Linear-parameter-varying approximation of nonlinear dynamics for model predictive flow control of urban multi-region systems

Abstract

An alternative approach for real-time networkwide traffic control in cities that has recently gained a lot of interest is perimeter flow control. The focus of the current work is to study two aspects that are not covered in the perimeter control literature, which are: (a) integration of appropriate external demand information that has been considered system disturbance in the derivation of feedback control laws in previous works, and (b) mathematical formulation of the original nonlinear problem in a linear-parameter-varying (LPV) form, so that optimal control can be applied in a (rolling horizon) model predictive concept. This work presents the mathematical analysis of the optimal control problem, as well as the approximations and simplifications that are assumed in order to derive the formulation of a linear optimization problem. The developed scheme is applied to microsimulation in order to better investigate its applicability to real life conditions. The simulation experiments demonstrate the effectiveness of the scheme compared to fixed-time control as all the performance indicators are improved significantly.

Centralized and Distributed Multi-Region Traffic Flow Control

“…The problem definition in this work differs from other papers, such as, [8], [21], in which they also take into consideration the origin and destination of vehicles. In this paper, the total aggregated demands and accumulation of vehicles are considered, information which is lower-level and easier to obtain and to work with in the macroscopic model.…”

“…This is similar to having a control architecture with two layers: u[k] is used for perimeter control as a first-layer controller, while a second-layer of distributed control optimizes locally the states of the regions. In the literature, the traffic demand for each region is a parameter that is usually not controlled but is rather part of the constraints when solving optimization problems as it is the case in [21]. A method for the management of this demand is proposed in [8], by setting a threshold; this amounts to instruct to vehicles to wait at the origin of their trip (boundary).…”