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Data-Driven Control: Balancing Transformation
0

Data-Driven Control: Balancing Transformation

Steve Brunton
11 min
Intermediate
Video
Theory

In this lecture, we derive the balancing coordinate transformation that makes the controllability and observability Gramians equal and diagonal. This is the critical step in balanced model...

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Dynamic Mode Decomposition (Examples)
0

Dynamic Mode Decomposition (Examples)

Steve Brunton
7 min
Intermediate
Video
Theory

In this video, we continue to explore the dynamic mode decomposition (DMD). In particular, we look at recent methodological extensions and application areas in fluid dynamics, disease...

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SVD and Alignment: A Cautionary Tale
0

SVD and Alignment: A Cautionary Tale

Steve Brunton
7 min
Intermediate
Video
Theory

This video describes the importance of data alignment when performing the singular value decomposition (SVD). Translations and rotations both present challenges for the SVD.

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Linear Regression 1 [Python]
0

Linear Regression 1 [Python]

Steve Brunton
6 min
Intermediate
Video
Application

This video describes how the singular value decomposition (SVD) can be used for linear regression in Python (part 1).

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Derivation of Rodrigues’ Rotation Formula
0

Derivation of Rodrigues’ Rotation Formula

Christopher Lum
43 min
Intermediate
Video
Theory

In this video we explain and derive Rodrigues’ Rotation Formula. This functions describes how to rotate an arbitrary vector about another arbitrary axis of rotation. This has applications to...

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NASA's General Mission Analysis Tool (GMAT)
0

NASA's General Mission Analysis Tool (GMAT)

NASA Technology Transfer Program
Advanced
Software
Application

NASA's GMAT is the worlds only enterprise, multi-mission, open source software system for space mission design, optimization, and navigation. The system supports missions in flight regimes...

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SVD: Eigenfaces 2 [Matlab]
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SVD: Eigenfaces 2 [Matlab]

Steve Brunton
8 min
Intermediate
Video
Application

This video describes how the singular value decomposition (SVD) can be used to efficiently represent human faces, in the so-called "eigenfaces" (Matlab code, part 2).

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MATLAB Sensor Array Analyzer App
0

MATLAB Sensor Array Analyzer App

Mathworks
Intermediate
App
Application

The Sensor Array Analyzer app enables you to construct and analyze common sensor array configurations. These configurations range from 1-D to 3-D arrays of antennas, sonar transducers, and...

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Data-Driven Control: Balanced Models with ERA
0

Data-Driven Control: Balanced Models with ERA

Steve Brunton
6 min
Intermediate
Video
Theory

In this lecture, we connect the eigensystem realization algorithm (ERA) to balanced proper orthogonal decomposition (BPOD). In particular, if enough data is collected, then ERA produces...

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Inner Products in Hilbert Space
0

Inner Products in Hilbert Space

Steve Brunton
8 min
Intermediate
Video
Theory

This video will show how the inner product of functions in Hilbert space is related to the standard inner product of vectors of data.

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Dynamic Mode Decomposition (Code)
0

Dynamic Mode Decomposition (Code)

Steve Brunton
8 min
Intermediate
Video
Application

In this video, we code up the dynamic mode decomposition (DMD) in Matlab and use it to analyze the fluid flow past a circular cylinder at low Reynolds number.

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