Algorithmes numriques en commande: tat de l'art et perspectives

An input device (such as a rotational hand crank) receives a constantly-applied motion, and outputs a signal to a controller which, in turn, sends an appropriate signal to an electric motor, which is connected to the chair via a mechanical transmission. The wheel is removably mounted in front of a wheelchair such that the front wheels of the chair are lifted above the ground. The device is generally steered manually, such as by pivoting an input device to one side.

[1]  Andrew P. Paplinski,et al.  Numerical Operations with Polynomial Matrices: Application To Multi-Variable Dynamic Compensator Design , 1992 .

[2]  Ilse C. F. Ipsen.  Accurate Eigenvalues for Fast Trains , 2004 .

[3]  P. Van Dooren,et al.  The basics of developing numerical algorithms , 2004 .

[4]  E. E. Osborne.  On pre-conditioning matrices , 1959, ACM '59.

[5]  Hans J. Stetter.  Numerical Polynomial Algebra : Concepts and Algorithms , 2000 .

[6]  A. Edelman,et al.  Polynomial roots from companion matrix eigenvalues , 1995 .

[7]  Michael Sebek,et al.  The polynomial toolbox for matlab , 1997 .

[8]  P. Dooren.  The Computation of Kronecker's Canonical Form of a Singular Pencil , 1979 .

[9]  F. Kraffer.  Polynomial matrix to state space conversion without polynomial reduction , 1996 .

[10]  Françoise Tisseur,et al.  Perturbation theory for homogeneous polynomial eigenvalue problems , 2003 .

[11]  G. Stewart,et al.  An Algorithm for Generalized Matrix Eigenvalue Problems. , 1973 .

[12]  N. Nichols,et al.  Robust pole assignment in linear state feedback , 1985 .

[13]  P. Van Dooren,et al.  The basics of developing numerical algorithms , 2004, IEEE Control Systems.

[14]  Didier Henrion,et al.  A Toeplitz algorithm for polynomial J-spectral factorization , 2004, Autom..

[15]  V. Pan,et al.  Polynomial and matrix computations (vol. 1): fundamental algorithms , 1994 .

[16]  Denyse Baillargeon,et al.  Bibliographie , 1929 .

[17]  Jovan D. Stefanovski.  Polynomial J-spectral factorization in minimal state space , 2003, Autom..

[18]  Nicholas J. Higham,et al.  The Conditioning of Linearizations of Matrix Polynomials , 2006, SIAM J. Matrix Anal. Appl..

[19]  A. Turing.  ROUNDING-OFF ERRORS IN MATRIX PROCESSES , 1948 .

[20]  William H. Press,et al.  Numerical recipes in C. The art of scientific computing , 1987 .

[21]  Vladimír Kučera,et al.  Diophantine equations in control - A survey , 1993, Autom..

[22]  Nicholas J. Higham,et al.  INVERSE PROBLEMS NEWSLETTER , 1991 .

[23]  H. Abou-Kandil,et al.  Matrix Riccati Equations in Control and Systems Theory , 2003, IEEE Transactions on Automatic Control.

[24]  V. Pan,et al.  Polynomial and Matrix Computations , 1994, Progress in Theoretical Computer Science.

[25]  L.C.G.J.M. Habets,et al.  Book review: Introduction to mathematical systems theory, a behavioral approach , 2000 .

[26]  T. Beelen,et al.  Numerical computation of a coprime factorization of a transfer function matrix , 1987 .

[27]  Didier Henrion,et al.  Detecting infinite zeros in polynomial matrices , 2005, IEEE Transactions on Circuits and Systems II: Express Briefs.

[28]  Didier Henrion,et al.  On the application of displacement structure methods to obtain null-spaces of polynomial matrices , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[29]  W. Wolovich.  State-space and multivariable theory , 1972 .

[30]  J. Rice.  A Theory of Condition , 1966 .

[31]  Peter Lancaster,et al.  The theory of matrices , 1969 .

[32]  Jack J. Dongarra,et al.  Guest Editors Introduction to the top 10 algorithms , 2000, Comput. Sci. Eng..

[33]  Xiaomei Yang.  Rounding Errors in Algebraic Processes , 1964, Nature.

[34]  A. Varga.  A Descriptor Systems Toolbox for MATLAB , 2000, CACSD. Conference Proceedings. IEEE International Symposium on Computer-Aided Control System Design (Cat. No.00TH8537).

[35]  Didier Henrion,et al.  NUMERICAL STABILITY OF BLOCK TOEPLITZ ALGORITHMS IN POLYNOMIAL MATRIX COMPUTATIONS , 2005 .

[36]  I. VÁŇOVÁ,et al.  Academy of Sciences of the Czech Republic , 2020, The Grants Register 2021.

[37]  A. Varga.  Computation of least order solutions of linear rational equations , 2004 .

[38]  Hong Zhang,et al.  NUMERICAL CONDITION OF POLYNOMIALS IN DIFFERENT FORMS , 2001 .

[39]  Jean-Luc Chabert,et al.  A history of algorithms: from the pebble to the microchip , 1999 .

[40]  J. C. Basilio,et al.  A robust solution of the generalized polynomial Bezout identity , 2004 .

[41]  G. W. Stewart,et al.  Matrix algorithms , 1998 .

[42]  Michael L. Overton,et al.  Numerical Computing with IEEE Floating Point Arithmetic , 2001 .

[43]  P. Dooren,et al.  The eigenstructure of an arbitrary polynomial matrix : Computational aspects , 1983 .

[44]  Vladimír Kucera,et al.  Discrete linear control: The polynomial equation approach , 1985, IEEE Transactions on Systems, Man, and Cybernetics.

[45]  高等学校計算数学学報編輯委員会編,et al.  高等学校計算数学学報 = Numerical mathematics , 1979 .

[46]  J. H. Wilkinson.  The algebraic eigenvalue problem , 1966 .

[47]  D. Henrion,et al.  BLOCK TOEPLITZ ALGORITHMS FOR POLYNOMIAL MATRIX NULL-SPACE COMPUTATION , 2004 .

[48]  Frann Coise Tisseur.  Backward Error and Condition of Polynomial Eigenvalue Problems , 1999 .

[49]  Adrian Roberts.  Polynomial Methods in Optimal Control and Filtering , 1993 .

[50]  Jan C. Willems,et al.  Introduction to mathematical systems theory: a behavioral approach, Texts in Applied Mathematics 26 , 1999 .

[51]  George Miminis,et al.  A direct algorithm for pole assignment of time-invariant multi-input linear systems using state feedback , 1988, Autom..

[52]  W. Press,et al.  Numerical Recipes in Fortran: The Art of Scientific Computing.@@@Numerical Recipes in C: The Art of Scientific Computing. , 1994 .

[53]  Michael Sebek,et al.  Reliable numerical methods for polynomial matrix triangularization , 1999, IEEE Trans. Autom. Control..

[54]  Charles L. Lawson,et al.  Basic Linear Algebra Subprograms for Fortran Usage , 1979, TOMS.

[55]  N.J. Higham,et al.  The sensitivity of computational control problems , 2004, IEEE Control Systems.

[56]  Paul Van Dooren,et al.  Normwise Scaling of Second Order Polynomial Matrices , 2004, SIAM J. Matrix Anal. Appl..

[57]  Zhonggang Zeng.  Computing multiple roots of inexact polynomials , 2005, Math. Comput..

[58]  Paul Van Dooren,et al.  Optimal Scaling of Companion Pencils for the QZ-Algorithm , 2003 .

[59]  Hans J. Stetter,et al.  Numerical polynomial algebra , 2004 .

[60]  Karl Meerbergen,et al.  The Quadratic Eigenvalue Problem , 2001, SIAM Rev..

[61]  Volker Mehrmann,et al.  Vector Spaces of Linearizations for Matrix Polynomials , 2006, SIAM J. Matrix Anal. Appl..

[62]  C. Paige,et al.  An algorithm for pole assignment of time invariant linear systems , 1982 .

[63]  A. Laub,et al.  Numerical linear algebra aspects of control design computations , 1985, IEEE Transactions on Automatic Control.

[64]  J. Neumann,et al.  Numerical inverting of matrices of high order , 1947 .

[65]  C. Reinsch,et al.  Balancing a matrix for calculation of eigenvalues and eigenvectors , 1969 .

[66]  Paul Van Dooren,et al.  Optimal scaling of block companion pencils , 2004 .

[67]  Juan Carlos Zúñiga Anaya,et al.  Comparison of algorithms for computing infinite structural indices of polynomial matrices , 2003, 2003 European Control Conference (ECC).

[68]  William H. Press,et al.  Numerical Recipes in FORTRAN - The Art of Scientific Computing, 2nd Edition , 1987 .

[69]  Cleve B. Moler,et al.  Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later , 1978, SIAM Rev..