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Invariance principle for transportation network

Traffic signal control strategies concern generally two distinct objectives: the prevention or reduction of the congestion. Traffic congestion appears when the traffic demand exceeds the capacity of the network. In this case, some lanes of the network are saturated and consequently an overflow occurs at some intersections. In this paper, we show that congestion can be avoided by forcing the number of vehicles to not exceed the level corresponding to the optimal operational traffic of each lane. By using the concept of positive invariance and Linear Matrix Inequalities (LMI), we derive a state feedback traffic light control law that achieves our objective and at the same time respecting both the constraints of state and control variables. The results of the simulations indicate that our control strategy guarantees a high degree of control benefit.