Abstract In this chapter we discuss the general question of the controllability of deterministic systems, mainly for linear systems, though some of the results are also true for nonlinear ones.

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Controllability

J.M. Skowronski · Elsevier eBooks · 1986

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Controllability

Georgi Smirnov · Graduate studies in mathematics · 2001

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controllability

Roberto Castelli, See Profile, Roberto Castelli et al. · 2013

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Controllability

Pure and applied mathematics · 2003

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Controllability

Herbert Runyon · RePEc: Research Papers in Economics

Budget

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Controllability

Lecture notes in mathematics · 2006

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Controllability

Angelo Marzollo · Courses and lectures · 1969

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Local controllability does imply global controllability

Ugo Boscain, Daniele Cannarsa, Valentina Franceschi et al. · Comptes Rendus Mathématique · 2023

We say that a control system is locally controllable if the attainable set from any state <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>x</mml:mi> </mml:math> contains an open neighborhood of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>x</mml:mi> </mml:math> , while it is controllable if the attainable set from any state is the entire state manifold. We show in this note that a control system satisfying local controllability is controllable. Our self-contained proof is alternative to the combination of two previous results by Kevin Grasse.

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Quantum subspace controllability implying full controllability

Francesca Albertini, Domenico D’Alessandro · Linear Algebra and its Applications · 2024

In the analysis of controllability of finite dimensional quantum systems, subspace controllability refers to the situation where the underlying Hilbert space splits into the direct sum of invariant subspaces, and, on each of such invariant subspaces, it is possible to generate any arbitrary unitary operation using appropriate control functions. This is a typical situation in the presence of symmetries for the dynamics. We investigate whether and when if subspace controllability is verified, the addition of an extra Hamiltonian to the dynamics implies full controllability of the system. Under the natural (and necessary) condition that the new Hamiltonian connects all the invariant subspaces, we show that this is always the case, except for a very specific case we shall describe. Even in this specific case, a weaker notion of controllability, controllability of the state ( Pure State Controllability ) is verified.

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Local controllability does imply global controllability

Ugo Boscain, Daniele Cannarsa, Valentina Franceschi et al. · arXiv (Cornell University) · 2021

We say that a control system is locally controllable if the attainable set from any state $x$ contains an open neighborhood of $x$, while it is controllable if the attainable set from any state is the entire state manifold. We show in this note that a control system satisfying local controllability is controllable. Our self-contained proof is alternative to the combination of two previous results by Kevin Grasse.

Cited by 0Open access