mathematica advanced numerical methods
TRANSCRIPT
STATE-OF-THE-ART ALGORITHMS FOR SYSTEMS AND CONTROL
KEY BENEFITS
Seamlessly integrates into the Control System Professional framework and takes advantage of the extensive graphical capabilities and automatic arbitrary-precision control in Mathematica.
Implements reliable and robust numerical algorithms, including several new methods for Lyapunov, Sylvester, and Riccati equations, to solve a wide class of control problems and linear algebra problems with applications in control theory.
Automatically selects suitable algorithms based on the application, but lets advanced users choose from several computationally viable numerical algorithms to solve each problem.
Includes a brief theoretical description of the algorithms and methods used in the package.
Advanced Numerical Methods extends the
scope of Control System Professional with
an extensive collection of state-of-the-
art numerical algorithms for the analysis
and design of linear control systems. It
seamlessly integrates into the Control
System Professional framework using the
same data structures and some of the
same function names. You can choose the
most appropriate algorithm for a given
task or have the package choose a suitable
method automatically based on the size
of the problem, the precision of the data,
and the accuracy required. Combined with
Mathematica’s extensive graphical capabilities
and automatic arbitrary-precision control,
Advanced Numerical Methods provides a
superior environment for solving industrial
and research control problems.
For more information, visit www.wolfram.com/anm.
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CONTROL SYSTEM PROFESSIONAL SUITE COMPONENT
STATE-OF-THE-ART ALGORITHMS FOR SYSTEMS AND CONTROL
Advanced Numerical Methods provides a large number of examples and case studies based on specific applications in engineering, manufacturing, and other fields.
STATE-OF-THE-ART ALGORITHMS FOR SYSTEMS AND CONTROL
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Solutions of the Lyapunov and Sylvester Matrix EquationsSchur methods for solving the Lyapunov equations Hessenberg-Schur methods for solving the Sylvester equations Direct computation of the Cholesky factors of the controllability and observability Gramians
Solutions of the Algebraic Riccati EquationsSchur, Newton’s, and matrix-sign methods for solving the discrete and continuous matrix algebraic Riccati equations Inverse-free methods based on the generalized eigenvector and the generalized Schur decompositions
Reduction to Controller-Hessenberg and Observer-Hessenberg FormsComputation of the block controller-Hessenberg and observer-Hessenberg forms
Controllability and Observability TestsControllability and observability tests using the controller-Hessenberg and observer-Hessenberg forms Controllability and observability tests using the Cholesky factors of the controllability and observability Gramians
Pole AssignmentRecursive, explicit QR, and Schur methods for multi-input systems RQ modification of the recursive method and the implicit RQ method for single-input systems Projection technique for the partial pole assignment problem
Feedback StabilizationPole assignment algorithms for feedback stabilization with constraints on the damping factor, settling time, damping ratio, and natural frequency Lyapunov shift and partial Lyapunov shift algorithms for feedback stabilization
Design of the Reduced-Order State Estimator (Observer)Reduced-order state estimator design using the pole assignment approach Reduced-order state estimator design using the recursive triangular, the block recursive triangular, the recursive bidiagonal, and the block recursive bidiagonal algorithms for solving the Sylvester-observer equation
Model ReductionSchur and square-root methods for selecting the dominant subsystem and model reduction
Model IdentificationSystem identification from the impulse responses, frequency responses, and generic input-output data
Miscellaneous Matrix Decompositions and FunctionsComputation of the generalized eigenvalues, generalized eigenvectors, and generalized Schur decomposition Computation of the ordered generalized Schur decomposition
Advanced Numerical Methods Features
For more information, visit www.wolfram.com/anm.
Advanced Numerical Methods adds numerous state-of-the-art algorithms to the familiar Control System Professional and Mathematica framework.
CONTROL SYSTEM PROFESSIONAL SUITE COMPONENT
STATE-OF-THE-ART ALGORITHMS FOR SYSTEMS AND CONTROL
Over 1900 built-in functions, including the world‘s largest collection of advanced algorithms for numeric and symbolic computation, discrete mathematics, statistics, data analysis, graphics, visualization, and general programming
Multi-paradigm symbolic programming language with support for procedural, functional, list-based, object-oriented, and symbolic programming constructs
Automatic precision control and support for exact integers of arbitrary length, rationals, floating-point real and complex numbers, and arbitrary-precision real and complex numbers
User-defined or automatic algorithm selection for optimal performance
Fully programmable 2D and 3D visualization with over 50 built-in plot types
Fully integrated piecewise functions
High-speed numerical linear algebra with performance equal to specialized numeric libraries
High-performance optimization and linear programming functions
Wide-ranging support for sparse matrices
Flexible import and export of over 70 data, image, and sparse matrix formats
Industrial-strength string manipulation
Highly optimized binary data I/O
Built-in universal database connectivity
Integrated web services support
Language bindings to C, Java, .NET, and scripting languages
MathematicaMark™ benchmarking tool
Toolkit for creating graphical user interfaces
General Mathematica
Features
TechnicalRequirements
Advanced Numerical Methods requires Mathematica 4.2 or later and Control System Professional 2 or later. Advanced Numerical Methods is available for Windows, Mac OS X, Linux, and Unix. For a more detailed list, see www.wolfram.com/mathematica/platforms.
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