Nonlinear State Estimation and Control for Freeway On‐Ramp Metering

Abstract

The work presented in this paper deals with freeway ramp metering using a differential flatness concept. Such an approach is deployed in the cases when the traffic data provided by loop detectors (or any measurements device), are partially unknown or missed, and/or the downstream measurement station, located at the vicinity of the controlled ramp, is faulty. The proposed solution rests on the estimation of the main variables using the “revised” method of numerical differentiation, i.e., estimation of the derivative of noisy time signals. Such an algebraic approach, which does not need any integration of differential equations, turns out to be quite robust with respect to perturbations inputs and measurements noises. Convincing numerical simulations are provided using a modified second‐order continuum macroscopic model. Furthermore, a comparative study using the Extended Kalman Filter (EKF), which is the most used in the area of traffic state estimators, is proposed in order to demonstrate the effectiveness of the strategy.

Control Schemes for Autonomous Car‐following Systems with two Classical Compensators

“…Abouaissa et al . dealt with freeway ramp metering with a differential flatness concept when the data collected from loop detectors are partially missing or unknown. The proposed solution depended on the estimation of the main variables.…”

Adaptive Iterated Extended KALMAN Filter for Relative Spacecraft Attitude and Position Estimation

“…In the Gaussian case, the prediction step is relatively simple . The common ways to predict the state mean and the corresponding error covariance include analytical linearization approaches used in extended Kalman filter (EKF) and Fourier‐Hermite Kalman filter , sigma point approaches used in unscented Kalman filter (UKF) and cubature Kalman filter (CKF) , and the approaches based on the numerical solution of differential equations . The update step is more difficult.…”