FUZZY LOGIC TRAFFIC SIGNAL CONTROL

Transcription

1 FUZZY LOGIC TRAFFIC SIGNAL CONTROL BY ZEESHAN RAZA ABDY PREPARED FOR DR NEDAL T. RATROUT

2 INTRODUCTION Signal control is a necessary measure to maintain the quality and safety of traffic circulation. Further development of present signal control has great potential to reduce travel times, vehicle and accident costs, and vehicle emissions. The development of detection and computer technology has changed traffic signal control from fixed-time open-loop regulation to adaptive feedback control. Present adaptive control methods, like the British MOVA, Swedish SOS (isolated signals) and British SCOOT (area-wide control), use mathematical optimization and simulation techniques to adjust the signal timing to the observed fluctuations of traffic flow in real time. The optimization is done by changing the green time and cycle lengths of the signals. In area-wide control the offsets between intersections are also changed. Several methods have been developed for determining the optimal cycle length and the minimum delay at an intersection but, based on uncertainty and rigid nature of traffic signal control, the global optimum is not possible to find out. As a result of growing public awareness of the environmental impact of road traffic many authorities are now pursuing policies to: manage demand and congestion; influence mode and route choice; improve priority for buses, trams and other public service vehicles; provide better and safer facilities for pedestrians, cyclists and other vulnerable road users;

3 reduce vehicle emissions, noise and visual intrusion; and improve safety for all road user groups. In adaptive traffic signal control the increase in flexibility increases the number of overlapping green phases in the cycle, thus making the mathematical optimization very complicated and difficult. For that reason, the adaptive signal control in most cases is not based on precise optimization but on the green extension principle. In practice, uniformity is the principle followed in signal control for traffic safety reasons. This sets limitations to the cycle time and phase arrangements. Hence, traffic signal control in practice are based on tailor-made solutions and adjustments made by the traffic planners. The modern programmable signal controllers with a great number of adjustable parameters are well suited to this process. For good results, an experienced planner and fine-tuning in the field is needed. Fuzzy control has proven to be successful in problems where exact mathematical modelling is hard or impossible but an experienced human can control the process operator. Thus, traffic signal control in particular is a suitable task for fuzzy control. Indeed, one of the oldest examples of the potentials of fuzzy control is a simulation of traffic signal control in an inter-section of two one-way streets. Even in this very simple case the fuzzy control was at least as good as the traditional adaptive control. In general, fuzzy control is found to be superior in complex problems with multiobjective decisions. In traffic signal control several traffic flows compete from the same time and space, and different priorities are often set to different traffic flows or vehicle groups. In addition, the optimization includes several simultaneous criteria, like the

4 average and maximum vehicle and pedestrian delays, maximum queue lengths and percentage of stopped vehicles. So, it is very likely that fuzzy control is very competitive in complicated real intersections where the use of traditional optimization methods is problematic. Benefits and disadvantages of fuzzy systems Fuzzy logic has been introduced and successfully applied to a wide range of automatic control tasks. The main benefit of fuzzy logic is the opportunity to model the ambiguity and the uncertainty of decision-making. Moreover, fuzzy logic has the ability to comprehend linguistic instructions and to generate control strategies based on priori communication. The point in utilizing fuzzy logic in control theory is to model control based on human expert knowledge, rather than to model the process itself. Indeed, fuzzy control has proven to be successful in problems where exact mathematical modelling is hard or impossible but an experienced human operator can control process. In general, fuzzy control is found to be superior in complex problems with multi-objective decisions. At present, there is a multitude of inference systems based on fuzzy technique. Most of them, however, suffer ill-defined foundations; even if they are mostly performing better that classical mathematical method, they still contain black boxes, e.g. de fuzzification, which are very difficult to justify mathematically or logically. For example,

5 fuzzy IF - THEN rules, which are in the core of fuzzy inference systems, are often reported to be generalizations of classical Modus Ponens rule of inference, but literally this not the case; the relation between these rules and any known many-valued logic is complicated and artificial. Moreover, the performance of an expert system should be equivalent to that of human expert: it should give the same results that the expert gives, but warn when the control situation is so vague that an expert is not sure about the right action. The existing fuzzy expert systems very seldom fulfil this latter condition. Many researches observe, however, that fuzzy inference is based on similarity. Kosko [7],for example, writes 'Fuzzy membership...represents similarities of objects to imprecisely defined properties'. Taking this remark seriously, we study systematically many-valued equivalence, i.e. fuzzy similarity. It turns out that, starting from the Lukasiewicz well-defined many-valued logic, we are able to construct a method performing fuzzy reasoning such that the inference relies only on experts knowledge and on well-defined logical concepts. Therefore we do not need any artificial defuzzification method (like Center of Gravity) to determine the final output of the inference. Our basic observation is that any fuzzy set generates a fuzzy similarity, and that these similarities can be combined to a fuzzy relation which turns out to a fuzzy similarity, too. We call this induced fuzzy relation total fuzzy similarity. Fuzzy IF - THEN inference systems are, in fact, problems of choice: compare each IF-part of the rule base with an actual input value, find the most similar case and fire the corresponding THEN-part; if it is not unique, use a criteria given by an expert to proceed. Based on the Lukasiewicz welldefined many valued logic, we show how this method can be carried out formally.

6 Hypothesis and Principles of Fuzzy Traffic Signal Control Traffic signal control is used to maximize the efficiency of the existing traffic systems [6]. However, the efficiency of traffic system can even be fuzzy. By providing temporal separation of rights of way to approaching flows, traffic signals exert a profound influence on the efficiency of traffic flow. They can operate to the advantage or disadvantage of the vehicles or pedestrians, depend on how the rights of ways are allocated. Consequently, the proper application, design, installation, operation, and maintenance of traffic signals is critical to the orderly safe and efficient movement of traffic at intersections. In traffic signal control, we can find some kind of uncertainties in many levels. The inputs of traffic signal control are inaccurate, and that means that we cannot handle the traffic of approaches exactly. The control possibilities are complicated, and handling these possibilities are an extremely complex task. Maximizing safety, minimizing environmental aspects and minimizing delays are some of the objectives of control, but it is difficult to handle them together in the traditional traffic signal control. The causeconsequence-relationship is also not possible to explain in traffic signal control. These are typical features of fuzzy control. Fuzzy logic based controllers are designed to capture the key factors for controlling a process without requiring many detailed mathematical formulas. Due to this fact, they have many advantages in real time applications. The controllers have a simple computational structure, since they do not require many numerical calculations. The IF- THEN logic of their inference rules does not require much computational time. Also, the

7 controllers can operate on a large range of inputs, since different sets of control rules can be applied to them. If the system related knowledge is represented by simple fuzzy IF- THEN-rules, a fuzzy-based controller can control the system with efficiency and ease. The main goal of traffic signal control is to ensure safety at signalized intersections by keeping conflict traffic flows apart. The optimal performance of the signalized intersections is the combination of time value, environmental effects and traffic safety. Our goal is the optimal system, but we need to decide what attributes and weights will be used to judge optimality. The entire knowledge of the system designer about the process, traffic signal control in this case, to be controlled is stored as rules in the knowledge base. Thus the rules have a basic influence on the closed-loop behaviour of the system and should therefore be acquired thoroughly. The development of rules is time consuming, and designers often have to translate process knowledge into appropriate rules. Sugeno and Nishida mentioned four ways to derive fuzzy control rules: 1. operators experience 2. control engineer's knowledge 3. fuzzy modelling of the operator's control actions 4. fuzzy modelling of the process Zimmermann added three sources more 5. crisp modeling of the process 6. heuristic design rules

8 7. on-line adaptation of the rules. Usually a combination of some of these methods is necessary to obtain good results. As in conventional control, increased experience in the design of fuzzy controllers leads to decreasing development times.. FUSICO PROJECT The main goals of FUSICO-research project are theoretical analysis of fuzzy traffic signal control, generalized fuzzy rules for traffic signal control using linguistic variables, validation of fuzzy control principles and calibration of membership functions, and development of a fuzzy adaptive signal controller. The vehicle-actuated control strategies, like SOS, MOVA and LHOVRA, are the control algorithms of the first generation. The fuzzy control algorithm can be one of the algorithms of the second generation, the generation of artificial intelligence (AI). The fuzzy control is capable of handling multi-objective, multi-dimensional and complicated traffic situations, like traffic signalling. The typical advantages of fuzzy control are simple process, effective control and better quality. FUSICO-project modelled the experience of policeman. The rule base development was made during the fall Mr. Kari J. Sane, experienced traffic signal planner, was working at the Helsinki University of Technology at this time. Everyday discussions and working groups helped us to model his experience to our rules.

9 In particular pathological traffic jams or situations where there are very few vehicles in circulation; there first-in-first-out is the only reasonable control strategy. The Algorithm is looking for the most similar IF-part to the actual input value, and the corresponding THEN-part is then fired. Three realistic traffic signal control systems were constructed by means of the Algorithm and a simulation model tested their performance. Similar simulations were made to a non-fuzzy and classical Mamdani style fuzzy inference systems, too. The results with respect to average vehicle and pedestrian delay or average vehicle delay were in most cases better on fuzzy similarity based control than on the other control systems. Comparisons between fuzzy similarity based control and Mamdani style fuzzy control also strength an assumption that, in approximate reasoning, a fundamental concept is many-valued similarity between objects rather than a generalization of classical Modus Ponens rule of inference. FUSICO PROJECT RESULTS The results of this project have indicated that fuzzy signal control is the potential control method for isolated intersections. The comparison results of Pappis-Mamdani control, fuzzy isolated pedestrian crossing and fuzzy two-phase control are good. The results of isolated pedestrian crossing indicate that the fuzzy control provides the effective compromise between the two opposing objectives, minimum pedestrian delay and minimum vehicle delay. The results of two-phase control and Pappis-Mamdani

10 control indicate that the application area of fuzzy control is very wide. The maximum delay improvement was more than 20 %, which means that the efficiency of fuzzy control can be better than the efficiency of traditional vehicle-actuated control. According to these results, we can say that the fuzzy signal control can be multiobjective and more efficient than conventional adaptive signal control nowadays. The biggest benefits can, probably, be achieved in more complicated intersections and environments. The FUSICO-project continues. The aim is to move step by step to more complicated traffic signals and to continue the theoretical work of fuzzy control. The first example will be the public transport priorities.

11 REFERENCES 1. M.G.H. Bell, Future Directions in Traffic Signal Control, Transportation Research 26 (992) R. Cignoli, M.L. D'Ottaviano, D. Mundici, Algebraic Foundations of many valued Reasoning, to appear. 3. P. H'ajek, Metamathematics of fuzzy logic, Kluwer Acad. Publishers, Dordrecht, U. H"ohle, On the Fundamentals of Fuzzy Set Theory. J. of Math. Anal. and Appl. 201 (1996) J. Niittym"aki, Isolated Traffic Signals - Vehicle Dynamics and Fuzzy Control, Thesis, Helsinki University of Technology, J. Niittym"aki, S. Kikuchi, Application of Fuzzy Logic of a Pedestrian Crossing Signal, Transportation Research Record No Intelligent Transportation Systems, Automated Highway Systems, Travel Information, and Artificial Intelligence. Washington D.C B. Kosko, The probability monopoly, IEEE Transactions of fuzzy systems, 2 (1994) C. Pappis, E. Mamdani, A fuzzy logic controller to a traffic junction,ieee transaction on systems, man and cybernetics Vol SMC-7 No 10, 1977, J. Pavelka, On fuzzy logic, I,II,III Zeitsch. f. Math. Logik. 25 (1979), 45-52, , D. Teodorovic, Fuzzy logic systems for transportation engineering: the state of the art. Transportation Research Part A 33 (1999) M. Sugeno, M. Nishida, Fuzzy control to model car. Fuzzy Sets and Systems 16 (1985) E. Turunen, Mathematics behind Fuzzy Logic, Advances in Soft Computing, Physica- Verlag, Heidelberg, L. Zadeh, Fuzzy Sets, Information and Control 8 (1965) H.-J. Zimmermann, Fuzzy Set Theory, Kluwer, Optimising fuzzy logic traffic signal control systems, Stuart Clement, Transport Systems Centre, University of South Australia. 15. Fuzzy Traffic Signal Control - Principles and Applications Jarkko Niittymäki, Dissertation for the degree of Doctor of Science in Technology, Department of Civil and Environmental Engineering,Helsinki University of Technology, Espoo, Finland. 16. Traffic Signal Control on Total Fuzzy Similarity based Reasoning, Jarkko Niittym"aki Helsinki University of Technology, P.O. Box 2100, FIN HUT, Finland 17. Chiu, S and Chand, S (1992) Adaptive traffic signal control using fuzzy logic, pp of Proceedings of the Intelligent Vehicles Symposium Detroit, Michigan, USA. Clement, SJ Bell, MGH Cassir, C and Grosso, S (1997a) Experiences with the Path Flow Estimator on a Leicester City street network, pp of Proceedings of the 21st Australasian Transport Research Forum Adelaide: University of South Australia.