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Related papers: Ensemble controllability by Lie algebraic methods

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In this paper we establish several results on approximate controllability of a semilinear wave equation by making use of a single multiplicative control. These results are then applied to discuss the exact controllability properties for the…

Optimization and Control · Mathematics 2019-01-16 Mohamed Ouzahra

This paper introduces and solves a structural controllability problem for ensembles of switched linear systems. All individual systems in the ensemble are sparse and governed by the same sparsity pattern, and undergo switching among…

Optimization and Control · Mathematics 2026-03-18 Haoyu Yin , Yi Li , Ouyang Du , Bruno Sinopoli , Xudong Chen

In this paper, we consider families of linear systems (linear ensembles) defined by matrix pairs $\big( A(\theta),B(\theta) \big)$ depending on a parameter $\theta \in \p$ that is varying over a compact subset $\p$ of the complex plane. In…

Optimization and Control · Mathematics 2020-10-27 Gunther Dirr , Michael Schönlein

We address the study of controllability of a closed quantum system whose dynamical Lie algebra is generated by adjacency matrices of graphs. We characterize a large family of graphs that renders a system controllable. The key property is a…

Quantum Physics · Physics 2012-01-10 Chris Godsil , Simone Severini

We develop an epsilon-controlled algebraic L-theory, extending our earlier work on epsilon-controlled algebraic K-theory. The controlled L-theory is very close to being a generalized homology theory; we study analogues of the homology exact…

Geometric Topology · Mathematics 2009-03-19 Andrew Ranicki , Masayuki Yamasaki

This paper provides a full controlled version of algebraic $K$-theory. This includes a rich array of assembly maps; the controlled assembly isomorphism theorem identifying the controlled group with homology; and the stability theorem…

K-Theory and Homology · Mathematics 2007-05-23 Frank Quinn

The objective of this paper is to study the controllability of discrete-time linear control systems in solvable Lie groups. In the special case of nilpotent Lie groups, a necessary and sufficient condition for controllability is…

Optimization and Control · Mathematics 2024-06-11 Thiago Cavalheiro , Alexandre Santana , João Cossich , Victor Ayala

We study the controllability of a closed control-affine quantum system driven by two or more external fields. We provide a sufficient condition for controllability in terms of existence of conical intersections between eigenvalues of the…

Mathematical Physics · Physics 2015-06-17 Ugo Boscain , Jean-Paul Gauthier , Francesco Rossi , Mario Sigalotti

Ensemble control deals with the problem of using a finite number of control inputs to simultaneously steer a large population (in the limit, a continuum) of control systems. Dual to the ensemble control problem, ensemble estimation deals…

Systems and Control · Computer Science 2019-05-02 Xudong Chen

We consider a bilinear control problem for the wave equation on a torus of arbitrary dimension. We show that the system is globally approximately controllable in arbitrarily small times from a dense family of initial states. The control…

Optimization and Control · Mathematics 2023-05-22 Eugenio Pozzoli

We investigate a class of higher-order nonlinear dispersive equations posed on the circle, subject to additive forcing by a finite-dimensional control. Our main objective is to establish approximate controllability by using the…

Analysis of PDEs · Mathematics 2025-04-25 Debanjit Mondal

This paper explores the controllability and state tracking of ensembles from the perspective of optimal transport theory. Ensembles, characterized as collections of systems evolving under the same dynamics but with varying initial…

Systems and Control · Electrical Eng. & Systems 2024-12-18 Reza Hadadi

In finite dimensions, controllability of bilinear quantum control systems can be decided quite easily in terms of the "Lie algebra rank condition" (LARC), such that only the systems Lie algebra has to be determined from a set of generators.…

Quantum Physics · Physics 2018-12-24 Michael Keyl

In control theory, researchers need to understand a system's local and global behaviors in relation to its initial conditions. When discussing observability, the main focus is on the ability to analyze the system using an output space…

Optimization and Control · Mathematics 2025-03-26 Thiago Matheus Cavalheiro , Alexandre José Santana , Victor Ayala

We present a method of design of control systems for $n$ bodies in the real line $\Bbb R^1$ and on the unit circle $ S^1$, to be collision-free and controllable. The problem reduces to designing a control-affine system in $\Bbb R^n$ and in…

Optimization and Control · Mathematics 2023-05-19 Chong-Kyu Han , Donghoon Park

It is well-known that the controllability of finite-dimensional nonlinear systems can be established by showing the controllability of the linearized system. However, this classical result does not generalize to infinite-dimensional…

Optimization and Control · Mathematics 2021-07-29 Bernd Kolar , Markus Schöberl

In this paper, we propose an adaptive control law for completely unknown scalar linear systems based on Lie-bracket approximation methods. We investigate stability and convergence properties for the resulting Lie-bracket system, compare our…

Optimization and Control · Mathematics 2021-10-26 Marc Weber , Christian Ebenbauer , Bahman Gharesifard

An overview and synthesis of results and criteria for open-loop controllability of Hamiltonian quantum systems obtained using Lie group and Lie algebra techniques is presented. Negative results for open-loop controllability of dissipative…

Quantum Physics · Physics 2007-05-23 S. G. Schirmer , I. C. H. Pullen , A. I. Solomon

In this article, we investigate the problem of simultaneously steering an uncountable family of finite dimensional time-varying linear systems. We call this class of control problems Ensemble Control, a notion coming from the study of spin…

Dynamical Systems · Mathematics 2008-10-29 Jr-Shin Li

This paper is devoted to the study of controllability of linear systems on generalized Heisenberg groups. Some general necessary controllability conditions and some sufficient ones are provided. We introduce the notion of decoupled systems,…

Optimization and Control · Mathematics 2015-10-15 Mouhamadou Dath , Philippe Jouan