In control theory, a control-Lyapunov function (CLF) is an extension of the idea of Lyapunov function to systems with control inputs. The ordinary Lyapunov function is used to test whether a dynamical system is (Lyapunov) stable or (more restrictively) asymptotically stable. Lyapunov stability means that if the system starts in a state in some domain D, then the state will remain in D for all time. For asymptotic stability, the state is also required to converge to . A control-Lyapunov function is used to test whether a system is asymptotically stabilizable, that is whether for any state x there exists a control such that the system can be brought to the zero state asymptotically by applying the control u. The theory and application of control-Lyapunov functions were developed by and Eduardo D. Sontag in the 1980s and 1990s. (Wikipedia).
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
Fuzzy control of inverted pendulum
Fuzzy control of inverted pendulum, State-feedback controller is designed based on T-S fuzzy model with the consideration of system stability and performance.
From playlist Demonstrations
What Is Gain Scheduling? | Control Systems in Practice
Often, the best control system is the simplest. When the system you’re trying to control is highly nonlinear, this can lead to very complex controllers. This video continues our discussion on control systems in practice by talking about a simple form of nonlinear control: gain scheduling.
From playlist Control Systems in Practice
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
What Control Systems Engineers Do | Control Systems in Practice
The work of a control systems engineer involves more than just designing a controller and tuning it. Over the course of a project, designing the controller might be a relatively small part of your day-to-day job. Depending on the size and phase of the project, your responsibilities and the
From playlist Control Systems in Practice
What Is PID Control? | Understanding PID Control, Part 1
Chances are you’ve interacted with something that uses a form of this control law, even if you weren’t aware of it. That’s why it is worth learning a bit more about what this control law is, and how it helps. PID is just one form of feedback controller. It is the simplest type of contro
From playlist Understanding PID Control
Aaron Ames: "Safety-Critical Control of Autonomous Systems"
Mathematical Challenges and Opportunities for Autonomous Vehicles 2020 Workshop II: Safe Operation of Connected and Autonomous Vehicle Fleets "Safety-Critical Control of Autonomous Systems" Aaron Ames - California Institute of Technology Abstract: Guaranteeing safe behavior is a critical
From playlist Mathematical Challenges and Opportunities for Autonomous Vehicles 2020
Lyapunov Stability via Sperner's Lemma
We go on whistle stop tour of one of the most fundamental tools from control theory: the Lyapunov function. But with a twist from combinatorics and topology. For more on Sperner's Lemma, including a simple derivation, please see the following wonderful video, which was my main source of i
From playlist Summer of Math Exposition Youtube Videos
4 Ways to Implement a Transfer Function in Code | Control Systems in Practice
Check out the other videos in the series: Part 1 - What Does a Controls Engineer Do? https://youtu.be/ApMz1-MK9IQ Part 2 - What Is Gain Scheduling? https://youtu.be/YiUjAV1bhKs Part 3 - What Is Feedforward Control? https://youtu.be/FW_ay7K4jPE Part 4 - Why Time Delay Matters https://youtu
From playlist Control Systems in Practice
Eigenvalues and Modes of Linear Systems
In this video we discuss how the eigenvalues of the A matrix lead to the modes of a linear state space system. We will also examine how to chose initial conditions to excite a specific mode. In other words, we use a carefully chosen initial condition to ensure that the state response of
From playlist Control Theory
Chaotic properties of spin lattices at high temperatures by Boris V. Fine
PROGRAM THERMALIZATION, MANY BODY LOCALIZATION AND HYDRODYNAMICS ORGANIZERS: Dmitry Abanin, Abhishek Dhar, François Huveneers, Takahiro Sagawa, Keiji Saito, Herbert Spohn and Hal Tasaki DATE : 11 November 2019 to 29 November 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore How do is
From playlist Thermalization, Many Body Localization And Hydrodynamics 2019
A Toy Model for Time Evolving QFT on Lattice with Controllable Chaos by David Berenstein
Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography DATE:27 January 2018 to 03 February 2018 VENUE:Ramanujan Lecture Hall, ICTS Bangalore The program "Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography" aims to
From playlist Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography
Peter Benner: Matrix Equations and Model Reduction, Lecture 5
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From playlist Gene Golub SIAM Summer School Videos
Amir Ali Ahmadi, Princeton University
January 31, Amir Ali Ahmadi, Princeton University Two Problems at the Interface of Optimization and Dynamical Systems We propose and/or analyze semidefinite programming-based algorithms for two problems at the interface of optimization and dynamical systems: In part (i), we study the po
From playlist Spring 2020 Kolchin Seminar in Differential Algebra
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
Transfer Functions: Introduction and Implementation
In this video we introduce transfer functions and show how they can be derived from a set of linear, ordinary differential equations. We also examine how to use a transfer function to predict the output of system to a given input. Topics and time stamps: 0:38 – Example using an aircraft
From playlist Control Theory
Spatio-temporal chaos in a driven dissipative Duffing chain: an OTOC... by Amit Kumar Chatterjee
DISCUSSION MEETING: 7TH INDIAN STATISTICAL PHYSICS COMMUNITY MEETING ORGANIZERS : Ranjini Bandyopadhyay, Abhishek Dhar, Kavita Jain, Rahul Pandit, Sanjib Sabhapandit, Samriddhi Sankar Ray and Prerna Sharma DATE: 19 February 2020 to 21 February 2020 VENUE: Ramanujan Lecture Hall, ICTS Ba
From playlist 7th Indian Statistical Physics Community Meeting 2020
C. Favre - Degeneration of measures of maximal entropy
Consider any meromorphic family of endomorphisms of the complex projective plane parameterized by the punctured unit disk. We shall explain how to describe the behaviour of their measures of maximal entropy when one approaches the central fiber. This generalizes works by Demarco and Fab
From playlist Complex analytic and differential geometry - a conference in honor of Jean-Pierre Demailly - 6-9 juin 2017
Stanford Seminar - Model Predictive Control of Hybrid Dynamical Systems
Ricardo Sanfelice UC Santa Cruz November 8, 2019 Hybrid systems model the behavior of dynamical systems in which the states can evolve continuously and, at isolate time instances, exhibit instantaneous jumps. Such systems arise when control algorithms that involve digital devices are appl
From playlist Stanford AA289 - Robotics and Autonomous Systems Seminar
The Step Response | Control Systems in Practice
Check out the other videos in this series: https://www.youtube.com/playlist?list=PLn8PRpmsu08pFBqgd_6Bi7msgkWFKL33b This video covers a few interesting things about the step response. We’ll look at what a step response is and some of the ways it can be used to specify design requirements f
From playlist Control Systems in Practice