text: import math
  import numpy as np
  
  from selfdrive.car.toyota.carcontroller import SteerLimitParams
  from selfdrive.car import apply_toyota_steer_torque_limits
  from selfdrive.controls.lib.drive_helpers import get_steer_max, DT
  from common.numpy_fast import clip
  from cereal import log
  
  
  class LatControlINDI(object):
    def __init__(self, CP):
      self.angle_steers_des = 0.
  
      A = np.matrix([[1.0, DT, 0.0],
                     [0.0, 1.0, DT],
                     [0.0, 0.0, 1.0]])
      C = np.matrix([[1.0, 0.0, 0.0],
                     [0.0, 1.0, 0.0]])
  
      # Q = np.matrix([[1e-2, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 10.0]])
      # R = np.matrix([[1e-2, 0.0], [0.0, 1e3]])
  
      # (x, l, K) = control.dare(np.transpose(A), np.transpose(C), Q, R)
      # K = np.transpose(K)
      K = np.matrix([[7.30262179e-01, 2.07003658e-04],
                     [7.29394177e+00, 1.39159419e-02],
                     [1.71022442e+01, 3.38495381e-02]])
  
      self.K = K
      self.A_K = A - np.dot(K, C)
      self.x = np.matrix([[0.], [0.], [0.]])
  
      self.enfore_rate_limit = CP.carName == "toyota"
  
      self.RC = CP.lateralTuning.indi.timeConstant
      self.G = CP.lateralTuning.indi.actuatorEffectiveness
      self.outer_loop_gain = CP.lateralTuning.indi.outerLoopGain
      self.inner_loop_gain = CP.lateralTuning.indi.innerLoopGain
      self.alpha = 1. - DT / (self.RC + DT)
  
      self.reset()
  
    def reset(self):
      self.delayed_output = 0.
      self.output_steer = 0.
      self.counter = 0
  
    def update(self, active, v_ego, angle_steers, angle_steers_rate, steer_override, CP, VM, path_plan):
      # Update Kalman filter
      y = np.matrix([[math.radians(angle_steers)], [math.radians(angle_steers_rate)]])
      self.x = np.dot(self.A_K, self.x) + np.dot(self.K, y)
  
      indi_log = log.Live100Data.LateralINDIState.new_message()
      indi_log.steerAngle = math.degrees(self.x[0])
      indi_log.steerRate = math.degrees(self.x[1])
      indi_log.steerAccel = math.degrees(self.x[2])
  
      if v_ego < 0.3 or not active:
        indi_log.active = False
        self.output_steer = 0.0
        self.delayed_output = 0.0
      else:
        self.angle_steers_des = path_plan.angleSteers
        self.rate_steers_des = path_plan.rateSteers
  
        steers_des = math.radians(self.angle_steers_des)
        rate_des = math.radians(self.rate_steers_des)
  
        # Expected actuator value
        self.delayed_output = self.delayed_output * self.alpha + self.output_steer * (1. - self.alpha)
  
        # Compute acceleration error
        rate_sp = self.outer_loop_gain * (steers_des - self.x[0]) + rate_des
        accel_sp = self.inner_loop_gain * (rate_sp - self.x[1])
        accel_error = accel_sp - self.x[2]
  
        # Compute change in actuator
        g_inv = 1. / self.G
        delta_u = g_inv * accel_error
  
        # Enforce rate limit
        if self.enfore_rate_limit:
          steer_max = float(SteerLimitParams.STEER_MAX)
          new_output_steer_cmd = steer_max * (self.delayed_output + delta_u)
          prev_output_steer_cmd = steer_max * self.output_steer
          new_output_steer_cmd = apply_toyota_steer_torque_limits(new_output_steer_cmd, prev_output_steer_cmd, prev_output_steer_cmd, SteerLimitParams)
          self.output_steer = new_output_steer_cmd / steer_max
        else:
          self.output_steer = self.delayed_output + delta_u
  
        steers_max = get_steer_max(CP, v_ego)
        self.output_steer = clip(self.output_steer, -steers_max, steers_max)
  
        indi_log.active = True
        indi_log.rateSetPoint = float(rate_sp)
        indi_log.accelSetPoint = float(accel_sp)
        indi_log.accelError = float(accel_error)
        indi_log.delayedOutput = float(self.delayed_output)
        indi_log.delta = float(delta_u)
        indi_log.output = float(self.output_steer)
  
      self.sat_flag = False
      return float(self.output_steer), float(self.angle_steers_des), indi_log
  