Related papers: Controlling a nonlinear Fokker-Planck equation via…
Nonlinear optimal control problems in Hilbert spaces are considered for which we derive approximation theorems for Galerkin approximations. Approximation theorems are available in the literature. The originality of our approach relies on…
The optimal control of problems that are constrained by partial differential equations with uncertainties and with uncertain controls is addressed. The Lagrangian that defines the problem is postulated in terms of stochastic functions, with…
The paper is concerned with an optimal control problem governed by the rate-independent system of quasi-static perfect elasto-plasticity. The objective is to optimize the stress field by controlling the displacement at prescribed parts of…
The article examines a linear-quadratic Neumann control problem that is governed by a non-coercive elliptic equation. Due to the non-self-adjoint nature of the linear control-to-state operator, it is necessary to independently study both…
An optimal control problem in the space of Borel measures governed by the Poisson equation is investigated. The characteristic feature of the problem under consideration is the Tikhonov regularization term in form of the transportation…
We study a family of optimal control problems under a set of controlled-loss constraints holding at different deterministic dates. The characterization of the associated value function by a Hamilton-Jacobi-Bellman equation usually calls for…
We make some remarks on a variant of the classical Tikhonov regularization in optimal control under PDEs which allows for a certain flexibility in dealing with non-linearities and state restrictions, in the sense that differential…
In this paper, we present a spectral optimal control framework for Fokker-Planck equations based on the standard ground state transformation that maps the Fokker-Planck operator to a Schrodinger operator. Our primary objective is to…
This paper considers the stochastic linear quadratic optimal control problem in which the control domain is nonconvex. By the functional analysis and convex perturbation methods, we establish a novel maximum principle. The application of…
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…
In this contribution, we study an optimal control problem for the celebrated nonlocal Cahn-Hilliard equation endowed with the singular Flory-Huggins potential in the three-dimensional setting. The control enters the governing state system…
This work deals with optimal control problems as a strategy to drive bifurcating solution of nonlinear parametrized partial differential equations towards a desired branch. Indeed, for these governing equations, multiple solution…
Here and in a follow-on paper, we consider a simple control problem in which the underlying dynamics depend on a parameter $a$ that is unknown and must be learned. In this paper, we assume that $a$ is bounded, i.e., that $|a| \le…
The paper investigates stability properties of solutions of optimal control problems for semilinear parabolic partial differential equations. H\"older or Lipschitz dependence of the optimal solution on perturbations are obtained for…
We reformulate a class of non-linear stochastic optimal control problems introduced by Todorov (2007) as a Kullback-Leibler (KL) minimization problem. As a result, the optimal control computation reduces to an inference computation and…
This paper firstly presents the necessary and sufficient conditions for a kind of discrete-time robust stochastic optimal control problem with convex control domains. As it is an "inf sup problem", the classical variational method is…
In this paper, we are concerned with a stochastic optimal control problem of mean-field type under partial observation, where the state equation is governed by the controlled nonlinear mean-field stochastic differential equation, moreover…
This paper consists of a detailed and novel stochastic optimal control analysis of a coupled non-linear dynamical system. The state equations are modeled as additional food provided prey-predator system with Holling Type-III functional…
The purpose of this work is to study an optimal control problem for a semilinear elliptic partial differential equation with a linear combination of Dirac measures as a forcing term; the control variable corresponds to the amplitude of such…
In this paper, a novel design scheme is introduced to solve the optimal control problem for nonlinear systems with unsymmetrical and state-dependent input constraints. By introducing an initial stabilizing control policy as the baseline of…