Related papers: A sufficient optimality condition for non-linear d…
A general maximum principle (necessary and sufficient conditions) for an optimal control problem governed by a stochastic differential equation driven by an infinite dimensional martingale is established. The solution of this equation takes…
In this paper, we study a time-inconsistent stochastic optimal control problem with a recursive cost functional by a multi-person hierarchical differential game approach. An equilibrium strategy of this problem is constructed and a…
This paper deals with optimal control problems of integral equations, with initial-final and running state constraints. The order of a running state constraint is defined in the setting of integral dynamics, and we work here with…
This paper is concerned with the derivation of necessary conditions for the optimal shape of a design problem governed by a non-smooth PDE. The main particularity thereof is the lack of differentiability of the nonlinearity in the state…
Necessary conditions for existence of normal extremals in optimal control of systems subject to nonholonomic constraints are derived as solutions of a constrained second order variational problems. In this work, a geometric interpretation…
We present necessary and sufficient optimality conditions for finite time optimal control problems for a class of hybrid systems described by linear complementarity models. Although these optimal control problems are difficult in general…
The current article examines the approximate controllability problem for non-instantaneous impulsive fractional evolution equations of order $1<\alpha<2$ with state-dependent delay in separable reflexive Banach spaces. In order to establish…
In this note, we demonstrate that a locally semiconvex viscosity supersolution to a possibly degenerate fully nonlinear elliptic Hamilton-Jacobi-Bellman (HJB) equation is differentiable along the directions spanned by the range of the…
This paper presents sufficient conditions for optimal control of systems with dynamics given by a linear operator, in order to obtain an explicit solution to the Bellman equation that can be calculated in a distributed fashion. Further, the…
We prove strong stationarity conditions for optimal control problems that are governed by a prototypical rate-independent evolution variational inequality, i.e., first-order necessary optimality conditions in the form of a primal-dual…
This paper investigates a Hamilton-Jacobi (HJ) analysis to solve finite-horizon optimal control problems for high-dimensional systems. Although grid-based methods, such as the level-set method [1], numerically solve a general class of HJ…
For an infinite-horizon continuous-time optimal stopping problem under non-exponential discounting, we look for an optimal equilibrium, which generates larger values than any other equilibrium does on the entire state space. When the…
This work is a continuation of the previous one in [{\it Optimization} (2023)], where the existence of optimal solutions and first-order necessary optimality conditions in both Pontryagin's maximum principle form and the variational form…
An optimal control problem for the continuity equation is considered. The aim of a "controller" is to maximize the total mass within a target set at a given time moment. The existence of optimal controls is established. For a particular…
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 study the time-inconsistent linear quadratic optimal control problem for forward-backward stochastic differential equations with potentially indefinite cost weighting matrices for both the state and the control variables. Our research…
Within this chapter, we discuss control in the coefficients of an obstacle problem. Utilizing tools from H-convergence, we show existence of optimal solutions. First order necessary optimality conditions are obtained after deriving…
This paper studies an optimal stochastic impulse control problem in a finite horizon with a decision lag, by which we mean that after an impulse is made, a fixed number units of time has to be elapsed before the next impulse is allowed to…
We consider the optimal control of singular nonlinear partial differential equation which is the distributional formulation of the multiphase Stefan type free boundary problem for the general second order parabolic equation. Boundary heat…
We examine the problem of two-point boundary optimal control of nonlinear systems over finite-horizon time periods with unknown model dynamics by employing reinforcement learning. We use techniques from singular perturbation theory to…