human
1.2 Controller Initialization
Here we initialize an IDM controller class and the __init__ function storing class attributes.
The Intelligent Driver Model is a car-following model specifying vehicle dynamics by a differential equation for acceleration $\dot{v}$. The differential equation follows:
$$\dot{v} = a \left[ 1- \left( \frac{v}{v_0} \right)^\delta -\left( \frac{s^}{h} \right)^2 \right] \textbf{, with } \ s^ := s_0 + \max \left( 0, vT + \frac{v\Delta v}{2\sqrt{ab}} \right)$$
The IDM parameters are: desired speed $v_0$, time gap $T$, min gap $s_0$, acceleration exponent $\delta$, acceleration term $a$, and comfortable deceleration $b$. $h$ is the vehicle headway (the distance to the vehicle ahead) and $\Delta v$ is the velocity difference compared to the lead vehicle (current velocity - lead velocity).
assistant
#Here is the Python code you requested.
class IDMController(BaseController):
    def __init__(self, veh_id, v0=30, T=1, a=1, b=1.5, 
                 delta=4, s0=2, s1=0, time_delay=0.0, 
                 dt=0.1, noise=0, fail_safe=None, car_following_params=None):
        """
        veh_id: str
            unique vehicle identifier
        car_following_params: SumoCarFollowingParams
            see parent class
        v0: float, optional
            desirable velocity, in m/s (default: 30)
        T: float, optional
            safe time headway, in s (default: 1)
        b: float, optional
            comfortable deceleration, in m/s2 (default: 1.5)
        delta: float, optional
            acceleration exponent (default: 4)
        s0: float, optional
            linear jam distance, in m (default: 2)
        s1: float, optional
            nonlinear jam distance, in m (default: 0)
        dt: float, optional
            timestep, in s (default: 0.1)
        noise: float, optional
            std dev of normal perturbation to the acceleration (default: 0)
        fail_safe: str, optional
            type of flow-imposed failsafe the vehicle should posses, defaults
            to no failsafe (None)
        """
        
        BaseController.__init__(self, veh_id, car_following_params,
                                delay=time_delay, fail_safe=fail_safe,
                                noise=noise)
        self.v0 = v0
        self.T = T
        self.a = a
        self.b = b
        self.delta = delta
        self.s0 = s0
        self.s1 = s1
        self.dt = dt