Biblio

In this paper, we propose a compositional scheme for the construction of abstractions for networks of control systems by using the interconnection matrix and joint dissipativity-type properties of subsystems and their abstractions. In the proposed framework, the abstraction, itself a control system (possibly with a lower dimension), can be used as a substitution of the original system in the controller design process. Moreover, we provide a procedure for constructing abstractions of a class of nonlinear control systems by using the bounds on the slope of system nonlinearities. We illustrate the proposed results on a network of linear control systems by constructing its abstraction in a compositional way without requiring any condition on the number or gains of the subsystems. We use the abstraction as a substitute to synthesize a controller enforcing a certain linear temporal logic specification. This example particularly elucidates the effectiveness of dissipativity-type compositional reasoning for large-scale systems.

In this paper we consider connected and autonomous vehicles (CAV) in a traffic network as moving waves defined by their frequency and phase. This outlook allows us to develop a multi-layer decentralized control strategy that achieves the following desirable behaviors: (1) safe spacing between vehicles traveling down the same road, (2) coordinated safe crossing at intersections of conflicting flows, (3) smooth velocity profiles when traversing adjacent intersections. The approach consist of using the Kuramoto equation to synchronize the phase and frequency of agents in the network. The output of this layer serves as the reference trajectory for a back-stepping controller that interfaces the first-order dynamics of the phase-domain layer and the second order dynamics of the vehicle. We show the performance of the strategy for a single intersection and a small urban grid network. The literature has focused on solving the intersection coordination problem in both a centralized and decentralized manner. Some authors have even used the Kuramoto equation to achieve synchronization of traffic lights. Our proposed strategy falls in the rubric of a decentralized approach, but unlike previous work, it defines the vehicles as the oscillating agents, and leverages their inter-connectivity to achieve network-wide synchronization. In this way, it combines the benefits of coordinating the crossing of vehicles at individual intersections and synchronizing flow from adjacent junctions.