Traffic network control based on hybrid dynamical system modeling and mixed integer nonlinear programming with convexity analysis

This paper presents a new framework for traffic flow control based on an integrated model description by means of a hybrid dynamical system. The geometrical information on the traffic network is characterized by a hybrid Petri net (HPN). Then, the algebraic behavior of the traffic flow is transformed into a mixed logical dynamical system (MLDS) form to introduce an,optimization technique. These expressions involve both a continuous evolution of the traffic flow and an event-driven behavior of the traffic light. The HPN allows us to easily formulate the problem for a complicated and large-scale traffic network due to its graphical understanding. The MLDS enables us to optimize the control,policy for a traffic light by means of its algebraic manipulability and use of the model predictive control framework. Since the behavior represented by the HPN can be directly transformed into the corresponding MLDS form, the seamless incorporation of two different modeling schemes provides a systematic design scenario for traffic flow control.