*Jun*

#### Reflections on Traffic Modeling and Control Research for Spring 2017

Ahmed Allibhoy [[ Internal only ]]**System Identification**
I began the quarter by attempting to tackle the problem of finding a data driven microscopic traffic model that could be used for analyzing the behavior of traffic jams and for testing the effectiveness of autonomous controllers. This work data gathered through experiments performed by Nakayama and Sugiyama and builds on work done here. In particular, I was interested in seeing whether the models that Nakayama and Sugiyama generated could be improved by considering the relative velocity between vehicles (The former model only takes into account relative distances). The initial attempt was to use a prediction-error approach to system identification. This approach consists of fixing the input variables and finding the system which minimizes the squared difference between predicted and actual outputs at each time step, for all time steps. The results were mixed, and the identified system failed to reproduce the qualitative behavior one sees in empirical observations. This is partially due to limitations of prediction error methods, which only look at the error of predicted outputs at single time-steps rather than considering the error over an entire trajectory. Eventually a good driver model simply by using "common sense" to choose reasonable values for the tunable parameters of the model. Although individual driver trajectories predicted by the system may be vastly different than what is observed in the data, the qualitative behavior of the system as a whole is the same.

**Stabilization of Traffic Flow**
The next problem I focused on was the design of a controller which actually stabilizes traffic flow. Dan Work and others demonstrated that this is actually possible when they were able to use a single autonomous vehicle to stabilize the flow of 22 vehicles in a ring road. However their proposed controllers have significant limitations. The first controller, called the FollowerStopper, requires one to have prior knowledge of the optimal equilibrium velocity which is impractical in real world scenarios. The second, a PI controller with saturation, determines the equilibrium velocity by measuring the equilibrium velocity over a single revolution in the ring. This controller doesn’t require any prior knowledge of the optimal equilibrium velocity, but will only work on a ring road of that size with the same density of vehicles. Given the work of Work, it seems that the problem of stabilization can be reduced to determining the optimal equilibrium velocity of a road through local measurements. Once this is determined, one can use Work’s controller to target that velocity and stabilize traffic flow. Before designing a controller it was necessary to find a way to quantify the performance of a controller. There are three metrics we use, 1. the oscillation of the system at steady-state, 2. the settling time of the system, and 3. the throughput of the system at steady state. At the end of the quarter I was able to evaluate the Work’s controllers with respect to metrics 1 and 3. Unfortunately we still don’t have a controller that is not subject to the limitations above which also performs better than Work’s controllers with respect to the given metrics.

**Looking Ahead**
Looking ahead, I hope to 1. find a way to determine the equilibrium velocity of a road from local measurements, 2. design a controller to maintain this velocity and hopefully stabilize traffic flow, 3. evaluate this controller with respect to the performance metrics outlined above, 4. demonstrate quantitatively that this is more effective than Dan Work’s controller. My goal is to accomplish this by the end of summer and be able to publish these results in a conference paper for ICRA.