Control Barrier Function Auxiliary Function Visualization

Finished

The following code is used to visualize the exponential decay of the auxiliary function in the Control Barrier Function. This is the GIF version generated by the ChatGPT. When generate GIF, please pay attention to the init() function. The index error is annoying.

import numpy as np
import matplotlib.pyplot as plt
import matplotlib.animation as animation

k = 1.0
h0 = 20
t = np.linspace(0, 6, 500)  # Adjusted time range for better visualization

def y(t, h0, k):
    return h0 * np.exp(-k * t)

y_t = y(t, h0, k)

# Create a figure and axis
fig, ax = plt.subplots(figsize=(8, 6))

# Initialize the plot elements: a line and a point
line, = ax.plot([], [], color='blue', linewidth=2, label=r'$y(t) = y(0) e^{-kt}$')
point, = ax.plot([], [], 'ro')  # Point to highlight the current y(t)
time_template = 'Time = %.1f s'
time_text = ax.text(0.05, 0.9, '', transform=ax.transAxes, fontsize=12)

# Set up the plot limits and labels
ax.set_xlim(0, 6)
ax.set_ylim(-0.1, h0 + 1)
ax.set_title('Exponential Decay: $y(t) = y(0) e^{-kt}$', fontsize=14)
ax.set_xlabel('Time', fontsize=12)
ax.set_ylabel('Value', fontsize=12)
ax.axhline(0, color='grey', linewidth=1, linestyle='--')
ax.axhline(h0, color='grey', linewidth=1, linestyle='--')
ax.grid(True)
ax.legend()

# Initialization function: plot background for each frame
def init():
    line.set_data([], [])
    point.set_data([], [])
    time_text.set_text('')
    return line, point, time_text

# Animation function: this is called sequentially
def animate(i):
    if i == 0:
        return init()
    # Create the data to plot
    this_time = t[:i]
    this_y = y_t[:i]
    # Update the line and the point
    line.set_data(this_time, this_y)
    point.set_data([this_time[-1]], [this_y[-1]])  # Wrap in lists to ensure sequences
    # Update the time text
    time_text.set_text(time_template % this_time[-1])
    return line, point, time_text

# Create an animation
ani = animation.FuncAnimation(fig, animate, frames=len(t), init_func=init, interval=50, blit=True)

# Save the animation as a GIF
ani.save('exponential_decay.gif', writer='pillow', fps=20)

# Show the animation
plt.show()