Supervisory control for collision avoidance in vehicular networks using discrete event abstractions

Abstract

Abstract-We consider the problem of collision avoidance at vehicular intersections for a set of controlled and uncontrolled vehicles that are linked by wireless communication. Each vehicle is modeled by a first order system. We use a disturbance to account for bounded model uncertainty. We construct a discrete event system abstraction and formulate the problem in the context of supervisory control for discrete event systems with uncontrollable events. This allows us to mitigate computational limitations related to the presence of continuous dynamics and infinite state spaces. For solving the resulting supervisory control problem at the discrete event level, we develop an algorithm that exploits the structure of the transition map to compute the supremal controllable sublanguage more efficiently than standard algorithms. We present implementation results on an intersection with several vehicles.

Hierarchical-Distributed Optimized Coordination of Intersection Traffic

“…In the first set of simulations we simulated the signal-based algorithm and the proposed hierarchical-distributed (HD) algorithm for different values of µ and with W T = 1 in the cost function (2). For each µ, 10 trials were conducted, each for 1 minute of simulation time.…”

“…Literature review: Much of the literature in the area of coordination-based intersection management focuses on collision avoidance of vehicles within the intersection. Supervisory intersection management (intervention only when required to maintain safety by avoiding collisions) is explored using discrete event abstractions in [2] and reachable set computations in [3], [4]. The works [5], [6] and references therein describe a multiagent simulation approach in which, upon a reservation request from a vehicle, an intersection manager accepts or rejects the reservation based on a simulation.…”

Survey on automated symbolic verification and its application for synthesising cyber‐physical systems

“…In order to avoid that problem, refined controllers have been proposed, which aim to provide some invariant properties for closed-loop systems, e.g. safety [177,178], reachability [174,179], stability [169,173], and safety/reachability properties, considering quantisation effects [180].…”

Computing Robust Controlled Invariant Sets of Linear Systems

“…Let x ∈ K, and pick x r ∈R ε and x i ∈ N δ i , i ∈ [1; n] so that x = x r + n i=1 x i . SinceR ε satisfies (19), we can pick u r ∈Ū ε so that Ax r + Bu r + W ⊆R ε , which implies that Ax r + Bu r + W + ρB ⊆R ε + N δ n . Moreover, for x i ∈ N δ i , we pick u i ∈ δB so that Ax i + Bu i ∈ N δ i−1 .…”

“…We would like to point out that constrains sets in the form of (11) arise in a variety of different situations, see e.g. [19], and are particularly important in the synthesis problems with respect to safe linear temporal logic specifications [13].…”