Related papers: Optimality conditions for optimal control of multi…
The paper is devoted to deriving necessary optimality conditions in a general optimal control problem for dynamical systems governed by controlled sweeping processes with hard-constrained control actions entering both polyhedral moving sets…
We consider optimal control of the scalar wave equation where the control enters as a coefficient in the principal part. Adding a total variation penalty allows showing existence of optimal controls, which requires continuity results for…
The aim of this paper is to derive a maximum principle for a control problem governed by a stochastic partial differential equation (SPDE) with locally monotone coefficients. In particular, necessary conditions for optimality for this…
The purpose of this paper is to establish first and second order necessary optimality conditions for optimal control problems of stochastic evolution equations with control and state constraints. The control acts both in the drift and…
We study the optimal control problem for a control-affine system, where we want to minimize the $L^1$ norm of the control. First, we show how Pontryagin Maximum Principle (PMP) applies to this problem and we divide the extremal trajectories…
We formulate and study the infinite dimensional linear programming (LP) problem associated with the deterministic discrete time long-run average criterion optimal control problem. Along with its dual, this LP problem allows one to…
This work addresses an optimal control problem constrained by a degenerate kinetic equation of parabolic-hyperbolic type. Using a hypocoercivity framework we establish the well-posedness of the problem and demonstrate that the optimal…
This paper is concerned with providing the maximum principle for a control problem governed by a stochastic evolution system on a separable Hilbert space. In particular, necessary conditions for optimality for this stochastic optimal…
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…
This paper is concerned with a linear quadratic (LQ, for short) optimal control problem with fixed terminal states and integral quadratic constraints. A Riccati equation with infinite terminal value is introduced, which is uniquely solvable…
This paper presents Lax formulae for solving the following optimal control problems: minimize the maximum (or the minimum) cost over a time horizon, while satisfying a state constraint. We present a viscosity theory, and by applying the…
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…
In this paper we discuss the optimal control of a quasilinear parabolic state equation. Its form is leaned on the kind of problems arising for example when controlling the anisotropic Allen-Cahn equation as a model for crystal growth.…
We consider optimal control problems for systems governed by mean-field stochastic differential equations, where the control enters both the drift and the diffusion coefficient. We study the relaxed model, in which admissible controls are…
We present an optimal control problem to guide the selection of morphology classes arising in organic solar cells. The study focuses on phase separation processes in polymer solvent mixtures, with particular attention to solvent evaporation…
This paper is concerned with a shape optimization problem governed by a non-smooth PDE, i.e., the nonlinearity in the state equation is not necessarily differentiable. We follow the functional variational approach of [40] where the set of…
The DPG method with optimal test functions for solving linear quadratic optimal control problems with control constraints is studied. We prove existence of a unique optimal solution of the nonlinear discrete problem and characterize it…
A special class of optimal control problems with complementarity constraints on the control functions is studied. It is shown that such problems possess optimal solutions whenever the underlying control space is a first-order Sobolev space.…
This paper deals with second-order optimality conditions for a quasilinear elliptic control problem with a nonlinear coefficient in the principal part that is countably $PC^2$ (continuous and $C^2$ apart from countably many points). We…
Stochastic optimal control problems with constraints on the probability distribution of the final output are considered. Necessary conditions for optimality in the form of a coupled system of partial differential equations involving a…