Some nonlinear systems can be approximated by switching bilinear systems. In this paper, we proposed a method to design state-based stabilizing controller for switching bilinear systems. Based on the similarity between switching bilinear systems and switching linear systems, corresponding switching linear systems are obtained for switching bilinear systems by applying state-based feedback control laws. Instead, we consider asymptotically stabilizing the corresponding switching linear system through solving a number of relaxed LMI conditions. Stabilizing controllers for switching bilinear systems can be derived based on the results of the corresponding switching linear systems. The stability of the controller is proved step by step through the decreasing of the multiple Lyapunov functions along the state trajectory. The effectiveness of the method is demonstrated by both a theoretical example and an example of urban traffic network with traffic signals.

This article is concerned with the design and performance optimization of feedback controllers for state-based switching bilinear systems (SBLSs), where subsystems take the form of bilinear systems in different state space polyhedra. First, by further dividing the subregions into smaller regions and designing region-dependent feedback controllers in the resulting regions, the SBLSs can be transformed into corresponding switching linear systems (SLSs). Then, for these SLSs, by imposing contractility conditions on the Lyapunov functions, an upper bound on the infinite horizon quadratic cost can be obtained. Optimizing this upper bound yields the controller design. The optimization problem is formulated as a linear matrix inequalities optimization problem, which can be solved efficiently. Finally, the stability of the close-loop system under the proposed controller is established step by step through a decreasing overall Lyapunov function.

In order to investigate the stochastic features in urban traffic dynamics, we propose a Stochastic Link Flow Model (SLFM) for signalized traffic networks with demand uncertainties. In the proposed model, the link traffic state is described using four different link state modes, and the probability for each link state mode is determined based on the stochastic link states. The SLFM model is expressed as a finite mixture approximation of the link state probabilities and the dynamic link flow models for all the four link state modes. Using data from microscopic traffic simulator SUMO, we illustrate that the proposed model can provide a reliable estimation of the link traffic states, and as well as good estimations on the link state uncertainties propagating within a signalized traffic network.

Presents corrections to the paper, “Integrated urban traffic control for the reduction of travel delays and emissions,” (Lin, S., et al), IEEE Trans. Intell. Transp. Syst., vol. 14, no. 4, pp. 1609–1619, Dec. 2013.