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Abstract
This research aims to develop, enhance, and validate infrastructure-based hierarchical control framework designs for improving the mobility of large-scale heterogeneous traffic networks. This research defines heterogeneity as a multi-vehicle traffic network consisting of Human-Driven Vehicles (HDVs) and Autonomous Vehicles (AVs), distinguished by their operational characteristics and controllability. AVs have gained huge interest across private industry, academia, government, and the public because they promise higher road efficiency, improved safety, better energy consumption, and improved emissions. However, the widespread adoption of autonomous vehicle technology will likely take place over several years (if not decades) as the technology becomes more widely accepted by the general public and more cost-effective. Therefore, there will be a long period of time when we have both AVs and HDVs sharing the same road and it is essential to develop traffic management strategies that take the uncertainty associated with the heterogeneity in the traffic networks into account. Furthermore, it is crucial to understand the extent to which these control strategies improve the performance of the traffic network. To capture the realistic nature of large-scale heterogeneous traffic networks, we adopt the heterogeneous (multi-class) METANET model wherein the density and velocity dynamics of each vehicle class in each cell are described mathematically. In order to achieve a higher-fidelity traffic model, we considered state- and class-dependent model parameters to better capture the complex underlying dynamics of a heterogeneous traffic network. Moreover, in this research, we propose a hierarchical distributed infrastructure-based control framework to manage large-scale heterogeneous traffic networks. At the lower-level, we employed the Distributed Filtered Feedback Linearization (D-FFL) controller. The purpose of this controller is to track the desired density of each vehicle class in the target cells which is set by the upper-level controller. D-FFL tracks the reference density by controlling the suggested velocity of vehicles in the target cell and its upstream cell. The D-FFL controller requires only limited model information, specifically, knowledge of the vector relative degree and the dynamic-inversion matrix, which is the nonlinear extension of the high-frequency-gain matrix for linear systems. The controller inputs derived by the classic feedback linearization control approach (ideal control inputs) and the control inputs generated by the D-FFL are mathematically equivalent. However, the feedback linearization method requires full knowledge of the plant model and measurement of the disturbance of the system which is hard to achieve based on the complex underlying dynamics of the heterogeneous traffic network.At the upper-level, in our initial design, a Distributed Extremum-Seeking (D-ES) controller is designed and implemented which aims to find the optimal operating densities of each vehicle class in the target cells over time. D-ES is a model-free, real-time adaptive control algorithm that is useful for adapting control parameters to unknown system dynamics and unknown mappings from control parameters to an objective function. The gradient-based D-ES comprises three essential components: the dither signals, the gradient estimator, and the optimizer operating at progressively slower time scales. The primary objective of the upper-level controller in our research is to achieve two main goals simultaneously: the maximization of the average flow of the target cell to mitigate traffic congestion and the minimization of the flow difference between the target cell and the upstream flow to prevent the propagation of congestion in the backward direction. The desired densities are then fed into the lower-level controller as the reference model. To improve the performance of the designed hierarchical controller and reduce the convergence time, we designed and implemented Newton Extremum Seeking (NES) at the upper level of the hierarchy to feed the optimal density of target cells to the lower-level controller. One of the key distinctions between the Newton algorithm and the gradient algorithm is that the convergence of the former is not solely contingent on the second derivative (Hessian) of the cost map and it is user-assignable. In fact, this allows for the deliberate synchronization of all parameters to converge at a uniform pace, resulting in straightforward paths leading to the optimal point in a shorter time. Moreover, to address the potential loss in optimality that may arise due to continuous sinusoidal perturbations around the optimal point, we propose a switched control scheme to be added to the NES structure. The proposed switched control scheme involves reducing the amplitude of perturbations after convergence, specifically within a neighborhood around the desired state. The switch is determined by utilizing a Lyapunov function that is based on an averaged model of the NES feedback system. This Lyapunov function is designed to approximate the proximity to the desired state, and based on this estimate, the switch is activated to reduce the perturbation size. The enhanced upper-level controller design is named Lyupanov-based Switch Newton Extremum Seeking (LSNES) which is then combined with the FFL to form the hierarchical control framework. Finally, we established a MATLAB-VISSIM COM interface that allows closed-loop control of a simulated traffic scenario in PTV-VISSIM to test and validate the effectiveness of the distributed ES-FFL and LSNES-FFL control approaches in large-scale traffic networks. The simulation results show that our initial control framework design can effectively reduce congestion and prevent congestion back-propagation during peak hours in homogeneous and heterogeneous traffic networks. We further compare our novel control framework design with common model-free macroscopic traffic control approaches. By implementing our improved hierarchical control framework, we also show that the Lyupanov-based Switch Newton Extremum Seeking-FFL (LSNES-FFL) control framework has a %42 faster convergence rate with respect to the conventional ES-FFL method.