Related papers: Maximum Principle for State-Constrained Optimal Co…

We consider in this paper, mixed relaxed-singular stochastic control problems, where the control variable has two components, the first being measure-valued and the second singular. The control domain is not necessarily convex and the…

In this paper, we study the maximum principle of mean field type control problems when the volatility function depends on the state and its measure and also the control, by using our recently developed method. Our method is to embed the…

We prove a duality relation and an integration by parts formula for fractional operators with a general analytical kernel. Based on these basic results, we are able to prove a new Gronwall's inequality and continuity and differentiability…

We consider a stochastic control problem where the set of strict (classical) controls is not necessarily convex and the the variable control has two components, the first being absolutely continuous and the second singular. The system is…

We study linear-quadratic optimal control problems for Voterra systems, and problems that are linear-quadratic in the control but generally nonlinear in the state. In the case of linear-quadratic Volterra control, we obtain sharp necessary…

In this paper, we consider stochastic optimal control of systems driven by stochastic differential equations with irregular drift coefficient. We establish a necessary and sufficient stochastic maximum principle. To achieve this, we first…

In this paper we derive a necessary optimality condition for a local optimal solution of some control problems. These optimal control problems are governed by a semi-linear Vettsel boundary value problem of a linear elliptic equation. The…

We analyze an optimal control problem for systems of integral equations of Volterra type with two independent variables. These systems generalize both, the hyperbolic control problems for systems of Goursat-Darboux type, and the optimal…

In this paper we are concerned with a class of stochastic Volterra integro-differential problems with completely monotone kernels, where we assume that the noise enters the system when we introduce a control. We start by reformulating the…

In the present paper, the maximum principle for finite horizon state constrained problems from the book by R. Vinter [\textit{Optimal Control}, Birkh\"auser, Boston, 2000; Theorem~9.3.1] is analyzed via parametric examples. The latter has…

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…

Optimal control problems of forward-backward stochastic Volterra integral equations (FBSVIEs, in short) with closed control regions are formulated and studied. Instead of using spike variation method as one may imagine, here we turn to…

The Volterra integral equations of the first kind with piecewise smooth kernel are considered. Such equations appear in the theory of optimal control of the evolving systems. The existence theorems are proved. The method for constructing…

This paper focuses on the optimal control of a class of stochastic Volterra integral equations. Here the coefficients are regular and not assumed to be of convolution type. We show that, under mild regularity assumptions, these equations…

Here we derive a nonsmooth maximum principle for optimal control problems with both state and mixed constraints. Crucial to our development is a convexity assumption on the "velocity set". The approach consists of applying known…

This work studies a class of singular Volterra integral equations that are (controlled) and can be applied to memory-related problems.For optimum controls, we prove a second-order Pontryagin type maximal principle.

We consider a stochastic control problem, where the control domain is convex and the system is governed by a nonlinear backward stochastic differential equation. With a L1 terminal data, we derive necessary optimality conditions in the form…

We investigate optimal control problems with $L^0$ constraints, which restrict the measure of the support of the controls. We prove necessary optimality conditions of Pontryagin maximum principle type. Here, a special control perturbation…

This work establishes a general stochastic maximum principle for partially observed optimal control of semi-linear stochastic partial differential equations in a nonconvex control domain. The state evolves in a Hilbert space driven by a…

In this article, we explore two distinct issues. Initially, we examine the utilization of the Pontriagin maximum principle in relation to fractional delay differential equations. Additionally, we discuss the optimal approach for solving the…