Related papers: Beyond bilinear controllability : applications to …
Some simple examples from quantum physics and control theory are used to illustrate the application of the theory of Lie systems. We will show, in particular, that for certain physical models both of the corresponding classical and quantum…
The main purpose of this paper is the study of second-order optimality conditions for the bilinear control of a strongly degenerate parabolic equation. The equation is degenerate at the boundary of the spatial domain. The well-posedness of…
The optimal control problem for open quantum systems can be formulated as a time-dependent Lindbladian that is parameterized by a number of time-dependent control variables. Given an observable and an initial state, the goal is to tune the…
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…
We consider the problem of controlling a linear dynamical system from bilinear observations with minimal quadratic cost. Despite the similarity of this problem to standard linear quadratic Gaussian (LQG) control, we show that when the…
Feedback-based control is the de-facto standard when it comes to controlling classical stochastic systems and processes. However, standard feedback-based control methods are challenged by quantum systems due to measurement induced…
For linear infinite systems the approximate controllability problem by control constraints is considered. Controllability conditions represented via system parameters are obtained. Partial differential control systems and control systems…
In this article a special class of nonlinear optimal control problems involving a bilinear term in the boundary condition is studied. These kind of problems arise for instance in the identification of an unknown space-dependent Robin…
In this work we study the global approximate multiplicative controllability for the linear degenerate parabolic Cauchy-Neumann problem $$ \{{array}{l} \displaystyle{v_t-(a(x) v_x)_x =\alpha (t,x)v\,\,\qquad {in} \qquad Q_T…
We prove a bilinear form sparse domination theorem that applies to many multi-scale operators beyond Calder\'on-Zygmund theory, and also establish necessary conditions. Among the applications, we cover large classes of Fourier multipliers,…
We study time-optimal protocols for controlling quantum systems which show several avoided level crossings in their energy spectrum. The structure of the spectrum allows us to generate a robust guess which is time-optimal at each crossing.…
In this paper we prove an approximate controllability result for the bilinear Schr\"odinger equation. This result requires less restrictive non-resonance hypotheses on the spectrum of the uncontrolled Schr\"odinger operator than those…
We study quantum control of the full hyperfine manifold in the ground-electronic state of alkali atoms based on applied radio frequency and microwave fields. Such interactions should allow essentially decoherence-free dynamics and the…
A central challenge in quantum computing is to identify more computational problems for which utilization of quantum resources can offer significant speedup. Here, we propose a hybrid quantum-classical scheme to tackle the quantum optimal…
Control systems are usually modeled by differential equations describing how physical phenomena can be influenced by certain control parameters or inputs. Although these models are very powerful when dealing with physical phenomena, they…
This dissertation presents and prove the viability of a non-standard method for controlling the state of a quantum system by modifying its boundary conditions instead of relying on the action of external fields. The standard approach to…
Quantum control is valuable for various quantum technologies such as high-fidelity gates for universal quantum computing, adaptive quantum-enhanced metrology, and ultra-cold atom manipulation. Although supervised machine learning and…
This paper considers the problem of determining an optimal control action based on observed data. We formulate the problem assuming that the system can be modelled by a nonlinear state-space model, but where the model parameters, state and…
We consider a linear Schr\"odinger equation, on a bounded interval, with bilinear control. Beauchard and Laurent proved that, under an appropriate non degeneracy assumption, this system is controllable, locally around the ground state, in…
Nonlinear dynamical systems can be made easier to control by lifting them into the space of observable functions, where their evolution is described by the linear Koopman operator. This paper describes how the Koopman operator can be used…