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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