Control barrier functions basic example in 1d

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Hortencia Alejandra Ramírez Vázquez
编辑： Voss 2024-11-14，21:13
Ran in:
Hi,
I'm trying to program a basic example of a control barrier functions, for a system of 1D. The idea is that this system should not go for the negatives values .
The dynamic of my system is defined by ,
The function h that is the constinst restriction is given by , such that
The enforce condition is given by,
The question is that I don't know how to program this example, I tried with the assumption that
But my code is not working.
This is my code
%% CASE: x \in R, x can only take positive values
%time interval
t_int = 0:0.001:20;
%initial condition
x_0 = 10;
b = 0.00000001;
%differential eqation
dxdt = @(t, x) -1 - x;
[t, x] = ode45(dxdt, t_int, x_0);
% Graficar la solución
figure;
plot(t, x);
xlabel('Time');
ylabel('x(t)');
grid on;
Can someone help me?
  2 个评论
Torsten
Torsten 2024-11-14，20:54
编辑：Torsten 2024-11-14，20:55
I'm completely unable to follow what you try to do.
William Rose
William Rose 2024-11-14，21:09
编辑：Voss 2024-11-14，21:13
Ran in:
@Hortencia Alejandra Ramírez Vázquez,
I agree with @Torsten. I am unable to understand the dynamics of hte system you wish to simulate. You define b in your code but uyou do not use b in the differential equation, and you do not refer to b in your explanation.
The differential equation you use in your code
dx/dt=-x-1
is a decaying exponential which decays to x=-1, with time constant=1.
%% CASE: x \in R, x can only take positive values
%time interval
tSpan = [0,20];
%initial condition
x_0 = 10;
b = 0.00000001; % not used
%differential eqation
dxdt = @(t, x) -1 - x;
[t, x] = ode45(dxdt, tSpan, x_0);
% Graficar la solución
figure;
plot(t, x);
xlabel('Time');
ylabel('x(t)');
grid on;

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