Uncertainty observer and stabilization for transportation network with constraints

• Published in: Journal of applied mathematics & computing Vol. 68; no. 2; pp. 1107 - 1133
• Main Authors: Sleiman, Mohamad, Bouyekhf, Rachid, AL CHAMI, Zaher, El Moudni, Abdellah
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2022; Springer Nature B.V
• Subjects: Applied mathematics; Computational Mathematics and Numerical Analysis; Control theory; Mathematical and Computational Engineering; Mathematics; Mathematics and Statistics; Mathematics of Computing; Original Research; State feedback; Theory of Computation; Traffic control; Traffic signals; Transportation networks; Uncertainty; Uncertainty observer; Urban transportation network; Stability; Traffic signal control; Linear matrix inequality (LMI)
• ISSN: 1598-5865; 1865-2085
• DOI: 10.1007/s12190-021-01561-6

The aim of this paper is to establish a control strategy in order to prevent the congestion in the transportation network subject to additive uncertainties. This is achieved by stabilizing the lanes around their nominal situations where the risk to generate congestion is very low. Firstly, by using the store and forward approach, the system is modeled as a linear discrete time model with additive uncertainties. Then, a state feedback traffic light control law that stabilizes the lanes while satisfying the constraints on both state and control variables is established. In order to estimate the uncertainties that may cause bad effects on the control performance, an observer is proposed to achieve this objective. As an illustrative example, many simulations are realized to show the effectiveness of our observer and our proposed control with different level of uncertainties.