Traffic Network Control From Temporal Logic Specifications

Abstract

We propose a framework for generating a signal control policy for a traffic network of signalized intersections to accomplish control objectives expressible using linear temporal logic. By applying techniques from model checking and formal methods, we obtain a correct-by-construction controller that is guaranteed to satisfy complex specifications. To apply these tools, we identify and exploit structural properties particular to traffic networks that allow for efficient computation of a finite state abstraction. In particular, traffic networks exhibit a componentwise monotonicity property which allows reach set computations that scale linearly with the dimension of the continuous state space.

Compositional controller synthesis for vehicular traffic networks

“…We adopt the signalized network traffic model presented in [3]. A traffic network topology (L, V) consists of a set of links L and a set of vertices (or intersections) V. Function η : L → V maps a link to its downstream vertex and τ : L → V ∪ maps a link to its upstream vertex.…”

“…Each partition of the continuous space exactly corresponds with a single state in the finite abstraction; thus, we refer to the two interchangeably. We construct an approximate quotient transition system [3] (or simply finite abstraction) of N 's continuous dynamics. Definition 1.…”

“…We only state key points about the LTL controller synthesis procedure, and refer the reader to [3][9] for a more details. The non-determinism in the translation relation → is viewed as an adversarial environment who seeks to prevent satisfaction of φ.…”

“…We thank Samuel Coogan for insightful discussions and providing the simulation and synthesis code from [3].…”

“…Congestion arises when there is inadequate downstream supply to fulfill an upstream link's demand. Previously, a control policy for a network of signalized intersections was synthesized by constructing a finite state abstraction of the continuous dynamics [3]. This paper's first contribution is to introduce supplydemand contracts between adjacent sub-networks so that satisfaction of a specification is ensured after a network is partitioned.…”