Parameter dependent freeway modelling

Abstract

The problem of modelling the complex behaviour of freeway flow leads to a nonlinear macroscopic model. Unfortunately, high dimensional non-linear characteristics could not be performed easily. The paper´s purpose is to introduce a new, general modelling formalism for freeway traffic flow modelling, respectively control. Linear Parameter Varying (LPV) systems represent a numerically tractable class of complex non-linear systems. The main idea is to derive some arbitrary, time dependent parameters by capturing the nonlinearities in the system. Even if the transformation of the full nonlinear model to affine and quasi Linear Parameter Varying (qLPV) system is not unique, an appropriate qLPV model is presented and a computationally low demanding form is given. More, the paper investigates the problem of selecting the adequate scheduling variables, endogenous parameters and some linear approximations giving a novel way to describe freeway traffic systems. An important aspect of the model selection is the feasibili ty of the resulted system throughout the controller and observer design. The paper describes the problem of quadratic stabilizability and detectability for LPV flow models. The Linear Matrix Inequality (LMI) conditions are developed to verify these important properties. Finally, a numeric example suggests the application of the LPV structure for a general freeway section with on- and off-ramps. The comparison of the simulation response of the non-linear and the derived nominal LPV model has also been investigated.