Related papers: On the solution stability of parabolic optimal con…
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…
This paper is concerned with a constrained stochastic linear-quadratic optimal control problem, in which the terminal state is fixed and the initial state is constrained to lie in a stochastic linear manifold. The controllability of…
We adopt the integral definition of the fractional Laplace operator and analyze an optimal control problem for a fractional semilinear elliptic partial differential equation (PDE); control constraints are also considered. We establish the…
In this paper, we analyze optimal control problems governed by semilinear parabolic equations. Box constraints for the controls are imposed and the cost functional involves the state and possibly a sparsity-promoting term, but not a…
The local stability of the solution map to a parametric boundary control problem governed by semilinear elliptic equations with finite mixed pointwise constraints is considered in this paper. We prove that the solution map is locally…
This paper focuses on the stability of solutions for a velocity-tracking problem associated with the two-dimensional Navier-Stokes equations. The considered optimal control problem does not possess any regularizer in the cost, and hence…
We consider optimal control problems for partial differential equations where the controls take binary values but vary over the time horizon, they can thus be seen as dynamic switches. The switching patterns may be subject to combinatorial…
Solving optimal control problems to determine a stabilizing controller involves a significant computational effort. Time-varying optimal control provides a remedy by designing a tracking system, given as an ordinary differential equation,…
We investigate the stability of time-periodic solutions of semilinear parabolic problems with Neumann boundary conditions. Such problems are posed on compact submanifolds evolving periodically in time. The discussion is based on the…
We consider a bilinear optimal control problem with pointwise tracking for a semilinear elliptic PDE in two and three dimensions. The control variable enters the PDE as a (reaction) coefficient and the cost functional contains point…
We prove a sufficient optimality condition for non-linear optimal control problems with delays in both state and control variables. Our result requires the verification of a Hamilton-Jacobi partial differential equation and is obtained…
We study optimal control problems that are governed by semilinear elliptic partial differential equations that involve non-Lipschitzian nonlinearities. It is shown that, for a certain class of such PDEs, the solution map is Fr\'{e}chet…
We consider a control-constrained parabolic optimal control problem without Tikhonov term in the tracking functional. For the numerical treatment, we use variational discretization of its Tikhonov regularization: For the state and the…
Along the optimal trajectory of an optimal control problem constrained by a semilinear parabolic partial differential equation, we prove the differentiability of the value function with respect to the initial condition and, under additional…
This paper provides necessary conditions of optimality for optimal control problems with time delays in both state and control variables. Different versions of the necessary conditions cover fixed end-time problems and, under additional…
We consider an optimal control problem constrained by a parabolic partial differential equation (PDE) with Robin boundary conditions. We use a well-posed space-time variational formulation in Lebesgue--Bochner spaces with minimal…
In this work we develop a new numerical approach for recovering a spatially dependent source component in a standard parabolic equation from partial interior measurements. We establish novel conditional Lipschitz stability and H\"{o}lder…
We address the crucial yet underexplored stability properties of the Hamilton--Jacobi--Bellman (HJB) equation in model-free reinforcement learning contexts, specifically for Lipschitz continuous optimal control problems. We bridge the gap…
This paper proposes a relaxed control regularization with general exploration rewards to design robust feedback controls for multi-dimensional continuous-time stochastic exit time problems. We establish that the regularized control problem…
In this paper, we investigate optimal control problems for Allen-Cahn equations with singular nonlinearities and a dynamic boundary condition involving singular nonlinearities and the Laplace-Beltrami operator. The approach covers both the…