Dynamical Systems by Steve L. Brunton

source: Steve Brunton        2016年4月23日

1 26:44 Sparse Identification of Nonlinear Dynamics (SINDy)--
This video illustrates a new algorithm for the sparse identification of nonlinear dynamics (SINDy).  In this work, we combine machine learning, sparse regression, and dynamical systems to identify nonlinear differential equations purely from measurement data.
From the Paper:
Discovering governing equations from data by sparse identification of nonlinear dynamical systems.
PNAS 113(15):3932—3937, 2016.
Steven L. Brunton, Joshua L. Proctor, and J. Nathan Kutz  
Code available at: http://faculty.washington.edu/sbrunto...
For more details, see our papers: https://scholar.google.com/citations?...
http://www.pnas.org/content/113/15/3932
http://arxiv.org/abs/1509.03580
2 31:31 Koopman Observable Subspaces & Finite Linear Representations of Nonlinear Dynamics for Control
3 4:38 Koopman Observable Subspaces & Nonlinearization
4 10:18 Koopman Operator Optimal Control
5 30:35 Compressed Sensing and Dynamic Mode Decomposition
6 47:07 Hankel Alternative View of Koopman (HAVOK) Analysis [FULL]
7 22:41 Hankel Alternative View of Koopman (HAVOK) Analysis [SHORT]
8 9:39 Magnetic field reversal and Measles outbreaks: HAVOK models of chaos
9 5:27 Linear model for chaotic Lorenz system [HAVOK]

Koopman Analysis by Steve L. Brunton

source: Steve Brunton    2015年10月22日


1 31:31 Koopman Observable Subspaces & Finite Linear Representations of Nonlinear Dynamics for Control--
This video illustrates the use of the Koopman operator to simulate and control a nonlinear dynamical system using a linear dynamical system on an observable subspace.
From the Paper:
Koopman observable subspaces and finite linear representations of nonlinear dynamical systems for control
by Steven L. Brunton, Bingni W. Brunton, Joshua L. Proctor, and J. Nathan Kutz
For more details, see our papers:
https://scholar.google.com/citations?...
http://arxiv.org/abs/1510.03007
http://arxiv.org/abs/1509.03580
2 4:38 Koopman Observable Subspaces & Nonlinearization
3 10:18 Koopman Operator Optimal Control
4 30:35 Compressed Sensing and Dynamic Mode Decomposition
5 47:07 Hankel Alternative View of Koopman (HAVOK) Analysis [FULL]
6 22:41 Hankel Alternative View of Koopman (HAVOK) Analysis [SHORT]
7 9:39 Magnetic field reversal and Measles outbreaks: HAVOK models of chaos
8 5:27 Linear model for chaotic Lorenz system [HAVOK]

Control Bootcamp by Steve L. Brunton

source: Steve Brunton    2017年1月23日
This course provides a rapid overview of optimal control (controllability, observability, LQR, Kalman filter, etc.). It is not meant to be an exhaustive treatment, but instead provides a high-level overview of some of the main approaches, applied to simple examples in Matlab.
These lectures follow Chapters 1 & 3 from: Machine learning control, by Duriez, Brunton, & Noack https://www.amazon.com/Machine-Learni...
Chapters available at: http://faculty.washington.edu/sbrunto...
Other great references: 
A course in robust control theory. Dullerud & Paganini: https://www.amazon.com/Course-Robust-...
Mathematical treatment based on linear algebra.
Multivariate feedback control. Skogestad & Postle thwaite
https://www.amazon.com/Multivariable-...
Applied treatment with an emphasis on design and practical considerations.

1 19:32 Overview: Overview lecture for bootcamp on optimal and modern control. In this lecture, we discuss the various types of control and the benefits of closed-loop feedback control. 
2 24:47 Linear Systems
3 19:30 Stability and Eigenvalues
4 30:46 Linearizing Around a Fixed Point
5 32:30 Controllability
6 10:49 Controllability, Reachability, and Eigenvalue Placement
7 5:47 Controllability and the Discrete-Time Impulse Response
8 15:24 Degrees of Controllability and Gramians
9 13:34 Controllability and the PBH Test
10 6:57 Cayley-Hamilton Theorem
11 10:30 Reachability and Controllability with Cayley-Hamilton
12 15:09 Inverted Pendulum on a Cart
13 12:55 Eigenvalue Placement for the Inverted Pendulum on a Cart
14 13:04 Linear Quadratic Regulator (LQR) Control for the Inverted Pendulum on a Cart
15 11:03 Motivation for Full-State Estimation
16 8:03 Observability
17 11:38 Full-State Estimation
18 6:11 Kalman Filter
19 8:20 Observability Example in Matlab
20 11:08 Observability Example in Matlab (Part 2)
21 22:12 Kalman Filter Example in Matlab
22 8:34 Linear Quadratic Gaussian (LQG)
23 13:26 LQG Example in Matlab
24 8:13 Introduction to Robust Control
25 12:16 Three Equivalent Representations of Linear Systems
26 18:30 Example Frequency Response (Bode Plot) for Spring-Mass-Damper
27 19:15 Laplace Transforms and the Transfer Function
28 14:47 Benefits of Feedback on Cruise Control Example
29 11:12 Benefits of Feedback on Cruise Control Example (Part 2)
30 23:17 Cruise Control Example with Proportional-Integral (PI) control
31 11:20 Sensitivity and Complementary Sensitivity
32 8:27 Sensitivity and Complementary Sensitivity (Part 2)
33 7:22 Loop shaping
34 12:21 Loop Shaping Example for Cruise Control
35 9:56 Sensitivity and Robustness
36 9:02 Limitations on Robustness
37 5:19 Cautionary Tale About Inverting the Plant Dynamics

Beginning Scientific Computing by Steve L. Brunton and ?

source: AMATH 301     2016年2月19日

1 49:34 Higher-order Integration Schemes: Higher-order numerical integration schemes are considered along the classic schemes of trapezoidal rule and Simpson’s rule.
2 46:59 Ordinary Differential Equations and Time-stepping
3 39:15 Data Fitting with Matlab
4 57:09 Linear Programming and Genetic Algorithms
5 47:10 Numerical Differentiation Methods
6 43:51 Eigenvalues and Eigenvectors
7 48:56 Unconstrained Optimization (Derivative Methods)
8 47:22 Iteration Methods for Ax-b
9 9:01 Supplement: Using ODE45 & Runge-Kutta methods
10 48:03 PCA for Face Recognition
11 48:55 Eigen-decompositions and Iterations
12 44:39 Least-Squares Fitting Methods
13 44:00 Polynomial Fits and Splines
14 45:21 Higher-order Accuracy Schemes for Differentiation and Integration
15 45:35 Unconstrained Optimization (Derivative-Free Methods)
16 44:49 Error and Stability of Time-stepping Schemes
17 43:40 FFT and Image Compression
18 45:16 General Time-stepping and Runge-Kutta Schemes
19 48:39 Theory of the Fourier Transform
20 48:03 Discrete Fourier Transform (DFT) and the Fast Fourier Transform (FFT)
21 44:36 The Singular Value Decomposition (SVD)
22 51:13 Principal Componenet Analysis (PCA)
23 4:40 Supplement: Big systems of ODEs
24 10:10 Supplement: Indexing equations
25 7:45 Supplement: Discrete Fourier Transform
26 5:53 Supplement: Mean Value Theorem
27 29:51 Application of Runge-Kutta to Lorenz Equation
28 41:07 Vectorized Time-step Integrators
29 49:30 Application of Runge-Kutta to Chaotic Dynamics and the Double Pendulum
30 6:07 Supplement: Vector fields and phase-planes
31 41:56 Vectors & Matrices
32 39:25 Logic, Loops, and Iterations
33 41:56 Vectors & Matrices
34 50:59 LU Matrix Decomposition for Ax=b
35 39:40 Gaussian Elimination for Ax=b
36 42:10 Linear Systems of Equations

Data Science for Biologists by Nathan Kutz, Bing Brunton and Steve L. Brunton

source: Data4Bio    2016年6月8日
Course Website: data4bio.com
Instructors:
Nathan Kutz: faculty.washington.edu/kutz
Bing Brunton: faculty.washington.edu/bbrunton
Steve Brunton: faculty.washington.edu/sbrunton

1 2:23 Data Science for Biologists: Introductory Overview
2 19:34 Numerical Calculus: Differential Equations, Part 3
3 10:43 Numerical Calculus: Differential Equations, Part 2
4 8:44 Numerical Calculus: Differential Equations, Part 1
5 8:40 The Basics: Introduction to Matlab, Part 1
6 13:26 The Basics: Introduction to Matlab, Part 3
7 10:17 The Basics: Introduction to Matlab, Part 2
8 10:05 The Basics: Introduction to Matlab, Part 4
9 7:43 Data Fitting: Matlab Implementation, Part 2
10 11:47 Data Fitting: Basic Curve Fitting, Part 3
11 17:55 Dimensionality Reduction: Principal Components Analysis, Part 3
12 5:38 Regression: Linear Regression, Part 1
13 8:24 Plotting and Visualizing Data: Plotting, Part 1
14 20:19  Plotting and Visualizing Data: Data Visualization, Part 1
15 18:50 Clustering and Classification: Introduction, Part 2
16 8:31 The Basics: Loops and Logic, Part 4
17 9:08 The Basics: Loops and Logic, Part 2
18 8:00 The Basics: Loops and Logic, Part 3
19 15:16 The Basics: Loops and Logic, Part 1
20 17:41 Plotting and Visualizing Data: Data Visualization, Part 2
21 13:08 Dimensionality Reduction: Eigenpets, Part 1
22 17:55 Numerical Calculus: Differentiation, Part 2
23 22:42 Dimensionality Reduction: Eigenpets, Part 2
24 8:07 Regression: Linear Regression, Part 3
25 7:59 Numerical Calculus: Integration, Part 2
26 6:37 Regression: Linear Regression, Part 2
27 15:25 Numerical Calculus: Differentiation, Part 1
28 17:56 Numerical Calculus: Integration, Part 1
29 13:10 Regression: Linear Regression, Part 4
30 9:03 Numerical Calculus: Differentiation, Part 3
31 27:08 Clustering and Classification: Introduction, Part 1
32 7:23 Regression: Beyond Linear Regression, Part 3
33 18:19 Fourier Transforms: Image Compression, Part 2
34 10:30 Fourier Transforms: Image Compression, Part 3
35 17:03 Regression: Beyond Linear Regression, Part 2
36 19:21 Clustering and Classification: Introduction, Part 3
37 12:27 Data Fitting: Matlab Implementation, Part 1
38 9:44 Regression: Beyond Linear Regression, Part 1
39 12:10 Fourier Transforms: Image Compression, Part 1
40 8:38 Clustering and Classification: Advanced Methods, Part 4
41 16:19 Dimensionality Reduction: Principal Components Analysis, Part 2
42 13:56 Dimensionality Reduction: Principal Components Analysis, Part 1
43 9:34 Regression: Model Selection and Validation, Part 2
44 12:06 Data Fitting: Basic Curve Fitting, Part 1
45 11:14 Data Fitting: Basic Curve Fitting, Part 2
46 10:10 Fourier Transforms: Discrete Fourier Transform, Part 1
47 27:01 Clustering and Classification: Advanced Methods, Part 1
48 11:59 Fourier Transforms: Fast Fourier Transform, Part 1
49 12:37 Regression: Model Selection and Validation, Part 3
50 9:17 Data Fitting: Basic Curve Fitting, Part 3
51 8:24 Plotting and Visualizing Data: Plotting, Part 2
52 10:20 Fourier Transforms: Fast Fourier Transform, Part 2
53 18:19 Fourier Transforms: Discrete Fourier Transform, Part 3
54 4:15 Data Fitting: Basic Curve Fitting, Part 4
55 16:50 Plotting and Visualizing Data: Plotting, Part 3
56 11:12 Regression: Model Selection and Validation, Part 1
57 16:41 Clustering and Classification: Advanced Methods, Part 2
58 9:29 Fourier Transforms: Fast Fourier Transform, Part 3
59 15:08 Fourier Transforms: Discrete Fourier Transform, Part 2
60 12:45 Dimensionality Reduction: High Dimensional Data, Part 1
61 16:39 Systems of Equations: Eigenvalues and Eigenvectors, Part 2
62 11:36 Systems of Equations: Eigenvalues and Eigenvectors, Part 1
63 11:01 Systems of Equations: Solving Linear Systems, Part 4
64 6:13 Data Fitting: Polynomial Fitting and Splines, Part 3
65 8:56 Systems of Equations: Solving Linear Systems, Part 1
66 17:22 Systems of Equations: Solving Linear Systems, Part 2
67 11:58 Systems of Equations: Eigenvalues and Eigenvectors, Part 4
68 7:35 Data Fitting: Polynomial Fitting and Splines, Part 2
69 11:19 Systems of Equations: Eigenvalues and Eigenvectors, Part 3
70 6:07 Plotting and Visualizing Data: Communicating with Data, Part 3
71 14:51 Plotting and Visualizing Data: Communicating with Data, Part 2
72 9:42 Plotting and Visualizing Data: Communicating with Data, Part 1
73 15:35 Systems of Equations: Modeling with Matrices and Vectors, Part 3
74 12:10 Systems of Equations: Modeling with Matrices and Vectors, Part 2
75 19:03 Clustering and Classification: Support Vector Machines and Decision Trees, Part 1
76 7:54 Clustering and Classification: Support Vector Machines and Decision Trees, Part 3
77 22:00 Clustering and Classification: Support Vector Machines and Decision Trees, Part 2
78 3:08 Data Science for Biologists: Introduction to the Lightboard
79 3:40 Data Science for Biologists: Introduction to Matlab
80 3:04 Data Science for Biologists: Syllabus

Finite-time Lyapunov exponents by Steve Brunton and ?

source: Steve Brunton       2015年9月29日  
Finite-time Lyapunov exponent (FTLE) field for an airfoil in a rapid pitch-up maneuver at low Reynolds number. The airfoil pitches up from 0 deg to 32 deg in a fraction of a convective time at Re=300. For more details, see our papers:

https://scholar.google.com/citations?... 

http://dx.doi.org/10.1063/1.3270044 

http://dx.doi.org/10.1017/jfm.2013.163

1 0:15 FTLE field for a pitching airfoil at low Reynolds number
2 0:15 FTLE field for a pitching airfoil at low Reynolds number (with Force)
3 0:27 Attracting FTLE field for plunging plate in a quiescent fluid
4 0:27 Repelling FTLE field for plunging plate in a quiescent fluid
5 0:27 Vorticity field for plunging plate in a quiescent fluid
6 0:14 FTLE field for a plunging plate at low Reynolds number
7 0:14 FTLE field for a pitching plate at low Reynolds number
8 0:49 FLTE field showing separation bubble bursting for flat plate airfoil
9 0:07 FTLE field for an airfoil in rapid plunge maneuver at low Reynolds number
10 0:10 Validation of forward-time FTLE field for vortex shedding
11 0:10 Validation of backward-time FTLE field for vortex shedding
12 0:41 Particles starting near positive-time LCS attract onto negative-time LCS
13 0:31 Particles starting near positive-time LCS attract onto negative-time LCS (zoom out)
14 0:26 Particle trajectories integrated through the double gyre illustrate heteroclinic tangle
15 0:02 Airfoil pitching about leading-edge (+/- 20 deg, Re=100), with FTLE visualization
16 0:02 Airfoil pitching about quarter-chord (+/- 20 deg, Re=100), with FTLE visualization
17 0:02 Airfoil pitching about mid-chord (+/- 20 deg, Re=100), with FTLE visualization
18 0:02 Airfoil pitching about three-quarter-chord (+/- 20 deg, Re=100), with FTLE visualization
19 0:02 Airfoil pitching about trailing-edge (+/- 20 deg, Re=100), with FTLE visualization
20 0:02 Airfoil pitching about leading-edge (+/- 27.1 deg, Re=100), with FTLE visualization
21 0:02 Airfoil pitching about quarter-chord (+/- 27.1 deg, Re=100), with FTLE visualization
22 0:02 Airfoil pitching about mid-chord (+/- 27.1 deg, Re=100), with FTLE visualization
23 0:02 Airfoil pitching about three-quarter-chord (+/- 27.1 deg, Re=100), with FTLE visualization
24 0:02 Airfoil pitching about trailing-edge (+/- 27.1 deg, Re=100), with FTLE visualization
25 0:02 Airfoil pitching about leading-edge (+/- 43.2 deg, Re=100), with FTLE visualization
26 0:02 Airfoil pitching about quarter-chord (+/- 43.2 deg, Re=100), with FTLE visualization
27 0:02 Airfoil pitching about mid-chord (+/- 43.2 deg, Re=100), with FTLE visualization
28 0:02 Airfoil pitching about three-quarter-chord (+/- 43.2 deg, Re=100), with FTLE visualization
29 3:00 Stirring Faces: Mixing in a Quiescent Fluid

Mechanical Engineering Analysis (Winter 2015) by Steve Brunton | University of Washington

source: Steve Brunton      2016年4月27日
ME565 - Mechanical Engineering Analysis (Winter 2015) by Steve Brunton | University of Washington
Notes: http://faculty.washington.edu/sbrunto...
Course Website: http://faculty.washington.edu/sbrunto...
http://faculty.washington.edu/sbrunton/

Lecture 1: Complex numbers and functions 49:02
2: Roots of unity, branch cuts, analytic functions, and the Cauchy-Riemann conditions 50:19
3: Integration in the complex plane (Cauchy-Goursat Integral Theorem) 50:13
4: Cauchy Integral Formula 47:59
5: ML Bounds and examples of complex integration 50:15
6: Inverse Laplace Transform and the Bromwich Integral 48:49
7: Canonical Linear PDEs: Wave equation, Heat equation, and Laplace's equation 50:18
8: Heat Equation: derivation and equilibrium solution in 1D (i.e., Laplace's equation) 49:28
9: Heat Equation in 2D and 3D. 2D Laplace Equation (on rectangle) 47:16
10: Analytic Solution to Laplace's Equation in 2D (on rectangle) 48:05
11: Numerical Solution to Laplace's Equation in Matlab. Intro to Fourier Series 48:58
12: Fourier Series 50:23
13: Infinite Dimensional Function Spaces and Fourier Series 49:03
14: Fourier Transforms 49:09
15: Properties of Fourier Transforms and Examples 48:22
16: Discrete Fourier Transforms (DFT) 48:39
16 Bonus: DFT in Matlab 7:45
17: Fast Fourier Transforms (FFT) and Audio 48:03
18: FFT and Image Compression 43:40
19: Fourier Transform to Solve PDEs: 1D Heat Equation on Infinite Domain 42:33
20: Numerical Solutions to PDEs Using FFT 50:20
21: The Laplace Transform 49:51
22: Laplace Transform and ODEs 49:48
23: Laplace Transform and ODEs with Forcing and Transfer Functions 49:24
24: Convolution integrals, impulse and step responses 50:25
25: Laplace transform solutions to PDEs 50:23
26: Solving PDEs in Matlab using FFT 50:16
27: SVD Part 1 50:12
28: SVD Part 2 48:46
29: SVD Part 3 47:19

Mechanical Engineering Analysis (Fall 2014) by Steve L. Brunton | University of Washington

source: Steve Brunton      2016年4月25日
ME564 - Mechanical Engineering Analysis (Fall 2014) by Steve L. Brunton | University of Washington
Notes: http://faculty.washington.edu/sbrunto...
Matlab code: http://faculty.washington.edu/sbrunto...
Course Website: http://faculty.washington.edu/sbrunto...
http://faculty.washington.edu/sbrunton/

Lecture 1: Overview of engineering mathematics 41:16 Overview of engineering mathematics and example weather model in Matlab.
2: Review of calculus and first order linear ODEs 48:43
3: Taylor series and solutions to first and second order linear ODEs 53:23
4: Second order harmonic oscillator, characteristic equation, ode45 in Matlab 51:38
5: Higher-order ODEs, characteristic equation, matrix systems of first order ODEs 49:19
6: Matrix systems of first order equations using eigenvectors and eigenvalues 48:07
7: Eigenvalues, eigenvectors, and dynamical systems 46:54
8: 2x2 systems of ODEs (with eigenvalues and eigenvectors), phase portraits 48:42
9: Linearization of nonlinear ODEs, 2x2 systems, phase portraits 48:40
10: Examples of nonlinear systems: particle in a potential well 50:20
11: Degenerate systems of equations and non-normal energy growth 50:15
12: ODEs with external forcing (inhomogeneous ODEs) 49:36
13: ODEs with external forcing (inhomogeneous ODEs) and the convolution integral 49:52
14: Numerical differentiation using finite difference 49:30
15: Numerical differentiation and numerical integration 48:37
16: Numerical integration and numerical solutions to ODEs 46:33
17: Numerical solutions to ODEs (Forward and Backward Euler) 50:24
18: Runge-Kutta integration of ODEs and the Lorenz equation 48:57
19: Vectorized integration and the Lorenz equation 48:12
20: Chaos in ODEs (Lorenz and the double pendulum) 49:00
21: Linear algebra in 2D and 3D: inner product, norm of a vector, and cross product 48:40
22: Div, Grad, and Curl 49:18
23: Gauss's Divergence Theorem 49:29
24: Directional derivative, continuity equation, and examples of vector fields 45:44
25: Stokes' theorem and conservative vector fields 49:52
26: Potential flow and Laplace's equation 45:57
27: Potential flow, stream functions, and examples 54:15
28: ODE for particle trajectories in a time-varying vector field 49:24