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Related papers: Control sets of linear systems on Lie groups

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The paper introduces and solves a structural controllability problem for continuum ensembles of linear time-invariant systems. All the individual linear systems of an ensemble are sparse, governed by the same sparsity pattern.…

Systems and Control · Electrical Eng. & Systems 2021-07-13 Xudong Chen

A new notion of controllability for quantum systems that takes advantage of the linear superposition of quantum states is introduced. We call such notion von Neumann controllabilty and it is shown that it is strictly weaker than the usual…

Quantum Physics · Physics 2015-06-04 A. Ibort , J. M. Pérez-Pardo

For homogeneous bilinear control systems, the control sets are characterized using a Lie algebra rank condition for the induced systems on projective space. This is based on a classical Diophantine approximation result. For affine control…

Optimization and Control · Mathematics 2022-08-01 Fritz Colonius , Juliana Raupp , Alexandre J. Santana

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

For affine control systems with bounded control range the control sets, i.e., the maximal subsets of complete approximate controllability, are studied using spectral properties. For hyperbolic systems there is a unique control set with…

Optimization and Control · Mathematics 2023-05-23 Fritz Colonius , Alexandre J. Santana , Juliana Setti

The purpose of this paper is to use the framework of Lie algebroids to study optimal control problems for affine connection control systems on Lie groups. In this context, the equations for critical trajectories of the problem are…

Optimization and Control · Mathematics 2014-06-16 L. Abrunheiro , M. Camarinha

In this paper, we study the well-posedness and approximate controllability of a class of network systems having delays and controls at the boundary conditions. The particularity of this work is that the network system is defined on infinite…

Optimization and Control · Mathematics 2022-08-24 Y. El Gantouh , S. Hadd , A. Rhandi

Problems involving control of large ensmebles of structurally identical dynamical systems, called \emph{ensemble control}, arise in numerous scientific areas from quantum control and robotics to brain medicine. In many of such applications,…

Optimization and Control · Mathematics 2020-08-10 Jr-Shin Li , Wei Zhang

The aim of this paper is to prove that a control affine system on a manifold is equivalent by diffeomorphism to a linear system on a Lie group or a homogeneous space if and only the vector fields of the system are complete and generate a…

Optimization and Control · Mathematics 2008-12-02 Philippe Jouan

In control theory, understanding the observability property of a system is crucial for effectively managing and controlling dynamical systems. This property empowers us to deduce the internal state of a system from its outputs over time,…

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

This paper examines the controllability for quantum control systems with SU(1,1) dynamical symmetry, namely, the ability to use some electromagnetic field to redirect the quantum system toward a desired evolution. The problem is formalized…

Optimization and Control · Mathematics 2007-08-24 Jian-Wu Wu , Chun-Wen Li , Jing Zhang , Tzyh-Jong Tarn

This paper deals with the controllability of linear one-dimensional hyperbolic systems. Reformulating the problem in terms of linear difference equations and making use of infinite-dimensional realization theory, we obtain both necessary…

Optimization and Control · Mathematics 2024-05-14 Yacine Chitour , Sébastien Fueyo , Guilherme Mazanti , Mario Sigalotti

In this paper, we develop a representation-theoretic formulation of discrete-time linear systems. We show that such systems are naturally viewed as representations of time groups acting on vector spaces, thereby endowing the state space…

Systems and Control · Electrical Eng. & Systems 2026-04-13 Subhrajit Sinha

The relaxation systems are an important subclass of the passive systems that arise naturally in applications. We exploit the fact that they have highly structured state-space realisations to derive analytical solutions to some simple…

Optimization and Control · Mathematics 2019-09-17 Richard Pates , Carolina Bergeling , Anders Rantzer

This paper studies the structural controllability of a class of uncertain switched linear systems, where the parameters of subsystems state matrices are either unknown or zero. The structural controllability is a generalization of the…

Systems and Control · Computer Science 2013-08-27 Xiaomeng Liu , Hai Lin , Ben M. Chen

The dynamical systems having both bosonic and fermionic variables play an important role in the theory of supersymmetry. This article addresses the control problems including both bosonic and fermionic variables on Lie supergroup as the…

Optimization and Control · Mathematics 2026-05-22 Aroonima Sahoo , Kishor Chandra Pati , Tofan Kumar Khuntia

Adaptive tracking control for rigid body dynamics is of critical importance in control and robotics, particularly for addressing uncertainties or variations in system model parameters. However, most existing adaptive control methods are…

Robotics · Computer Science 2025-02-11 Jiawei Tang , Shilei Li , Ling Shi

Lie systems form a class of systems of first-order ordinary differential equations whose general solutions can be described in terms of certain finite families of particular solutions and a set of constants, by means of a particular type of…

Mathematical Physics · Physics 2013-03-13 J. F. Cariñena , J. de Lucas

Reachable sets of nonlinear control systems can in general only be approximated numerically, and these approximations are typically very expensive to compute. In this paper, we explore a strategy for choosing the temporal and spatial…

Numerical Analysis · Mathematics 2023-07-24 Janosch Rieger , Kyria Wawryk

We introduce the concept of $\epsilon$-uncontrollability for random linear systems, i.e. linear system in which the usual matrices have been replaced by random matrices. We also estimate the $\epsilon$-uncontrollability in the case where…

Dynamical Systems · Mathematics 2020-11-24 John Leventides , Nick Poulios , Costas Poulios