Parallel Computation For Optimal Control Of Large-scale Connected Vehicles

Connected and Automated Vehicles(CAVs)take the advantages of information sharing and cooperative control and have a great potential to enhance traffic performance.Thanks to progress in cloud computation,it is possible to control multiple CAVs in a centralized way,which have the advantage of easy modeling and general implementation.In the centralized scheme,one common challenge is how to deal with the growing computation demand as the system size increases.Because of the inpendence between computation complexity and system scale,the existing methods can only have a good performance in small scale problem.This paper aims to deal with the cooperative automation for large-scale CAVs via parallel computation and cope with the asynchrony updates in parallel fashion,which will lay a foundation for the application of distributed parallel optimization on coordination of CAVs.Firstly,the coordiantion of large-scale CAVs is formulated as a centralized optimization problem.An interactive topology is used to describe the spatial collision avoidance relationships among neighbor vehicles via graph theory.Based on the topology,a cloud computation network is desgined to excute the following parallel algorithms.Because of complexities in formulation of CAVs coordination,the issue is handled in two aspects,i.e.,gloabl path palnning to generate reference for every single vehicle regardless of other vehicles and local trajectory following in a cooperative way to avoid collision with neighbors.Considering the advantages of MPC in dealing with dynamic environment,the optimization problem is coped in a receding finite horizon fashion.Secondly,ADMM is applied to decompose the coupling constraints among decision variables,leading to a parallel algorithm.We use Taylor series to linearize non-convex constraints,and introduce a set of consensus constraints to transform the centralized problem to a standard consensus optimization problem.A synchronous paralllel algorithm is firstly proposed to solve the cnsensus optimization problem by applying the Alternationg Direction Method of Multipliers(ADMM).The ADMM framework allows us to decompose the coupling constraints and decision variables,leading to parallel iterations for each vehicle in a synchronous fashion,which guarantees its scalability for large-scale scenario in theory.Thirdly,an asynchronous version of the parallel algorithm that allows the vehicles to update their varaables asynchronously in computation network is proposed.Enssentially,the asynchronous algorithm is a partial updating fashion.Based on this property,the asynchronous algorithm is analyzed in the view of Douglas-Rachford Splitting Method.Combined with the convergence of random sequence,the convergence and linear convergence rate of our asynchronous algorithm are proved.Finally,the proposed algorithms are validated by extensive numerical simulations.Three typical scenes are chosen to illustrate the effectiveness of the cooperative automation algorithm.Computation efficiency under different number of vehicles are simulated to illustrate the scalability of the parallel algorithm.The convergence of asynchronous algorithm is also validated.