text: import math
  import numpy as np
  
  from cereal import log
  from common.filter_simple import FirstOrderFilter
  from common.numpy_fast import clip, interp
  from common.realtime import DT_CTRL
  from selfdrive.car import apply_toyota_steer_torque_limits
  from selfdrive.car.toyota.values import CarControllerParams
  from selfdrive.controls.lib.drive_helpers import get_steer_max
  from common.params import Params
  from decimal import Decimal
  
  
  class LatControlINDI():
    def __init__(self, CP):
      self.angle_steers_des = 0.
  
      A = np.array([[1.0, DT_CTRL, 0.0],
                    [0.0, 1.0, DT_CTRL],
                    [0.0, 0.0, 1.0]])
      C = np.array([[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.array([[7.30262179e-01, 2.07003658e-04],
                    [7.29394177e+00, 1.39159419e-02],
                    [1.71022442e+01, 3.38495381e-02]])
  
      self.speed = 0.
  
      self.K = K
      self.A_K = A - np.dot(K, C)
      self.x = np.array([[0.], [0.], [0.]])
  
      self.enforce_rate_limit = CP.carName == "toyota"
  
      self.mpc_frame = 0
      self.params = Params()
  
      self._RC = (CP.lateralTuning.indi.timeConstantBP, CP.lateralTuning.indi.timeConstantV)
      self._G = (CP.lateralTuning.indi.actuatorEffectivenessBP, CP.lateralTuning.indi.actuatorEffectivenessV)
      self._outer_loop_gain = (CP.lateralTuning.indi.outerLoopGainBP, CP.lateralTuning.indi.outerLoopGainV)
      self._inner_loop_gain = (CP.lateralTuning.indi.innerLoopGainBP, CP.lateralTuning.indi.innerLoopGainV)
  
      self.RC = 0
      self.G = 0
      self.outer_loop_gain = 0
      self.inner_loop_gain = 0
  
      self.sat_count_rate = 1.0 * DT_CTRL
      self.sat_limit = CP.steerLimitTimer
      self.steer_filter = FirstOrderFilter(0., self.RC, DT_CTRL)
  
      self.live_tune_enabled = False
  
      self.reset()
  
      self.li_timer = 0
  
    def reset(self):
      self.steer_filter.x = 0.
      self.output_steer = 0.
      self.sat_count = 0.
      self.speed = 0.
  
    def live_tune(self, CP):
      self.mpc_frame += 1
      if self.mpc_frame % 300 == 0:
        self.outerLoopGain = float(Decimal(self.params.get("OuterLoopGain", encoding="utf8")) * Decimal('0.1'))
        self.innerLoopGain = float(Decimal(self.params.get("InnerLoopGain", encoding="utf8")) * Decimal('0.1'))
        self.timeConstant = float(Decimal(self.params.get("TimeConstant", encoding="utf8")) * Decimal('0.1'))
        self.actuatorEffectiveness = float(Decimal(self.params.get("ActuatorEffectiveness", encoding="utf8")) * Decimal('0.1'))
        self.RC = interp(self.speed, [0.], [self.timeConstant]) 
        self.G = interp(self.speed, [0.], [self.actuatorEffectiveness])
        self.outer_loop_gain = interp(self.speed, [0.], [self.outerLoopGain])
        self.inner_loop_gain = interp(self.speed, [0.], [self.innerLoopGain])
          
        self.mpc_frame = 0
  
    def _check_saturation(self, control, check_saturation, limit):
      saturated = abs(control) == limit
  
      if saturated and check_saturation:
        self.sat_count += self.sat_count_rate
      else:
        self.sat_count -= self.sat_count_rate
  
      self.sat_count = clip(self.sat_count, 0.0, 1.0)
  
      return self.sat_count > self.sat_limit
  
    def update(self, active, CS, CP, VM, params, curvature, curvature_rate):
      self.speed = CS.vEgo
  
      self.RC = interp(self.speed, self._RC[0], self._RC[1])
      self.G = interp(self.speed, self._G[0], self._G[1])
      self.outer_loop_gain = interp(self.speed, self._outer_loop_gain[0], self._outer_loop_gain[1])
      self.inner_loop_gain = interp(self.speed, self._inner_loop_gain[0], self._inner_loop_gain[1])
  
      self.li_timer += 1
      if self.li_timer > 100:
        self.li_timer = 0
        self.live_tune_enabled = self.params.get_bool("OpkrLiveTunePanelEnable")
      if self.live_tune_enabled:
        self.live_tune(CP)
  
      # Update Kalman filter
      y = np.array([[math.radians(CS.steeringAngleDeg)], [math.radians(CS.steeringRateDeg)]])
      self.x = np.dot(self.A_K, self.x) + np.dot(self.K, y)
  
      indi_log = log.ControlsState.LateralINDIState.new_message()
      indi_log.steeringAngleDeg = math.degrees(self.x[0])
      indi_log.steeringRateDeg = math.degrees(self.x[1])
      indi_log.steeringAccelDeg = math.degrees(self.x[2])
  
      steers_des = VM.get_steer_from_curvature(-curvature, CS.vEgo)
      steers_des += math.radians(params.angleOffsetDeg)
      indi_log.steeringAngleDesiredDeg = math.degrees(steers_des)
  
      rate_des = VM.get_steer_from_curvature(-curvature_rate, CS.vEgo)
      indi_log.steeringRateDesiredDeg = math.degrees(rate_des)
  
      if CS.vEgo < 0.3 or not active:
        indi_log.active = False
        self.output_steer = 0.0
        self.steer_filter.x = 0.0
      else:
        # Expected actuator value
        self.steer_filter.update_alpha(self.RC)
        self.steer_filter.update(self.output_steer)
  
        # 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
  
        # If steering pressed, only allow wind down
        if CS.steeringPressed and (delta_u * self.output_steer > 0):
          delta_u = 0
  
        # Enforce rate limit
        if self.enforce_rate_limit:
          steer_max = float(CarControllerParams.STEER_MAX)
          new_output_steer_cmd = steer_max * (self.steer_filter.x + 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, CarControllerParams)
          self.output_steer = new_output_steer_cmd / steer_max
        else:
          self.output_steer = self.steer_filter.x + delta_u
  
        steers_max = get_steer_max(CP, CS.vEgo)
        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.steer_filter.x)
        indi_log.delta = float(delta_u)
        indi_log.output = float(self.output_steer)
  
        check_saturation = (CS.vEgo > 10.) and not CS.steeringRateLimited and not CS.steeringPressed
        indi_log.saturated = self._check_saturation(self.output_steer, check_saturation, steers_max)
  
      return float(self.output_steer), float(steers_des), indi_log
  