-thrust space missions have highlighted the importance of designing trajectories that are robust against uncertainties. In its complete form, this process is formulated as a nonlinear constrained stochastic optimal control…
This paper investigates the near optimal control for a kind of linear stochastic control systems governed by the forward backward stochastic differential equations, where both the drift and diffusion terms are allowed to depend on controls…
The purpose of this paper is to derive some pointwise second-order necessary conditions for stochastic optimal controls in the general case that the control variable enters into both the drift and the diffusion terms. When the control…
In this paper, we aim to solve the high dimensional stochastic optimal control problem from the view of the stochastic maximum principle via deep learning. By introducing the extended Hamiltonian system which is essentially an FBSDE with a…
The paper deals with the control and regulation by integral controllers forthe nonlinear systems governed by scalar quasi-linear hyperbolic partial differentialequations. Both the control input and the measured output are located on the…
This paper is the first part of our series work to establish pointwise second-order necessary conditions for stochastic optimal controls. In this part, both drift and diffusion terms may contain the control variable but the control region…
This paper presents a new and straightforward procedure for solving bilinear quadratic optimal control problem. In this method, first the original optimal control problem is transformed into a nonlinear twopoint boundary value problem…
This paper first presents necessary and sufficient conditions for the solvability of discrete time, mean-field, stochastic linear-quadratic optimal control problems. Then, by introducing several sequences of bounded linear operators, the…
This paper addresses an open problem in the area of linear quadratic optimal control. We consider the regular, infinite-horizon, stability-modulo-a-subspace, indefinite linear quadratic problem under the assumption that the dynamics are…
We address the problem of computing a control for a time-dependent nonlinear system to reach a target set in a minimal time. To solve this minimal time control problem, we introduce a hierarchy of linear semi-infinite programs, the values…
The present study investigates a linear-quadratic Dirichlet control problem governed by a non-coercive elliptic equation posed on a possibly non-convex polygonal domain. Tikhonov regularization is carried out in an energy seminorm. The…
We consider a stochastic optimal control problem governed by a stochastic differential equation with delay in the control. Using a result of existence and uniqueness of a sufficiently regular mild solution of the associated…
In this article we study an optimal control problem subject to the Fokker-Planck equation \[ \partial_t \rho - \nu \Delta \rho - {\rm div } \big(\rho B[u]\big) = 0. \] The control variable $u$ is time-dependent and possibly…
We study linear-quadratic stochastic optimal control problems with bilinear state dependence for which the underlying stochastic differential equation (SDE) consists of slow and fast degrees of freedom. We show that, in the same way in…
This paper proposes an operator-theoretic framework that recasts the minimal value function of a nonlinear optimal control problem as an abstract bilinear form on a suitable function space. The resulting bilinear form is shown to satisfy an…
In this work, we propose and study a new approach to formulate the optimal control problem of second-order differential equations, with a particular interest in those derived from force-controlled Lagrangian systems. The formulation results…
We consider semilinear parabolic optimal control problems subject to Neumann boundary conditions, control constraints, and an infinite time horizon. The control constraints are pointwise in time, but they can be pointwise or integral in the…