Enhancing macroscopic fundamental diagram (MFD) dynamic models and improving perimeter control algorithms are the current main research challenges in the MFD research area. Over the last decade, different accumulation-based dynamic models, describing the traffic flow dynamics of one or multi-region systems, have been developed in different forms relying on vehicle conservation equations.

In this research, two enhanced accumulation-based models are developed by incorporating into model structure the time-delay (time-lag) effects as an important factor. The first model incorporates state delay in the MFD output to improve the dynamics, to better represent wave propagation and travel time evolution within the region, especially when the change in demand is fast. While in the second model delayed interconnections are introduced in the dynamic equations to model data processing and communication delays between interconnected regions. The two linearized models are formulated in interconnected forms. Then, the reference model adaptive control approach has been implemented to allow us designing distributed adaptive perimeter control laws. The developed adaptive control scheme postulates one controller structure, however, the controllers’ gains vary with time to adapt themselves against the model parameter uncertainties and state delays. The numerical results demonstrate the flexibility of the distributed adaptive perimeter controllers in handling different cases and various traffic situations with state delays.

增强宏观基本图（MFD）动态模型和改进边界控制算法是MFD研究领域当前的主要研究挑战。在过去的十年中，依靠车辆守恒方程以不同形式开发了描述一个或多个区域系统交通流量动态的基于累积的不同动态模型。

在这项研究中，通过将时间延迟（时滞）效应作为重要因素纳入模型结构，开发了两个增强的基于累积的模型。第一个模型在MFD输出中加入了状态延迟，以改善动态性能，以更好地表示区域内的波传播和传播时间演变，尤其是在需求变化很快的情况下。在第二个模型中，在动态方程式中引入了延迟互连，以对互连区域之间的数据处理和通信延迟进行建模。这两个线性模型以相互联系的形式表示。然后，已经实现了参考模型自适应控制方法，以允许我们设计分布式自适应周边控制律。开发的自适应控制方案假定一种控制器结构，但是，控制器的增益随时间变化，以适应模型参数的不确定性和状态延迟。数值结果证明了分布式自适应外围控制器在处理带有状态延迟的不同情况和各种交通情况时的灵活性。