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richard pates
Sweden
เข้าร่วมเมื่อ 2 พ.ค. 2012
Senior Lecturer at Lund University. Interested in control theory, mathematics, acting, running and pretty pictures.
If you're interested in my teaching material, please see the playlists section. For a more structured presentation along with lecture slides and exercises, see the course homepages given in the links below.
FRTF15: Control Theory -- This course is designed as a complement to a basic course in control, and goes through some of the mathematics that underpins classical frequency domain and state-space methods.
FRTN05: Nonlinear Control -- This is an introductory course in nonlinear control, covering topics such as Lyapunov functions, describing functions and the circle criterion.
FRTF05: Basic Course -- This is an introductory course in control, going through all the good stuff from Nyquist and Bode plots, to pole placement, to PID control system design.
If you're interested in my teaching material, please see the playlists section. For a more structured presentation along with lecture slides and exercises, see the course homepages given in the links below.
FRTF15: Control Theory -- This course is designed as a complement to a basic course in control, and goes through some of the mathematics that underpins classical frequency domain and state-space methods.
FRTN05: Nonlinear Control -- This is an introductory course in nonlinear control, covering topics such as Lyapunov functions, describing functions and the circle criterion.
FRTF05: Basic Course -- This is an introductory course in control, going through all the good stuff from Nyquist and Bode plots, to pole placement, to PID control system design.
An Alternative Look at Peg Solitaire
A video about peg solitaire, parity arguments, and biscuits.
This video is for educational purposes. There is a lot of fun mathematics going on under the hood, including connections to linear programming, Diophantine equations and the mysteriously named Fredholm alternative. If you're interested, check out my write up here:
www.richardpates.com/an-alternative-look-at-peg-solitaire-part-i/
A pretty accessible entry to the mathematics of peg solitaire that I used a lot is "Winning Ways for your mathematical plays, vol IV", by Berlekamp, Conway and Guy (google for pdfs).
0:00-2:03 -- Introduction
2:03-3:25 -- The rules of peg solitaire, and solution to the English board
3:25-4:23 -- Phone a friend
4:23-6:27 -- Parity prevents solution to the French board
6:27-6:58 -- Bending the rules
6:58-8:43 -- A Rational solution to the French board
Animations made with Manim:
www.manim.community/
Stock video and sound effects from Mixkit
mixkit.co/
Music in the video:
Track: Driving Ambition By Ahjay Stelino
License: Creative Commons Attribution 3.0 - CC BY 3.0
___________________________________________________
TRACK INFO
Title: Driving Ambition By Ahjay Stelino
Genre: Corporate / Motivation
Mood: Uplifting
________________________________________
CONTACT THE ARTIST
Website: ahjaystelino.com/
Contact: ahjaystelino.com/contact/
_________________________________________
#some2
This video is for educational purposes. There is a lot of fun mathematics going on under the hood, including connections to linear programming, Diophantine equations and the mysteriously named Fredholm alternative. If you're interested, check out my write up here:
www.richardpates.com/an-alternative-look-at-peg-solitaire-part-i/
A pretty accessible entry to the mathematics of peg solitaire that I used a lot is "Winning Ways for your mathematical plays, vol IV", by Berlekamp, Conway and Guy (google for pdfs).
0:00-2:03 -- Introduction
2:03-3:25 -- The rules of peg solitaire, and solution to the English board
3:25-4:23 -- Phone a friend
4:23-6:27 -- Parity prevents solution to the French board
6:27-6:58 -- Bending the rules
6:58-8:43 -- A Rational solution to the French board
Animations made with Manim:
www.manim.community/
Stock video and sound effects from Mixkit
mixkit.co/
Music in the video:
Track: Driving Ambition By Ahjay Stelino
License: Creative Commons Attribution 3.0 - CC BY 3.0
___________________________________________________
TRACK INFO
Title: Driving Ambition By Ahjay Stelino
Genre: Corporate / Motivation
Mood: Uplifting
________________________________________
CONTACT THE ARTIST
Website: ahjaystelino.com/
Contact: ahjaystelino.com/contact/
_________________________________________
#some2
มุมมอง: 857
วีดีโอ
Epic Pythagoras
มุมมอง 1.1K2 ปีที่แล้ว
Can the Pythagorean Theorem hold up against some epic music? There is only one way to find out... This video is for educational purposes. My main objective (which may have been lost in all the lightning strikes) was to emphasise the converse aspect of the Pythagorean theorem, and also showcase the technique of proof by contraposition. You can read more about all this here: www.richardpates.com/...
Lyapunov Stability via Sperner's Lemma
มุมมอง 6K2 ปีที่แล้ว
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 inspiration for covering this topic: th-cam.com/video/7s-YM-kcKME/w-d-xo.html Towards the end the video thing...
Optimal Estimates of Initial Conditions
มุมมอง 5303 ปีที่แล้ว
We solve the problem of optimally estimating an initial condition based on noisy measurements using least squares
More Least Squares
มุมมอง 4103 ปีที่แล้ว
We introduce and solve a second type of least squares problem that often comes up in regression or estimation problems
Minimum Energy Control
มุมมอง 1.8K3 ปีที่แล้ว
We use our intuition from the least norm least squares problem to find the input that drives our system to the origin with the least energy
Controllable and Observable Subspaces
มุมมอง 3K3 ปีที่แล้ว
We relate the left and right null spaces of the controllability and observability matrix to the unreachable and/or unobservable parts of the state space of an uncontrollable and/or unobservable part of a state-space model
The Kalman Decomposition
มุมมอง 9K3 ปีที่แล้ว
The Kalman decomposition reveals the controllable and observable parts of a state-space model. We introduce and discuss the basic concept, as well as the connections to transfer function poles and zeroes.
Observability
มุมมอง 1.7K3 ปีที่แล้ว
We briefly introduce the concept of an observable state-space model, and how we can test for observability using the observability matrix.
Controllability Tests
มุมมอง 2.1K3 ปีที่แล้ว
We explain and derive the basic test for controllability using the controllability matrix.
Controllability
มุมมอง 2.6K3 ปีที่แล้ว
We explain and derive the basic test for controllability using the controllability matrix.
Harmonic balance and the describing function
มุมมอง 1.5K3 ปีที่แล้ว
Harmonic balance and the describing function
The KYP lemma and the passivity theorem
มุมมอง 2.9K3 ปีที่แล้ว
The KYP lemma and the passivity theorem