Overview Of Related Works On Adaptive Traffic Control System

Complex Networks

Cities have been deluged with transportation vessels ranging from metro trains, vehicles, bikes and even auto rickshaws. The continuous use of these elements of road transport has led to traffic congestion which in turn has created a domino effect thus negatively affecting a number of businesses and personal time. The traffic management system in place in many cities has proven worse in handling this huge problem. Use of machine learning and cloud computing to minimize road traffic congestion has gained traction in countries like Malaysia and China. Data Mining plus Video and Image recognition are among the processes deployed to determine live traffic predictions, feeding the system with real-time data and recommendations thereof.

I am interested in understanding the overall structure of the complex adaptive traffic control system and how the structure affects the functioning of the system. I am also interested in understanding the deficiencies in the system. Understanding how different intersections of the road (nodes and edges) interact, and how it influences the observations and the predictions of the machine learning processes used, stand as my objective. I intend to use probabilistic network theory as one of my network science approaches plus a number of statistical tools.

Introduction

Improving traffic networks is critical in today's urbanized society. The traffic networks directly influence the health and wealth of a nation. Unfortunately, for developing countries, considering to improve traffic is off their budget but consequently the governments suffer high costs that arise from poor traffic control systems. Advanced economies like the United States, China and Australia are paying attention to improving traffic networks but still implementing the right mechanisms is at an all-time low. In 2012, surveys indicated the malfunctioning of current traffic control systems and the necessity to apply new methods and improvements in the United States of America.

Most traffic control systems are fixated to operate on a pre-calculated survey of traffic conditions. But traffic patterns do change and the pre-surveyed traffic condition gets outdated. What then can we do when we can no longer depend on outdated information? The use of Adaptive traffic control systems as opposed to to fixed-time plans has been one of the solutions in improving traffic flow. Adaptive traffic signal control may make use of appropriate dynamic programming, fuzzy logic, deep reinforcement learning, wireless sensor networks, vehicular communication or camera sensor and embedded system. Some of the adaptive signal control technologies are:

1. Split Cycle Offset Optimization Technique (SCOOT) – Optimizes Splits, Cycle and Offsets; real-time optimization of signal timing.
2. Sydney Coordinated Adaptive Traffic System (SCATS) – Optimizes Splits, Cycles and Offsets; selects from a library of stored signal timing plans.
3. Real Time Hierarchical Optimized Distributed Effective System (RHODES) – Mainly for diamond interchange locations.
4. Optimized Policies For Adaptive Control (OPAC) – The network is divided into independent sub-networks.
5. Virtual Fixed Cycle – consists of a distributed control strategy featuring a dynamic optimization algorithm that calculates signal timings to minimize performance.
6. ACS Lite – Operates with predetermined coordinated timing plans; automatically adjust splits and offsets accordingly.

The general architecture of these systems is based on a similar concept but there exits minor differences. Major problems of almost all the adaptive control systems is the dependency on the detectors to collect the data and send them to the controllers for processing procedure. A detector failure can paralyze the system. Another problem is adjusting on over-saturation. The interdependency of each intersection on its neighbors makes it extremely difficult to set the signal parameter values for a large complex traffic network with multiple intersections. Providing effective real-time traffic signal control for a large complex traffic network is an extremely challenging distributed control problem.

My approach is to make use of probabilistic networks and eigenvalue approaches to tackle the distributed control problem in adaptive traffic control systems. Application of multivariate statistical methods to adjacency matrices and the use of block-modeling and structural equivalence to determine groups of nodes sharing similar connectivity patterns in the network should be factored. It will be important to also consider knowledge of road networks/transport networks when building the solution. The intersections of the road network which are considered the nodes in this case will be covered with the measures of a node. It will behoove us to know the assortativity coefficient which brings to our understanding the connectivity of a node to others in a network. Other measures such as Shimbel index (nodal accessibility), eccentricity and betweenness centrality are of importance and will be discussed.

Related work

The design of distributed control for interconnected systems has received considerable attention in recent years. Research efforts have focused on two major issues, namely, the design of the optimal control under a priori specified structural constraints and the design of communication architectures of the distributed control. Since Witsenhausen’s work, much research related to the design of optimal distributed control has been focused on characterizing a class of easily solvable problems. One of the positive results showing that the problem for some cases becomes tractable is the work of Ho and Chu where a class of information structures, called partially nested, is defined for which an optimal control law for the LQG problem is linear. Briefly speaking, a plant-controller system is partially connected if controller C1 has access to all information available to controller C2 whenever the decision made by C2 affects the information available to C1.

Rotkowitz and Lall show that the class of quadratically invariant problems may be easily solvable via convex programming algorithms. This is one of the largest classes of tractable problems and it includes many previously known tractable cases. In addition, the authors show conditions where quadratic invariance holds for some sparsity structures, even in cases when the sparsity structures of the plant and the controller differ and provide a specific analytical relationship between quadratic invariance and adjacency matrices. Some authors suggest an independent approach to decentralized control which employs the theory of partially ordered sets to model communication constraints between subsystems. An interesting result regarding interconnection topology is reported which suggests that if the communication between the controllers incurs some cost, then, adding communication channels may degrade the system performance. Characterizing the structural properties of optimal distributed control law constitutes another important question. For spatially invariant systems, it is shown in that the linear quadratic controllers are also spatially invariant and the measurements from other subsystems are exponentially discounted with the distance between the controller and the subsystems. This spatial decaying property is further extended to systems on graphs in which motivates the search for inherently localized control law. The design of optimal control for spatially invariant systems can also be cast into a convex problem if the information in the controllers propagates at least as fast as in the plant as reported. It should be noted that the aforementioned work have a common feature: the structure of the control law has to be specified in advance, that is, they do not consider the problem of structure design, but only the design of the control gain itself. The introduction of communication network, however, offers an additional degree of freedom in designing the distributed control by jointly considering the control gain and its structure, i. e. the communication topology which also serves as design variables. Recently, some work have been devoted to designing the distributed control gain together with the communication topology for interconnected systems. The authors in consider the problem of maximization of the degree of decentralization, i. e. minimizing the number of communication links between the subsystems and the state feedback control laws subject to a given error performance in term of the H∞-norm between the centralized and the decentralized closed loop. The results are extended to the case of dynamic output feedback in by means of a weighted l1 relaxation and the development of an iterative algorithm based on LMIs to deal with the relaxed decentralized control problem.

The authors in consider a linear quadratic optimal control problem with an additional penalty on the number of communication links in the distributed control law. The combinatorial problem is reformulated as a sequence of weighted l1 problems by utilizing the weighted l1 norm to approximate the counting of the communication links. Furthermore, a class of systems is identified for which the weighted l1 problem can be reformulated as a semidefinite program, and thus, the solution can be computed efficiently. Apart from the systems which are interconnected through the dynamics, there are also contributions in multi-agent systems corresponding to communication topology design in recent years. Algebraic connectivity which is the second smallest eigenvalue of the Laplacian matrix is an important performance metric related to the convergence rate of multi-agent systems and its value depends on the communication topology of the network.

There has been some interesting approaches for tackling limited model information based control design problem, although not specifically tailored for it. For example, references introduce methods for designing sub-optimal decentralized control without a global dynamical model of the system. In these works, one key assumption is that the plant consists of an interconnection of weakly coupled subsystems. Then, under this assumption, an optimal control is designed for each subsystem using only the corresponding local model information and the obtained subcontrollers are connected to construct a global control law. In addition, the authors show that, when the coupling is negligible, this control law is satisfactory in terms of closed-loop stability and performance. However, as coupling strength increases, even closed-loop stability guarantees are lost. Note that the motivation behind their studies has been to design fully decentralized near-optimal control for large-scale dynamical systems and to avoid numerical complications stemming from the high dimension of the system, by splitting the original problem into several smaller ones.

Other approaches are based on receding horizon control and use decomposition methods to solve each step’s optimization problem in a decentralized manner with only limited information exchange between subsystems. Dual decomposition is used for distributed optimization of local controllers. On the analysis part, the authors deriscalable decentralized conditions that can guarantee robust stability for networks of linear interconnected, stable, linear time invariant systems. It is shown that robust stability of the entire network is guaranteed by satisfying local rules that only involve an agent and its neighboring dynamics. Recently, the authors present a rigorous characterization of the best closed-loop performance which can be attained through limited model information design and, furthermore, they study the trade-off between the closed-loop performance and the amount of exchanged information based on the work. Most of the results, however, assume that the structure of the control law is given a priori. The last, but yet important issue is the robustness of the whole system in the presence of interconnection failures.