Probabilistic controller synthesis for freeway traffic networks

Negar Mehr, Dorsa Sadigh, Roberto Horowitz

Abstract: Summary form only given. Traffic management and control in urban environments has been a problem of interest in the recent years due to the costs incurred by congestion delays, green house gas emission, fuel consumption, etc. This would require researchers to design better algorithms capable of maximizing network throughput and performance with the current existing infrastructure. The focus of this work is on designing control strategies that enhance traffic conditions in freeways. An effective control strategy for traffic regulation in freeways is shown to be ramp metering [3]. In order to encode required complex properties for efficient traffic management, control synthesis through temporal logic specifications are proved to be powerful and successful in traffic networks [1,2]. Nonetheless, in all these works, the assumption is that exogenous vehicular demands are known deterministically a priori. This is in contrast to the intrinsic stochastic nature of vehicular demands. In this work, we propose using Signal Temporal Logic (STL) for specifying desired properties in a probabilistic framework allowing for the demands to be treated as random variables. As controlling large scale traffic networks requires macroscopic models with continuous quantities, STL is a perfect candidate as a specification language. Furthermore, STL allows expressing rich temporal properties that encode safety, liveness, response, etc. We assume that the underlying distribution of demands is known and use sampling techniques to optimize for an empirical average of the expected total travel time of the network subject to STL constraints in an MPC fashion.