Related papers: Optimal control problems governed by time-fraction…
We consider optimal control problems governed by systems describing the flow of an incompressible second grade fluid with Dirichlet boundary conditions. We prove the existence of an optimal solution, derive the corresponding necessary…
We consider an optimal control problem in which the state is governed by an unilateral obstacle problem (with obstacle from below) and restricted by a pointwise state constraint (from above). In the presence of control constraints, we…
A tracking type optimal control problem for a nonlinear and nonlocal kinetic Fokker-Planck equation which arises as the mean field limit of an interacting particle systems that is subject to distance dependent random fluctuations is…
In this paper we consider an energy storage optimization problem in finite time in a model with partial information that allows for a changing economic environment. The state process consists of the storage level controlled by the storage…
A boundary control problem for the pure Cahn-Hilliard equations with possibly singular potentials and dynamic boundary conditions is studied and first-order necessary conditions for optimality are proved. Key words: Cahn-Hilliard equation,…
In this article we study optimization problems ruled by $\alpha$-fractional diffusion operators with volume constraints. By means of penalization techniques we prove existence of solutions. We also show that every solution is locally of…
Optimal control theory is usually formulated as an indirect method requiring the solution of a two-point boundary value problem. Practically, the solution is obtained by iterative forward and backward propagation of quantum wavepackets.…
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…
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.…
We consider a control problem constrained by the unsteady stochastic Stokes equations with nonhomogeneous boundary conditions in connected and bounded domains. In this paper, controls are defined inside the domain as well as on the…
This paper concerns an optimal control problem $(P)$ related to a nonlinear Fokker-Planck equation. The problem is deeply related to a stochastic optimal control problem $(P_S)$ for a McKean-Vlasov equation. The existence of an optimal…
This paper concerns some time optimal control problems of three different ordinary differential equations in $\mathbb{R}^2$. Corresponding to certain initial data and controls, the solutions of the systems quench at finite time. The goal to…
The optimal controller design problem for a linear, first-order spatially-invariant distributed parameter system is considered. Through a case study of the Linear Quadratic Regulator (LQR) problem for the diffusion equation over the torus,…
Infinite-dimensional linear conic formulations are described for nonlinear optimal control problems. The primal linear problem consists of finding occupation measures supported on optimal relaxed controlled trajectories, whereas the dual…
An optimal control problem for longitudinal motions of a thin elastic rod is considered. We suppose that a normal force, which changes piecewise constantly along the rod's length, is applied to the cross-section so that the positions of…
The purpose of this paper is to establish the first and second order necessary conditions for stochastic optimal controls in infinite dimensions. The control system is governed by a stochastic evolution equation, in which both drift and…
This work addresses the optimal covariance control problem for stochastic discrete-time linear time-varying systems subject to chance constraints. Covariance steering is a stochastic control problem to steer the system state Gaussian…
This paper is concerned with the distributed control and stabilization problems for linear discrete-time large scale systems with imposed constraints. The main contributions of this paper are: Firstly, by using the maximum principle…
The problems of optimizing the value of an arbitrary observable of the two-level system at both a fixed time and the shortest possible time is theoretically explored. Complete identification and classification along with comprehensive…
The aim of this work is to study the optimal control problems of flows governed by the incompressible third grade fluid equations with Navier-slip boundary conditions. After recalling a result on the well-posedness of the state equations,…