array(2) { ["lab"]=> string(3) "968" ["publication"]=> string(4) "7462" } Linear complementarity system approach to macroscopic freeway traffic modelling: uniqueness and convexity - 钟任新 | LabXing

钟任新

简介 城市交通系统建模/动态交通分配/最优控制和非线性控制/随机动态规划/自适应动态规划/强化学习与智能交通系统应用

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Linear complementarity system approach to macroscopic freeway traffic modelling: uniqueness and convexity

2015
期刊 Transportmetrica A: Transport Science
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The modified cell transmission model (MCTM) is formulated as a linear complementarity system (LCS) in this paper. The LCS formulation presented here consists of a discrete time linear system and a set of complementarity conditions. The discrete time linear system corresponds to the flow conservation equations while the complementarity conditions govern the sending and receiving functions defined by a series of ‘min’ operations in the MCTM. Technical difficulties encountered in application of the CTM and its extensions such as the hard nonlinearity caused by the ‘min’ operator can be avoided by the proposed LCS model. Several basic properties of the proposed LCS formulation, for example, existence and uniqueness of solution, are analysed based on the theory of linear complementarity problem. By this formulation, the theory of LCS developed in control and mathematical programming communities can be applied to the qualitative analysis of the CTM/MCTM. It is shown that the CTM/MCTM is equivalent to a convex programme which can be converted into a constrained linear quadratic control problem. It is found that these results are irrelevant to the cell partition, that is, different cell partitions will not change the uniqueness and convexity of solution. This property is essential for stability analysis and control synthesis. The proposed LCS formulation makes the CTM/MCTM convenient for the design of traffic state estimators, ramp metering controllers.