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Polcz Péter honlapja
Tartalomjegyzék
\[
\newenvironment{dcases}{\left\{\begin{array}{ll}}{\end{array}\right.}
\]
Simulate Example 1. of 2016_Bobiti.Lazar
Teljes Matlab script
kiegészítő függvényekkel .
File: d2018_01_20_ex1_sim.m
Directory: projects/2_sta/2018_01_20_2016_Bobiti.Lazar
Author: Peter Polcz (ppolcz@gmail.com)
Created on 2018. January 20.
Simulate a discrete-time dynamical system
syms x1 x2 real
x = [x1;x2];
It is given the following discrete-time (possibly nonlinear) dynamical system:
$$
x[k+1] = G\big(x[k]\big), \text{ with } x[k] \in \mathbb{R}^n.
$$
Let $n = 2$, and $G(x)$ be given as follows [1]:
G = [
x1/2 + x1^2 - x2^2
-x2/2 + x1^2
];
\begin{align}
G(x) =
\left(\begin{array}{c}
{x_{1}}^2+\frac{x_{1}}{2}-{x_{2}}^2 \\
{x_{1}}^2-\frac{x_{2}}{2} \\
\end{array}\right)
\end{align}
G_fh = matlabFunction(G, 'vars', {x});
[xx1,xx2] = meshgrid(linspace(-0.1,0.1,4));
figure, hold on
for i = 1:numel(xx1)
xx = simulate(G_fh, [xx1(i); xx2(i)], 10);
P = plot(xx(:,1), xx(:,2),'.-');
plot(xx(1,1), xx(1,2), '*', 'Color', P.Color);
end
function x = simulate(G, x0, N)
x = zeros(N,numel(x0));
x(1,:) = x0';
xi = x0;
for i = 2:N
xi = G(xi);
x(i,:) = xi';
end
end
References
[1] Bobiti, R. & Lazar, M. A sampling approach to finding Lyapunov functions for nonlinear discrete-time systems. 2016 European Control Conference (ECC), 2016, pg. 561-566
