Related papers: Constructive solution of a bilinear optimal contro…
We consider a control-constrained optimal control problem subject to time-harmonic Maxwell's equations; the control variable belongs to a finite-dimensional set and enters the state equation as a coefficient. We derive existence of optimal…
We address optimal control problems on the space of measures for an objective containing a smooth functional and an optimal transport regularization. That is, the quadratic Monge-Kantorovich distance between a given prior measure and the…
The past decade has demonstrated increasing interests in using optimal control based methods within coherent quantum controllable systems. The versatility of such methods has been demonstrated with particular elegance within nuclear…
The present work addresses a finite-horizon linear-quadratic optimal control problem for uncertain systems driven by piecewise constant controls. The precise values of the system parameters are unknown, but assumed to belong to a finite set…
Closed bipartite quantum systems subject to fast local unitary control are studied using quantum optimal control theory and a method of reduced control systems based on the Schmidt decomposition. Particular focus is given to the…
An iterative learning algorithm is presented for continuous-time linear-quadratic optimal control problems where the system is externally symmetric with unknown dynamics. Both finite-horizon and infinite-horizon problems are considered. It…
We consider the Schr\"odinger partial differential equation of a rotating symmetric rigid molecule (symmetric rotor) driven by a z-linearly polarized electric field, as prototype of degenerate infinite-dimensional bilinear control system.…
The problem of quantum state preparation is one of the main challenges in achieving the quantum advantage. Furthermore, classically, for multi-level problems, our ability to solve the corresponding quantum optimal control problems is rather…
This work contributes to the field of optimal control of bilinear systems. It concerns a continuous time, finite dimensional, bilinear state equation with a quadratic performance index to be minimized. The state equation is non-autonomous…
This paper aims to establish second order necessary conditions for optimal control in quantum stochastic systems. We employ a variational approach, analogous to methods in classical stochastic control, to analyze systems governed by quantum…
In this paper we study optimal control problems governed by a semilinear elliptic equation. The equation is nonmonotone due to the presence of a convection term, despite the monotonocity of the nonlinear term. The resulting operator is…
The mathematical modeling of numerous real-world applications results in hierarchical optimization problems with two decision makers where at least one of them has to solve an optimal control problem of ordinary or partial differential…
This article considers some control problems for closed and open two-level quantum systems. The closed system's dynamics is governed by the Schr\"odinger equation with coherent control. The open system's dynamics is governed by the…
We consider the problem of numerically solving the Schr\"odinger equation with a potential that is quasi periodic in space and time. We introduce a numerical scheme based on a newly developed multi-time scale and averaging technique. We…
Extended formulations are an important tool in polyhedral combinatorics. Many combinatorial optimization problems require an exponential number of inequalities when modeled as a linear program in the natural space of variables. However, by…
This paper investigates a new class of homogeneous stochastic control problems with cone control constraints, extending the classical homogeneous stochastic linear-quadratic (LQ) framework to encompass nonlinear system dynamics and…
Exploiting a fluid dynamic formulation for which a probabilistic counterpart might not be available, we extend the theory of Schroedinger bridges to the case of inertial particles with losses and general, possibly singular diffusion…
The present analysis deals with the regularity of solutions of bilinear control systems of the type $x'=(A+u(t)B)x$where the state $x$ belongs to some complex infinite dimensional Hilbert space, the (possibly unbounded) linear operators $A$…
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.…
Optimal control problems without control costs in general do not possess solutions due to the lack of coercivity. However, unilateral constraints together with the assumption of existence of strictly positive solutions of a pre-adjoint…