Related papers: Reachable Sets from Toy Models to Controlled Marko…
The exactly solvable model of two indistinguishable quantum particles (bosons or fermions) confined in a one-dimensional harmonic trap and interacting via finite-range soft-core interaction is presented and many properties of the system are…
In this paper, we solve the problem of simultaneously driving in minimum time to arbitrary final conditions, N two level quantum systems subject to independent controls. The solution of this problem is obtained via an explicit description…
This paper investigates the application of reachability analysis to the re-entry problem faced by vehicles entering Earth's atmosphere. The study delves into the time evolution of reachable sets for the system, particularly when subject to…
This work addresses a fundamental problem of controllability of open quantum systems, meaning the ability to steer arbitrary initial system density matrix into any final density matrix. We show that under certain general conditions open…
The recently developed formalism of Markovian master equations for quantum open systems with external periodic driving is applied to the theory of dynamical decoupling by periodic control. This new approach provides a more detailed…
In the paper, the problems of controllability and approximate controllability are studied for the control system $w_t=\Delta w$, $w_{x_1}(0,x_2,t)=u(t)\delta(x_2)$, $x_1>0$, $x_2\in\mathbb R$, $t\in(0,T)$, where $u\in L^\infty(0,T)$ is a…
In the first part of this paper we introduced an algorithm that uses reachable set approximation to approximate the minimum time function of linear control problems. To illustrate the error estimates and to demonstrate differences to other…
A $D$-dimensional Markovian open quantum system will undergo stochastic evolution which preserves pure states, if one monitors without loss of information the bath to which it is coupled. If a finite ensemble of pure states satisfies a…
Due to the presence of strong correlations, theoretical or experimental investigations of quantum many-body systems belong to the most challenging tasks in modern physics. Stimulated by tensor networks, we propose a scheme of constructing…
This paper studies the set of terminal state covariances that are reachable over a finite time horizon from a given initial state covariance for a linear stochastic system with additive noise. For discrete-time systems, a complete…
We present a method of computing backward reachable sets for nonlinear discrete-time control systems possessing continuous symmetries. The starting point is a dynamic game formulation of reachability analysis where control inputs aim to…
This paper studies Gramian-based reachability metrics for bilinear control systems. In the context of complex networks, bilinear systems capture scenarios where an actuator not only can affect the state of a node but also interconnections…
This paper studies reachability and null-controllability for difference inclusions involving convex processes. Such difference inclusions arise, for instance, in the study of linear discrete-time systems whose inputs and/or states are…
We investigate two interacting open quantum systems whose time evolutions are governed by Markovian master equations. We show a class of coupled systems whose interaction leaves invariant the steady state of one of the systems, i.e., only…
A theory of feedback controlled heat transport in quantum systems is presented. It is based on modelling heat engines as driven multipartite systems subject to projective quantum measurements and measurement-conditioned unitary evolutions.…
A control system consists of a plant component and a controller which periodically computes a control input for the plant. We consider systems where the controller is implemented by a feedforward neural network with ReLU activations. The…
This paper investigates one-step backward reachability for uncertain max-plus linear systems with additive disturbances. Given a target set, the problem is to compute the set of states from which there exists an admissible control input…
An open quantum system in contact with an infinite bath approaches equilibrium, while the state of the bath remains unchanged. If the bath is finite, the open system still relaxes to equilibrium, but it induces a dynamical evolution of the…
We aim at studying approximate null-controllability properties of a particular class of piecewise linear Markov processes (Markovian switch systems). The criteria are given in terms of algebraic invariance and are easily computable. We…
This paper explains some fundamental ideas of {\em feedback} control of quantum systems through the study of a relatively simple two-level system coupled to optical field channels. The model for this system includes both continuous and…