基于四元素构架的车辆队列动力学建模与分布式控制

发布时间：2018-02-01 21:17

本文关键词： 车辆队列分布式控制闭环稳定性鲁棒性能模型预测控制　出处：《清华大学》2015年硕士论文　论文类型：学位论文

【摘要】：车辆队列具有减缓交通拥堵、提高驾驶安全性和改进燃油经济性的潜力。现有研究多针对一种具体队列构型设计一类分析手段,缺乏一种普遍的建模分析框架,难以分析不同信息流拓扑结构下的车辆队列。为此,本文建立了一种车辆队列的四元素建模构架,研究了线性匀质队列的闭环稳定性和鲁棒性能,提出了一种适用于非线性异质队列的分布式模型预测控制设计方法,为信息流多样化车辆队列的性能分析和控制器设计奠定了基础。首先,基于多智能体协调控制视角,提出了一种车辆队列的四元素建模构架,并建立了各个元素的一般性数学描述。该构架将队列分解为四个基本模块:1)节点动力学;2)信息流拓扑结构;3)队列几何构型;4)分布式控制器。该模型为定量地刻画信息流拓扑结构、车辆动力学、控制器参数对队列性能的影响提供了统一性分析框架。其次,依托所提出的四元素构架,分析了线性匀质队列的闭环稳定性。利用矩阵因子分解将匀质队列动力学进行解耦,使得队列整体闭环稳定性等价多个小规模问题的稳定性。主要结论为:1)利用Routh Hurwitz稳定性判据,解析地建立了一类信息流拓扑结构下线性控制器参数的稳定区域。2)利用矩阵特征根分析,指出双向跟随式队列的稳定裕度随规模增加以12速度衰减3)利用Rayleigh-Ritz定理,从信息流拓扑结构选择和非对称控制提出了两种改善稳定裕度的方法。4)基于子系统Riccati方程的求解,给出了一种稳定控制器参数设计方法。然后,基于传递函数的无穷范数分析,讨论了有限能量扰动工况下线性匀质队列的鲁棒性能。研究发现:1)前车跟随式队列的鲁棒性能随规模呈指数增长,与线性控制器的增益选择无关。2)若每个跟随车辆均能获取领航车辆信息,形成前车-领航者跟随式结构,则其鲁棒性能至少与规模无关。3)双向跟随式队列的鲁棒性能随规模至少呈多项式(2)增长。最后,针对非线性异质队列,提出了一种分布式模型预测控制器设计方法。该控制器利用邻域车辆节点的预测轨迹信息构造子优化问题,能够适用于多种信息流拓扑结构。同时,将节点代价函数作为Lyapunov函数进行分析,针对单向信息流的车辆队列,给出了一种保证车辆队列渐近稳定的充分条件。
[Abstract]:Vehicle queue has the potential of reducing traffic congestion, improving driving safety and improving fuel economy. Most of the existing researches focus on the design of a specific queue configuration and lack of a general modeling and analysis framework. It is difficult to analyze the vehicle queue under different information flow topologies. In this paper, a four-element modeling framework of vehicle queue is established, and the closed-loop stability and robust performance of the linear homogeneous queue are studied. A design method of distributed model predictive control for nonlinear heterogeneous queues is proposed, which lays a foundation for performance analysis and controller design of diversified traffic queues. Based on the view of multi-agent coordinated control, a four-element modeling framework for vehicle queue is proposed. The general mathematical description of each element is established. The structure decomposes the queue into four basic modules: 1) node dynamics; 2) information flow topology; 3) queue geometry; 4) distributed controller. This model provides a unified analysis framework for quantificationally describing the effects of information flow topology, vehicle dynamics and controller parameters on queue performance. Based on the proposed four-element framework, the closed-loop stability of linear homogeneous queue is analyzed, and the dynamics of homogeneous queue is decoupled by matrix factorization. Make the global closed-loop stability of queue equivalent to the stability of several small scale problems. The main conclusion is: 1) using Routh / Hurwitz stability criterion. The stability region of linear controller parameters under a class of information flow topology is established analytically. 2) the matrix eigenvalue analysis is used. It is pointed out that the stability margin of the bidirectional follower queue attenuates by 12 speed with the increase of scale.) the Rayleigh-Ritz theorem is used. Two methods to improve the stability margin are proposed from the information flow topology selection and asymmetric control. 4) based on the solution of subsystem Riccati equation. In this paper, a parameter design method of stable controller is presented. Then, the infinite norm analysis based on transfer function is presented. The robust performance of linear homogeneous queue under finite energy disturbance is discussed. It is found that the robust performance of the follower queue increases exponentially with the scale of the queue. It is independent of gain selection of linear controller. 2) if every follower vehicle can obtain the information of pilotage vehicle, it can form the front vehicle-pilot follower structure. The robustness of the queue is at least. 3) the robustness of the bidirectional follower queue increases with the size of the queue. Finally, for the nonlinear heterogeneous queue, the robustness increases with the size of the queue. This paper presents a design method of distributed model predictive controller, which can be applied to a variety of information flow topologies by using the predictive trajectory information of adjacent vehicle nodes to construct sub-optimization problem. The node cost function is used as the Lyapunov function and a sufficient condition to ensure the asymptotic stability of the vehicle queue is given for the one-way traffic queue.
【学位授予单位】：清华大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：U491

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