The PID works like expected but I have problems with the MPC. The simulation stuck and on the console I get this warning: scipy/optimize/_optimize.py:353: RuntimeWarning: Values in x were outside bounds during a minimize step, clipping to bounds
What is wrong?

First of all thank you for sharing this code! But I have a question for this.
The vehicle model you use in car.py is non-linear.

def update_state(self, dt):
		A = np.array([
				[1, 0, 0],
				[0, 1, 0],
				[0, 0, 1]
					])
		B = np.array([
				[np.sin(self.x[2, 0] + np.pi/2)*dt,  0],
				[np.cos(self.x[2, 0] + np.pi/2)*dt,  0],
				[0			 , dt]
					])

		vel = np.array([
					[self.x_dot[0, 0]],
					[self.x_dot[2, 0]]
				])
		self.x = A@self.x + B@vel

In the MPC objective function, you directly use this model to derive all future states within the control hoziron, and use QP to solve it.

x, _ = controller_car.get_state()
z_k[:,i] = [x[0, 0], x[1, 0]]
cost += np.sum(self.Q@((desired_state-z_k[:,i])**2))

But in this case, the objective function is not quadratic, right? (it contains sin(x) ).
Is there any theoretical basis for doing this? Or did I misunderstand something? Hope for your responding, thank you!