The Scientific World Journal

Volume 2016 (2016), Article ID 6719459, 9 pages

http://dx.doi.org/10.1155/2016/6719459

## An Adaptive Fuzzy-Logic Traffic Control System in Conditions of Saturated Transport Stream

Department of Information Technology, Tashkent State Technical University, 100095 Tashkent, Uzbekistan

Received 26 December 2015; Accepted 16 May 2016

Academic Editor: Oleg H. Huseynov

Copyright © 2016 N. R. Yusupbekov et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This paper considers the problem of building adaptive fuzzy-logic traffic control systems (AFLTCS) to deal with information fuzziness and uncertainty in case of heavy traffic streams. Methods of formal description of traffic control on the crossroads based on fuzzy sets and fuzzy logic are proposed. This paper also provides efficient algorithms for implementing AFLTCS and develops the appropriate simulation models to test the efficiency of suggested approach.

#### 1. Introduction

One of the most important and promising tasks of transport systems in modern cities is to satisfy the needs of both state and citizens in efficient transport services. Prior studies investigated methods of improving operational efficiency of transport management systems in different countries [1, 2]. The results demonstrate that the most promising direction is the development and implementation of intelligent transport systems (ITS). Intelligent transportation system (ITS) is an integration of advanced information and communication technologies, computer-aided control and traffic management, transport infrastructure, vehicles, and users, to improve safety and efficiency of road traffic [3].

Today, the scope of the ITS implementation ranges from solving problems of traffic-light management and road safety to increasing the efficiency of the existing transport system. Capabilities of the ITS are not limited to improving the safety and efficiency of the transporting processes. It builds information retrieval systems, focused on the identification of vehicles, the analysis of traffic situations, and detecting violations. Furthermore, ITS allows searching violators, stolen vehicles, and suspected criminals. Such operations are based on remote video monitoring, collection, and intellectual processing of large amounts of data, as well as automatic generation of analytical reports. The reports include both simple and integrated decision-making mechanisms.

The review of the extant ITS projects showed that the latest advances in information and communications technologies, control systems theory, data mining, and analysis techniques are not widely implemented in road traffic management. The reason is the lack of extensive research and efficient methods of synthesis of multilevel intelligent systems in conditions of fuzziness of parameters of the road traffic. There are a number of studies on automating the development of control systems and their components. They are focused on developing and improving the systems of coordinated traffic management on highways and adaptive management that addresses problems of vehicle throughput [2–4]. Furthermore, there are a number of studies that focus on optimizing the traffic-light management [3–8]. A significant number of works are devoted to the development of technical methods for measuring the parameters of road traffic and their processing [4–9]. However, these works are highly scattered and focus on solving local problems of automated control of road traffic. They do not take into account that the improvement of road traffic in a particular area may lead to deterioration of the traffic situation on the other site. Another factor that is not considered by previous studies is that synthesized parameters of traffic-light management systems are optimal only under certain conditions—when the parameters of road traffic do not change over time (or change in short intervals). In most cases, the synthesis of control systems of road traffic does not consider unpredictable traffic situations, fuzziness of the parameters of the road traffic.

Therefore, developing conceptual framework and effective methods of structural and parametric synthesis of control systems of road traffic and development of information technology support systems on their basis is important.

#### 2. Statement of a Problem

Below, we consider a class of traffic control systems with imprecise information about the object, in which the qualitative characteristics of the road traffic are dominant.

In general, for synthesis of the traffic control systems, the object of control can be formally represented as follows:where is the range of conditions (e.g., object, output); is a model of the crossroad, represented by the graph in the space ; are the vertices (nodes) of the graph, corresponding to the nodes of possible branches of the road traffic; is the plurality of arcs of the graph (road section, connecting nodes of possible branches of road traffic) with corresponding weight coefficients as (intensity of road traffic, density of road traffic, and average speed on this particular road section); is the plurality of characteristics and determinants, describing the state of the control object Ω and taking their values each in his own set of values ; is the range of output values (observed processes, parameters, estimates, etc.); is the range of controls (decisions); is the time (discrete or continuous); is the description of the dynamics of the state of the object, the reaction of the dynamic system in a particular state to control actions; is the output, describing the observation process of the control object (obtaining estimates, opinions, etc.); are some external uncontrollable factors, conditions, and others that have an impact on the dynamics of the control object.

The analysis of transport flows on the crossroads as controlled objects demonstrated that their mathematical model should be able to deal with information fuzziness and describe random values and processes invariantly to their distribution. Mathematical models should also provide math formalism to express expert knowledge, rich empiricism, and heuristics.

According to aforementioned requirements, a generalized dynamic model of the object controls (OC) can be defined as the following linear equation with fuzzy state space [9, 10]:with fuzzy initial conditionswhere , are the fuzzy operations of multiplication and addition; is a control signal (scalar) that accepts discrete numerical value; is the state space vector, is the output variables vector, is the membership function (MF) of the state space of the object controls, ;are the matrix of the fuzzy coefficients of the model, where

Some th state space vector as a time function can be described as fuzzy relation [1, 3]:

At a fixed time, this variable can be expressed as a fuzzy set:

A similar description is th output variable:

Initial conditions and the number of variables of the state vector also can be described as the following fuzzy sets:

Suppose that the membership functions of the input and output linguistic variables are defined as the following analytical functions:

In (10) and (11), the coefficients , , , , , , , , , and are mood, width, and slope of the membership functions of the input and output linguistic variables. These coefficients allow forming high variety of shapers of membership functions. They can also act as indicators of information fuzziness for a formal model of the control objects, which are provided as state space equation (2).

We assume that the indicators of quality of the control system (e.g., time of transient process, overshoot, and bug tracking) are given as the following utility functions generated by experts,under certain limitations for variables’ state space and control signal:where is membership function of the quality index of the control system, provided as (6). Then, the problem of the synthesis of control system, for control objects provided as in a fuzzy state equation (2), with the quality evaluation indicator (12) and the system of constraints (13), can be formulated as described below.

First, it is necessary to synthesize control systems with embedded adaptive adjustment parameters of the controller for object controls (2). All signals should be limited in (13) and the transient processes in the system have to satisfy the predetermined quality parameters (12).

For a given statement of the problem, gradient speed search algorithm in the parametric form, with a proportional-integral controller and circuit bootstrapping can be selected [2, 3]. Among available methods of adaptive control with robust characteristics, the gradient speed search algorithm is the least complex. It also fits the constraints on the control signal and its velocity. Then, the control signal is generated based on the fuzzy set values of state space parameters, according to the following modified control signal: where , is discretization step, are the parameters of the adaptive controller; is a signal mismatch between the actual parameters of the state vector and desirable model parameters; is the membership function of the signal mismatch, provided as (10); , , , , ; are the integrated parameters of the state vector; , are the coefficients, obtained by Lyapunov’s decision equation and the matrix equation with reference model .

The synthesis of the control law based on fuzzy model can increase the robustness of the gradient speed search algorithm; it can also maintain limitations of the phase trajectories in certain areas under uncompensated information fuzziness [11, 12].

Quality indicators of the control systems are based not only on the best possible dynamic characteristics of object controlling , but also on the parameters of its fuzziness , , , , , , , , , and , provided as (10) and (11).

Reducing the information fuzziness and, consequently, improving the quality control can be achieved by optimizing the parameters of the membership functions of the input and output linguistic variables and fuzzy-logic controllers. This is the core idea of the algorithm for traffic control systems in crossroads, presented in this study.

#### 3. The Concept of the Problem Synthesis Adaptive Fuzzy-Logic Traffic Control Systems

Let us consider the problem of synthesis of fuzzy control system of road traffic under conditions of intense traffic in more detail.

We suppose that there is a crossroad regulated with an equal number of intersecting lanes and well-known traffic intensity of , , , . The directions of traffic 1 and 3 are perpendicular to the directions 2 and 4.

We introduce the following terms: is the duration of the green signal of the traffic light to the first direction of the traffic , ; is the duration of the green signal of the traffic light to the opposite direction of the traffic , .

Taking into consideration the principle of progressive correction, the control object can be defined as (2). The control process assumes that there is a target goal and the control system functions to achieve it. The quality of functioning (criterion of efficiency) of the control system (12) assumes a degree of adaptability to fulfill its task—ensuring a safe traffic with a minimum delay. Therefore, the problem of optimal traffic control at crossroads can be defined as follows.

It is necessary to identify control signals and (the duration of the green signal of the traffic light for each lane) so that the actual state of the traffic was as close as possible to the desired state, when the control signals have certain limitations and the system exposed uncontrolled external and parametric impacts .

That is, it is necessary to find such parameters of the traffic control system that the total delay at the crossroads is minimal [12, 13]:orunder the constraintswhere and are the delay evaluation function and penalty function for the length of queue in front of the stop line of the traffic light in directions 1 and 3, respectively; and are the delay evaluation function and penalty function for the length of queue in front of the stop line of the traffic light in directions 2 and 4, respectively; is the duration of green signal of traffic light in the* i-stage*; , , , and are the number of vehicles entered and left the control zone at the crossroad in the th phase, respectively; and are the minimum and maximum duration of the green signal of the traffic light, respectively; and are the length of the queue in front of the stop line at directions 1 and 3 and 2 and 4 in the th stage, respectively; is the maximum allowed length of the queue in front of the stop line.

In general, the process control system at the T-shaped crossroads can be rearranged as a feedback control system with adaptive fuzzy-logic controller (Figure 1). In the proposed scheme, the input vector is converted into fuzzy-logic controller (FLC) through fuzzification block. Next, fuzzy inference is performed based on rule base, which results in a fuzzy output variable . The output values from the FLC are then transferred from the fuzzy region to accurate region through defuzzification block [14, 15].