Degrees of Controllability and Gramians [Control Bootcamp]
This lecture discusses degrees of controllability using the controllability Gramian and the singular value decomposition of the controllability matrix. These lectures follow Chapter 8 from: "Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control" by Brunton
From playlist Control Bootcamp
Controllability of a Linear System: The Controllability Matrix and the PBH Test
In this video we explore controllability of a linear system. We discuss two methods to test for controllability, the controllability matrix as well as the PBH test. Topics and time stamps: 0:00 – Introduction and definition. 1:04 – Controllability of a dog. 3:48 – Controllability matrix.
From playlist Control Theory
Example of Gram-Schmidt Orthogonalization
Linear Algebra: Construct an orthonormal basis of R^3 by applying the Gram-Schmidt orthogonalization process to (1, 1, 1), (1, 0, 1), and (1, 1, 0). In addition, we show how the Gram-Schmidt equations allow one to factor an invertible matrix into an orthogonal matrix times an upper tria
From playlist MathDoctorBob: Linear Algebra I: From Linear Equations to Eigenspaces | CosmoLearning.org Mathematics
This video provides a lesson on dependent function and verifying given functions are linear dependent. Site: http://mathispower4u.com
From playlist Second Order Differential Equations
Kristi Morgansen: "Analytical & Empirical Tools for Nonlinear Network Observability in Autonomou..."
Mathematical Challenges and Opportunities for Autonomous Vehicles 2020 Workshop IV: Social Dynamics beyond Vehicle Autonomy "Analytical and Empirical Tools for Nonlinear Network Observability in Autonomous Systems" Kristi Morgansen - University of Washington Abstract: A fundamental eleme
From playlist Mathematical Challenges and Opportunities for Autonomous Vehicles 2020
Controllability [Control Bootcamp]
This lecture explores when a linear system is controllable. We begin with the simple test in terms of the rank of the controllability matrix on a few intuitive examples. Chapters available at: http://databookuw.com/databook.pdf These lectures follow Chapter 8 from: "Data-Driven Science
From playlist Control Bootcamp
Peter Benner: Matrix Equations and Model Reduction, Lecture 4
Peter Benner from the Max Planck Institute presents: Matrix Equations and Model Reduction; Lecture 4
From playlist Gene Golub SIAM Summer School Videos
Data-Driven Control: Balanced Truncation Example
In this lecture, we explore the balanced truncation procedure on an example in Matlab. In particular, we demonstrate the ability of a balancing transformation to make the controllability and observability Gramians equal and diagonal. Code: faculty.washington.edu/sbrunton/DataDrivenCont
From playlist Data-Driven Control with Machine Learning
Everything You Need to Know About Control Theory
Control theory is a mathematical framework that gives us the tools to develop autonomous systems. Walk through all the different aspects of control theory that you need to know. Some of the concepts that are covered include: - The difference between open-loop and closed-loop control - How
From playlist Control Systems in Practice
Fastest Identification in Linear Systems by Alexandre Proutiere
Program Advances in Applied Probability II (ONLINE) ORGANIZERS: Vivek S Borkar (IIT Bombay, India), Sandeep Juneja (TIFR Mumbai, India), Kavita Ramanan (Brown University, Rhode Island), Devavrat Shah (MIT, US) and Piyush Srivastava (TIFR Mumbai, India) DATE: 04 January 2021 to 08 Januar
From playlist Advances in Applied Probability II (Online)
Data-Driven Control: Change of Variables in Control Systems
In this lecture, we discuss how linear control systems transform under a change of coordinates in the state variable. This will be useful to derive balancing transformations that identify the most jointly controllable and observable states. https://www.eigensteve.com/
From playlist Data-Driven Control with Machine Learning
Nithin Govindarajan: "Spline-based separable expansions for approximation, regression & classifi..."
Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021 Workshop I: Tensor Methods and their Applications in the Physical and Data Sciences "Spline-based separable expansions for approximation, regression and classification" Nithin Govindarajan - KU Leuven, ESAT ST
From playlist Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021
PROGRAM NAME :WINTER SCHOOL ON STOCHASTIC ANALYSIS AND CONTROL OF FLUID FLOW DATES Monday 03 Dec, 2012 - Thursday 20 Dec, 2012 VENUE School of Mathematics, Indian Institute of Science Education and Research, Thiruvananthapuram Stochastic analysis and control of fluid flow problems have
From playlist Winter School on Stochastic Analysis and Control of Fluid Flow
Data-Driven Control: Balancing Transformation
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 reduction (balanced truncation), where a handful of the most controllable and observable state direc
From playlist Data-Driven Control with Machine Learning
Control Bootcamp: Observability Example in Matlab (Part 2)
This video continues to explore observability in Matlab on the example system of an inverted pendulum on a cart. We look at the observability Gramian. Code available at: faculty.washington.edu/sbrunton/control_bootcamp_code.zip These lectures follow Chapters 1 & 3 from: Machine learnin
From playlist Control Bootcamp
Controllability, Reachability, and Eigenvalue Placement [Control Bootcamp]
This lecture explains the equivalence of controllability, reachability, and the ability to arbitrarily place eigenvalues of the closed loop system. Chapters available at: http://databookuw.com/databook.pdf These lectures follow Chapter 8 from: "Data-Driven Science and Engineering: Machin
From playlist Control Bootcamp
Gene Golub's SIAM summer school, Matrix Equations and Model Reduction, Lecture 1
Gene Golub's SIAM summer school presents Matrix Equations and Model Reduction by Peter Benner; Lecture 1
From playlist Gene Golub SIAM Summer School Videos
Passivity-Based Control to Guarantee Stability | Control Systems in Practice
Learn about passivity-based control to guarantee closed-loop stability of feedback systems. Consider different ways to assess the stability of systems other than looking at gain and phase margin. Control System Toolbox: https://bit.ly/3LyCeHa?s_eid=PSM_15028 -----------------------------
From playlist Control Systems in Practice