Modeling and Optimization of Traffic Flow in Urban Areas - Czech ...

14 Chapter 2 Simple Light Controled Intersection ModelE [s]16001200Queue 1Queue 280040000 1 2 3 4 5 6 7 x 10 4(a) LQRt [s]E [s]16001200Queue 1Queue 280040000 1 2 3 4 5 6 7 x 10 4 t [s](b) NMPCFig. 2.5: Mean waiting timesMagn 03]. The same cost function (2.13) was used as an objective function.For the NMPC algorithm we must select a control horizon and a predictionhorizon. The prediction horizon T ph is a time interval that the controlleruses for simulating the nonlinear model. The control horizon is a time intervalover which the controller optimizes the control signal. In our case, bothhorizons were set to the 90 s, which is equal to the cycle time C. Controlloop schema is shown on Fig. 2.6.For convex problems, the NMPC can find an optimal switching time t swby convex optimization [Boyd 04]. Our optimization problem is not convex,however. Instead, we find the optimal t sw by enumerating all t sw ∈ (0, C)and simulating the response. The simulated intersection model responsewhen applying the NMPC control law is shown on the Fig. 2.5(b).NMPC allows tuning of the control law to be modified in a number of