IEEE Transactions on Automatic Control, ISSN 0018-9286, 05/2019, Volume 64, Issue 5, pp. 1772 - 1783

Nonlinear observer design for systems whose state-space evolves on Lie groups is considered. The proposed method is similar to previously developed nonlinear...

Linear systems | Technological innovation | nonlinear systems | Lie groups | Observers | Harmonic analysis | Cost function | Velocity measurement | Noise measurement | DESIGN | ATTITUDE TRACKING | REJECTION | MATRICES | OBSERVER | observers | GYRO | AUTOMATION & CONTROL SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Group velocity | Time invariant systems | Innovations | Linear filters | Mathematical models | Disturbance observers | Asymptotic methods | Nonlinear systems | Invariants

Linear systems | Technological innovation | nonlinear systems | Lie groups | Observers | Harmonic analysis | Cost function | Velocity measurement | Noise measurement | DESIGN | ATTITUDE TRACKING | REJECTION | MATRICES | OBSERVER | observers | GYRO | AUTOMATION & CONTROL SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Group velocity | Time invariant systems | Innovations | Linear filters | Mathematical models | Disturbance observers | Asymptotic methods | Nonlinear systems | Invariants

Journal Article

Journal of Mathematical Sciences, ISSN 1072-3374, 9/2018, Volume 233, Issue 5, pp. 659 - 665

In this paper, the authors describe homomorphisms of Lie groups into the groups u(R) of invertible elements of rings R for a large class of rings R, which...

Mathematics, general | Mathematics | Algebra | LIE GROUPS | MATRICES | RINGS | MATHEMATICAL METHODS AND COMPUTING

Mathematics, general | Mathematics | Algebra | LIE GROUPS | MATRICES | RINGS | MATHEMATICAL METHODS AND COMPUTING

Journal Article

3.
Geometry and dynamics in Gromov hyperbolic metric spaces

: with an emphasis on non-proper settings

2017, Mathematical surveys and monographs, ISBN 9781470434656, Volume 218, xxxv, 281 pages

Geometry, Hyperbolic | Ergodic theory | Measure and integration | Fuchsian groups and their generalizations | Infinite-dimensional Lie groups and their Lie algebras: general properties | Hyperbolic groups and nonpositively curved groups | Special aspects of infinite or finite groups | Semigroups of transformations, etc | Metric spaces | Conformal densities and Hausdorff dimension | Structure and classification of infinite or finite groups | Relations with number theory and harmonic analysis | Classical measure theory | Group theory and generalizations | Other groups of matrices | Complex dynamical systems | Lie groups | Hyperbolic spaces | Semigroups | Groups acting on trees | Topological groups, Lie groups | Dynamical systems and ergodic theory | Hausdorff and packing measures

Book

Advances in Mathematics, ISSN 0001-8708, 2009, Volume 222, Issue 4, pp. 1461 - 1501

We show that under suitable assumptions, we have a one-to-one correspondence between classical groups and free quantum groups, in the compact orthogonal case....

Quantum group | Noncrossing partition | MATHEMATICS | INTEGRATION | QUANTUM PERMUTATION-GROUPS | DUALITY | COMPACT MATRIX PSEUDOGROUPS

Quantum group | Noncrossing partition | MATHEMATICS | INTEGRATION | QUANTUM PERMUTATION-GROUPS | DUALITY | COMPACT MATRIX PSEUDOGROUPS

Journal Article

2016, 2nd edition., Student mathematical library, ISBN 1470427222, Volume 79., viii, 239

Group theory and generalizations | Research exposition (monographs, survey articles) | Matrix groups | Representation theory of groups | General properties and structure of real Lie groups | Compact groups | Lie groups | Linear algebraic groups and related topics | Linear algebraic groups over the reals, the complexes, the quaternions | Topological groups, Lie groups | Group rings of finite groups and their modules | Linear algebraic groups

Book

2007, Graduate texts in mathematics, ISBN 0387302638, Volume 235, xii, 198

Book

IEEE Signal Processing Letters, ISSN 1070-9908, 11/2017, Volume 24, Issue 11, pp. 1719 - 1723

Many physical systems evolved on matrix Lie groups and mixture filtering designed for such manifolds represent an inevitable tool for challenging estimation...

probability hypothesis density filter | Uncertainty | Algebra | Merging | mixture reduction | Estimation | Gaussian distribution | Tools | Radar tracking | multitarget tracking | Estimation on matrix lie groups | ENGINEERING, ELECTRICAL & ELECTRONIC

probability hypothesis density filter | Uncertainty | Algebra | Merging | mixture reduction | Estimation | Gaussian distribution | Tools | Radar tracking | multitarget tracking | Estimation on matrix lie groups | ENGINEERING, ELECTRICAL & ELECTRONIC

Journal Article

International Journal of Geometric Methods in Modern Physics, ISSN 0219-8878, 04/2018, Volume 15, Issue 4

We study right-invariant (respectively, left-invariant) Poisson-Nijenhuis structures (P-N) on a Lie group G and introduce their infinitesimal counterpart, the...

Poisson-Nijenhuis structures | integrable dynamical systems | Lie bialgebras and coboundary Lie bialgebras | ALGEBRAS | PHYSICS, MATHEMATICAL

Poisson-Nijenhuis structures | integrable dynamical systems | Lie bialgebras and coboundary Lie bialgebras | ALGEBRAS | PHYSICS, MATHEMATICAL

Journal Article

IEEE Transactions on Automatic Control, ISSN 0018-9286, 08/2018, Volume 63, Issue 8, pp. 2465 - 2480

This paper is concerned with the problem of continuous-time nonlinear filtering of stochastic processes evolving on connected Riemannian manifolds without...

Manifolds | Symmetric matrices | Estimation | Stochastic processes | Nonlinear filters | Particle filters | Kalman filters | Mathematical model | Covariance matrices | Stochastic Processes | LOCALIZATION | VECTOR OBSERVATIONS | SPACECRAFT ATTITUDE ESTIMATION | EUCLIDEAN GROUP | AUTOMATION & CONTROL SYSTEMS | VISUAL TRACKING | ENGINEERING, ELECTRICAL & ELECTRONIC | Euclidean geometry | Filtration | Computer simulation | Attitudes | Poisson equation | Manifolds (mathematics) | Invariants | Extended Kalman filter | Riemann manifold | Numerical analysis | Algorithms | Quaternions | Feedback | Lie groups | Differential equations | Brownian movements | Formulas (mathematics) | Geometric constraints

Manifolds | Symmetric matrices | Estimation | Stochastic processes | Nonlinear filters | Particle filters | Kalman filters | Mathematical model | Covariance matrices | Stochastic Processes | LOCALIZATION | VECTOR OBSERVATIONS | SPACECRAFT ATTITUDE ESTIMATION | EUCLIDEAN GROUP | AUTOMATION & CONTROL SYSTEMS | VISUAL TRACKING | ENGINEERING, ELECTRICAL & ELECTRONIC | Euclidean geometry | Filtration | Computer simulation | Attitudes | Poisson equation | Manifolds (mathematics) | Invariants | Extended Kalman filter | Riemann manifold | Numerical analysis | Algorithms | Quaternions | Feedback | Lie groups | Differential equations | Brownian movements | Formulas (mathematics) | Geometric constraints

Journal Article

2009, MAA textbooks, ISBN 0883857596, xii, 177

Book

IEEE Sensors Journal, ISSN 1530-437X, 05/2018, Volume 18, Issue 9, pp. 3780 - 3788

In this paper, we present a novel visual-inertial navigation algorithm for low-cost and computationally constrained vehicle in global positioning system denied...

Manifolds | Jacobian matrices | Uncertainty | Three-dimensional displays | filtering on manifold | Vision-aided inertial navigation | EKF-based multi-sensor fusion | Sensors | matrix Lie group | Mathematical model | SYSTEM | PHYSICS, APPLIED | FUSION | VISION | REPRESENTATIONS | SENSORS | EXTENDED KALMAN FILTER | ENGINEERING, ELECTRICAL & ELECTRONIC | INSTRUMENTS & INSTRUMENTATION | NAVIGATION

Manifolds | Jacobian matrices | Uncertainty | Three-dimensional displays | filtering on manifold | Vision-aided inertial navigation | EKF-based multi-sensor fusion | Sensors | matrix Lie group | Mathematical model | SYSTEM | PHYSICS, APPLIED | FUSION | VISION | REPRESENTATIONS | SENSORS | EXTENDED KALMAN FILTER | ENGINEERING, ELECTRICAL & ELECTRONIC | INSTRUMENTS & INSTRUMENTATION | NAVIGATION

Journal Article

International Journal of Geometric Methods in Modern Physics, ISSN 0219-8878, 08/2016, Volume 13, Issue 7

In this paper, we obtain the classical r-matrices of real two- and three-dimensional Jacobi-Lie bialgebras. In this way, we classify all non-isomorphic real...

Jacobi-Lie bialgebra | classical r -matrix | Jacobi-Lie group | PHYSICS, MATHEMATICAL | classical r-matrix

Jacobi-Lie bialgebra | classical r -matrix | Jacobi-Lie group | PHYSICS, MATHEMATICAL | classical r-matrix

Journal Article

IEEE Transactions on Circuits and Systems for Video Technology, ISSN 1051-8215, 10/2015, Volume 25, Issue 10, pp. 1576 - 1585

In this paper, we study discriminative analysis of symmetric positive definite (SPD) matrices on Lie groups (LGs), namely, transforming an LG into a...

Manifolds | Measurement | visual classification | Visualization | Symmetric matrices | Algebra | Discriminative analysis | graph embedding | Lie group | Kernel | Covariance matrices | Lie group (LG) | KERNEL | ROBUST | REPRESENTATION | FRAMEWORK | CLASSIFICATION | COVARIANCE | ENGINEERING, ELECTRICAL & ELECTRONIC | Usage | Symmetric functions | Lie groups

Manifolds | Measurement | visual classification | Visualization | Symmetric matrices | Algebra | Discriminative analysis | graph embedding | Lie group | Kernel | Covariance matrices | Lie group (LG) | KERNEL | ROBUST | REPRESENTATION | FRAMEWORK | CLASSIFICATION | COVARIANCE | ENGINEERING, ELECTRICAL & ELECTRONIC | Usage | Symmetric functions | Lie groups

Journal Article

Advances in Mathematics, ISSN 0001-8708, 10/2017, Volume 319, pp. 522 - 566

We introduce a Frechet Lie group structure on the Riordan group. We give a description of the corresponding Lie algebra as a vector space of infinite lower...

Stabilizers | Exponential map | Finite dimensional Riordan groups | Lie algebra | Riordan group | Frechet Lie group | MATHEMATICS | MATRICES | Algebra

Stabilizers | Exponential map | Finite dimensional Riordan groups | Lie algebra | Riordan group | Frechet Lie group | MATHEMATICS | MATRICES | Algebra

Journal Article

IEEE Transactions on Signal Processing, ISSN 1053-587X, 12/2009, Volume 57, Issue 12, pp. 4734 - 4743

Averaging is a common way to alleviate errors and random fluctuations in measurements and to smooth out data. Averaging also provides a way to merge structured...

Symmetric matrices | Adaptive systems | Fluctuations | Multidimensional systems | Independent component analysis | Biomedical measurements | complex-valued independent component analysis | unitary group | Quantum computing | Signal processing algorithms | DNA | matrix Lie groups | positive-definite matrices | Averaging on curved spaces | Biomedical signal processing | orthogonal group | Complex-valued independent component analysis | Matrix Lie groups | Positive-definite matrices | Orthogonal group | Unitary group | COMPLEX | LEARNING ALGORITHMS | UNIQUENESS | ENGINEERING, ELECTRICAL & ELECTRONIC | Signal processing | Usage | Functions, Orthogonal | Analysis | Genetic algorithms | Algorithms | Error analysis | Mathematical analysis | Fluctuation | Lie groups | Matrices | Matrix methods

Symmetric matrices | Adaptive systems | Fluctuations | Multidimensional systems | Independent component analysis | Biomedical measurements | complex-valued independent component analysis | unitary group | Quantum computing | Signal processing algorithms | DNA | matrix Lie groups | positive-definite matrices | Averaging on curved spaces | Biomedical signal processing | orthogonal group | Complex-valued independent component analysis | Matrix Lie groups | Positive-definite matrices | Orthogonal group | Unitary group | COMPLEX | LEARNING ALGORITHMS | UNIQUENESS | ENGINEERING, ELECTRICAL & ELECTRONIC | Signal processing | Usage | Functions, Orthogonal | Analysis | Genetic algorithms | Algorithms | Error analysis | Mathematical analysis | Fluctuation | Lie groups | Matrices | Matrix methods

Journal Article

16.
Full Text
Numerical Methods for Stochastic Differential Equations in Matrix Lie Groups Made Simple

IEEE Transactions on Automatic Control, ISSN 0018-9286, 12/2018, Volume 63, Issue 12, pp. 4035 - 4050

A large number of significant applications involve numerical solution of stochastic differential equations (SDE's) evolving in Lie groups such as...

Geometry | Biological system modeling | stochastic differential equations (SDE's) | Indium tin oxide | Stochastic processes | stochastic Lie group integrators | Differential equations | Mathematical model | Standards | Geometric integration | MOTION | RUNGE-KUTTA METHODS | ATTITUDE ESTIMATION | EUCLIDEAN GROUP | AUTOMATION & CONTROL SYSTEMS | VISUAL TRACKING | ENGINEERING, ELECTRICAL & ELECTRONIC | Economic models | Accessibility | Computer simulation | Mathematical analysis | Differential geometry | Numerical methods | Lie groups | Matrix methods

Geometry | Biological system modeling | stochastic differential equations (SDE's) | Indium tin oxide | Stochastic processes | stochastic Lie group integrators | Differential equations | Mathematical model | Standards | Geometric integration | MOTION | RUNGE-KUTTA METHODS | ATTITUDE ESTIMATION | EUCLIDEAN GROUP | AUTOMATION & CONTROL SYSTEMS | VISUAL TRACKING | ENGINEERING, ELECTRICAL & ELECTRONIC | Economic models | Accessibility | Computer simulation | Mathematical analysis | Differential geometry | Numerical methods | Lie groups | Matrix methods

Journal Article

Foundations of Computational Mathematics, ISSN 1615-3375, 4/2016, Volume 16, Issue 2, pp. 493 - 530

In this article, a unified approach to obtain symplectic integrators on $$T^{*}G$$ T ∗ G from Lie group integrators on a Lie group $$G$$ G is presented. The...

Primary 65P10 | Linear and Multilinear Algebras, Matrix Theory | Mathematics | Symplectic integrators | 70G65 | 70G75 | 70HXX | Secondary 37M15 | Order theory | Numerical Analysis | Lie groups | Applications of Mathematics | Math Applications in Computer Science | Computer Science, general | Economics, general | MATHEMATICS | MATHEMATICS, APPLIED | RUNGE-KUTTA METHODS | VARIATIONAL INTEGRATORS | DIFFERENTIAL-EQUATIONS | MANIFOLDS | COMPUTER SCIENCE, THEORY & METHODS | Runge-Kutta method | Integrators | Foundations | Computation | Texts | Mathematical models | Formulas (mathematics)

Primary 65P10 | Linear and Multilinear Algebras, Matrix Theory | Mathematics | Symplectic integrators | 70G65 | 70G75 | 70HXX | Secondary 37M15 | Order theory | Numerical Analysis | Lie groups | Applications of Mathematics | Math Applications in Computer Science | Computer Science, general | Economics, general | MATHEMATICS | MATHEMATICS, APPLIED | RUNGE-KUTTA METHODS | VARIATIONAL INTEGRATORS | DIFFERENTIAL-EQUATIONS | MANIFOLDS | COMPUTER SCIENCE, THEORY & METHODS | Runge-Kutta method | Integrators | Foundations | Computation | Texts | Mathematical models | Formulas (mathematics)

Journal Article

Asian Journal of Control, ISSN 1561-8625, 11/2018, Volume 20, Issue 6, pp. 2088 - 2100

The present work describes a symbolic formulation based on Lie groups and graph theory to obtain the dynamic equations of tree‐structure robotic mechanisms...

Tree‐structure mechanisms | graph theory | geometric modelling | robotics dynamic modelling | Lie groups | Tree-structure mechanisms | AUTOMATION & CONTROL SYSTEMS | Robotics industry | Usage | Machine vision | Models | College teachers | Mechanical engineering | Robots | Robotics

Tree‐structure mechanisms | graph theory | geometric modelling | robotics dynamic modelling | Lie groups | Tree-structure mechanisms | AUTOMATION & CONTROL SYSTEMS | Robotics industry | Usage | Machine vision | Models | College teachers | Mechanical engineering | Robots | Robotics

Journal Article

Journal of Mathematical Physics, ISSN 0022-2488, 12/2019, Volume 60, Issue 12, p. 123508

We consider random stochastic matrices M with elements given by Mij = |Uij|2, with U being uniformly distributed on one of the classical compact Lie groups or...

PHYSICS, MATHEMATICAL | UNIVERSALITY | UNITARY | Eigenvalues | Permutations | Mathematical analysis | Matrix methods | Group theory | Lie groups

PHYSICS, MATHEMATICAL | UNIVERSALITY | UNITARY | Eigenvalues | Permutations | Mathematical analysis | Matrix methods | Group theory | Lie groups

Journal Article

Computational Mechanics, ISSN 0178-7675, 2013, Volume 52, Issue 6, pp. 1281 - 1299

We propose a variational procedure for the recovery of internal variables, in effect extending them from integration points to the entire domain. The objective...

Interpolation | Internal variables | Variational methods | Recovery | Lie groups | MATRIX | MESHES | RELAXATION | FORMULATION | DEFORMATION | REFINEMENT | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | MINIMIZATION | ERROR | LOGARITHM | Algebra | Variables | Finite element method | Lagrange multiplier | Deformation | Lagrange multipliers | Mathematical analysis | Mapping | Polynomials

Interpolation | Internal variables | Variational methods | Recovery | Lie groups | MATRIX | MESHES | RELAXATION | FORMULATION | DEFORMATION | REFINEMENT | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | MINIMIZATION | ERROR | LOGARITHM | Algebra | Variables | Finite element method | Lagrange multiplier | Deformation | Lagrange multipliers | Mathematical analysis | Mapping | Polynomials

Journal Article

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