Control barrier functions basic example in 1d

Question

Hortencia Alejandra Ramírez Vázquez 2024-11-14

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2166403-control-barrier-functions-basic-example-in-1d

编辑： Ashok 2024-11-25，8:40

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
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Torsten 2024-11-14

编辑：Torsten 2024-11-14

I'm completely unable to follow what you try to do.

William Rose 2024-11-14

编辑：Voss 2024-11-14

在 MATLAB Online 中打开

@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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Answer 1

Ashok 2024-11-25，8:40

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链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2166403-control-barrier-functions-basic-example-in-1d#answer_1549323

编辑：Ashok 2024-11-25，8:40

在 MATLAB Online 中打开

Hey @Hortencia Alejandra Ramírez Vázquez,

From the equations mentioned in the query, it seems the condition for the system is incorrectly stated as

, and should instead be

, where

is a class-K function. Additionally, the equation

, suggests that the class-K function is chosen to be

.

To ensure the condition

on the control input, u can be chosen as

, where ρ is a positive constant. However, the below line in the shared code suggests that the constant is chosen as

which is contradictory.

dxdt = @(t, x) -1 - x;

To resolve the issue, replace ‘-1’ in the above line with some positive constant. Here’s a plot showing the system response for different values of ρ.