# | Title | Category | Description |
---|---|---|---|
1 | MATLAB/Simulinkによる現代制御入門 | Universal | Lyapunov in Chap. 7, pp. 140 |
2 | Multi-objective filter design for uncertain stochastic time-delay systems.pdf | Exponentially stable | Exponentially stable lemma in page 3, pp. 151, lemma 1 |
3 | Observers for Nonlinear Stochastic Systems.pdf | Exponentially stable | The origin of lemma 1 of LIT#2 |
4 | Basic Lyapunov theory.pdf | Properties | GAS, stability theorems (exponential), Lasalle's theorem, candidate |
5 | Lyapunov Stability Theory.pdf | Exponentially stable | Exponential stability based on state in page 3, Exponential stability theorem based on Lyapunov functional in page 6 |
6 | Basic Concepts of Stability Theory | Stability | A tutorial help understanding Lyapunov stability |
7 | Equilibrium Points of Linear Autonomous Systems | Universal | Types of equilibrium points, phase portrait, especially for singular transition matrix |
8 | Method of Lyapunov Functions | Trajectory | * help understanding phase trajectory, derivatives, monotonicity |
9 | Nonlinear Systems (3rd Edition).pdf | ROA | Region of Attraction in pp.312 |
10 | MATLAB/Simulinkと実機で学ぶ制御工学 | Experiment | Experiment platform based on lego NXT |
11 | Making an Inverted Pendulum using LEGO MINDSTORMS EV3 | Experiment | Another experiment platform based on lego EV3 |
12 | 台車の振幅制限を考慮した倒立振子の安定化制御 | ROA | Calculation of ROA boundary |
13 | Exact Asymptotic Stability Analysis and Region-of-Attraction Estimation for Nonlinear Systems | ROA | |
14 | Nonlinear Systems and Control Lecture # 11 Exponential Stability & Region of Attraction | ROA | Curriculum slides of Michigan State University |
15 | Lasalle 不変原理による 2 次系の漸近安定性の証明 | Asymptotical stability | |
16 | Riccati & Lyapunov equations | LQR | Riccati LQR and Lyapunov theory |
17 | Markov過程の量子化を用いたLyapunov関数の構築 | Quantum | |
18 | Quantum stochastic calculus | Quantum | |
19 | Itô's lemma | Quantum |
( moment of inertia ) | |||
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1 | 1 | 1 | 1 |
[X,Y] = meshgrid(-7:0.1:7,-10:0.1:10);
Z = Y.^2 + 9.8*(1-cos(X));
surf(X,Y,Z)
xlabel('angle')
ylabel('angular velocity')
[X,Y] = meshgrid(-7:0.1:7,-10:0.1:10);
Z = -Y.^2;
surf(X,Y,Z)
xlabel('angle')
ylabel('angular velocity')
x=-pi:pi/20:pi;
y=x';
z = y.^2 + 9.8*(1-cos(x));
[px,py] = gradient(z);
figure
contour(x,y,z)
hold on
quiver(x,y,px,py)
hold off
xlabel('angle')
ylabel('angular velocity')
x=-pi:pi/20:pi;
y=x';
z = y.^2 + 9.8*(1-cos(x));
vx = y*ones(1,41);
vy=-9.8*sin(x)-y*ones(1,41);
figure
contour(x,y,z)
hold on
quiver(x,y,vx,vy)
hold off
xlabel('angle')
ylabel('angular velocity')
syms x(t)
[V] = odeToVectorField(diff(x, 2) == -diff(x,1) - 9.8*sin(x));
M = matlabFunction(V,'vars', {'t','Y'});
sol = ode45(M,[0 20],[2 2]);
z = linspace(0,20,1000);
x1 = deval(sol,z,1);
x2 = deval(sol,z,2);
figure
hold on;
plot(x1,x2);
xlabel('angle')
ylabel('angular velocity')
hold off;
figure
hold on;
fplot(@(x)deval(sol,x,1), [0, 20])
xlabel('time')
ylabel('angle')
hold off;
figure
hold on;
fplot(@(x)deval(sol,x,2), [0, 20])
xlabel('time')
ylabel('angular velocity')
hold off;
...
fplot(@(x) 0.5*deval(sol,x,2).^2+9.8-9.8*cos(deval(sol,x,1)), [0, 20])
fplot(@(x) -deval(sol,x,2).^2, [0, 20])