Optimal traffic signal control for an $M\times N$ traffic network
Yinfei Li Shuping Chen
Journal of Industrial & Management Optimization 2008, 4(4): 661-672 doi: 10.3934/jimo.2008.4.661
This paper discusses the optimal traffic control signal setting for an $M \times N$ rectangular road traffic network. By introducing the concepts of synchronization rate and non-synchronization degree, a mathematical model is constructed and an optimization problem is posed. Then, a new iterative algorithm is developed to solve this optimal traffic control signal setting problem. Convergence properties for this iterative algorithm are established. Finally, a numerical example is solved to illustrate the effectiveness of the method.
keywords: optimization. intersection traffic signal setting synchronization Urban traffic network
Kok Lay Teo Shuping Chen
Journal of Industrial & Management Optimization 2005, 1(1): i-i doi: 10.3934/jimo.2005.1.1i
It is with great pleasure that we bring to you the inaugural issue of the Journal of Industrial and Management Optimization (JIMO), published by the American Institute of Mathematical Sciences.
keywords: Management optimization.
A unified theory of maximum principle for continuous and discrete time optimal control problems
Zaidong Zhan Shuping Chen Wei Wei
Mathematical Control & Related Fields 2012, 2(2): 195-215 doi: 10.3934/mcrf.2012.2.195
Traditionally, the time domains that are widely used in mathematical descriptions are limited to real numbers for the case of continuous-time optimal control problems or to integers for the case of discrete-time optimal control problems. In this paper, based on a family of "needle variations", we derive maximum principle for optimal control problem on time scales. The results not only unify the theory of continuous and discrete optimal control problems but also conclude problems involving time domains in partly continuous and partly discrete ingredients. A simple optimal control problem on time scales is discussed in detail. Meanwhile, the results also unify the theory of some hybrid systems, for example, impulsive systems.
keywords: maximum principle Ekeland's variational principle optimal control Time scales impulsive control.

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