Exact controllability of linear dynamical systems: A~geometrical approach

García-Planas, M. Isabel

doi:10.21136/am.2017.0427-15

Cited by 6 publications

(2 citation statements)

References 10 publications

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“…Liu et al [10] suggest "the maximum coincidence algorithm" based on the network representation of the matrix, to select the control nodes to ensure that systems are controllable; Yuan et al in [11] exhibit a general framework based on the maximum multiplicity theory to investigate the exact controllability of multiplex interrelated networks, focusing the study on the controllability amount defined by the minimum set of drivers that are needed to control steering the whole system toward any desired state but the authors do not construct the possible drivers. García-Planas in [12] builds the matrices (drivers) based on the eigenvalues of the matrix A and of its geometric multiplicity. Given a linear dynamical system such as (4) for plainness, from now on, we will write the pair of matrices as (A, B).…”

Section: The Systemmentioning

confidence: 99%

Controllability of Brain Neural Networks in Learning Disorders—A Geometric Approach

García-Planas

García-Camba

2022

Mathematics

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The human brain can be interpreted mathematically as a linear dynamical system that shifts through various cognitive regions promoting more or less complicated behaviors. The dynamics of brain neural network play a considerable role in cognitive function and therefore of interest in the bid to understand the learning processes and the evolution of possible disorders. The mathematical theory of systems and control makes available procedures, concepts, and criteria that can be applied to ease the perception of the dynamic processes that administer the evolution of the brain with learning and its control with treatment in case of disorder. In this work, a geometric study through the conception of exact controllability is comprehended to detect the minimum set and the location of the driving nodes of learning. We will describe the different roles of the nodes in the control of the paths of brain networks and show the transition of some driving nodes and the preservation of the rest in the course of learning in patients with some learning disability.

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Section: The Systemmentioning

confidence: 99%

Controllability of Brain Neural Networks in Learning Disorders—A Geometric Approach

García-Planas

García-Camba

2022

Mathematics

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“…Another important aspect of control is the notion exact controllability concept following definition given in [7], [24]. This concept is based on the maximum multiplicity to identify the minimum set of driver nodes required to achieve full control of networks with arbitrary structures and link-weight distributions.…”

Section: Introductionmentioning

confidence: 99%

Control properties of multiagent dynamical systems modelling brain neural networks

García-Planas¹

2020

2020 International Conference on Mathematics and Computers in Science and Engineering (MACISE)

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The control of linear dynamical systems is a strategy that the brain uses to control its own intrinsic dynamics. The brain structure can be modelled as a networked system that is expressly interesting system to control because of the role of the underlying architecture, which predisposes some components to particular control motions. The concept of brain cognitive control defined by neuroscientists is related to the mathematical concept of control defined by physicists, mathematicians, and engineers, where the state of a complex system can be adjusted by a particular input. The in-depth study on the controllability and structural controllability character of linear dynamical systems, despite being very difficult, could help to regulate the brain cognitive function. Small advances in the study can favour the study and action against learning difficulties such as dyscalculia or other disturbances like the phenomena of forgetting. Between different aspects in which we can study the controllability we have the notion of structural controllability and exact controllability. In this talk, we revise these concepts for linear dynamical systems and multiagent neural networks.

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Minimal Set of Generators of Controllability Space for Singular Linear Systems

García-Planas

2019

Recent Advances in Differential Equations and Applications

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Exact controllability of linear dynamical systems: A~geometrical approach

Cited by 6 publications

References 10 publications

Controllability of Brain Neural Networks in Learning Disorders—A Geometric Approach

Controllability of Brain Neural Networks in Learning Disorders—A Geometric Approach

Control properties of multiagent dynamical systems modelling brain neural networks

Minimal Set of Generators of Controllability Space for Singular Linear Systems

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