# Intelligent Transportation Design Based on Iterative Learning

Authors: Yinpu Ma; Kai Liu
Journal: Journal of Mathematics
 (2022)

---

## Abstract

Most of the existing traffic optimization control methods are based on accurate mathematical models. As an uncertain and complex system, the urban traffic system faces difficulty in accurately calibrating the model parameters. Therefore, the existing methods become very difficult in the actual application process. Based on the massive data contained in the urban traffic system and the repetitive characteristics of traffic flow, this paper proposes a hierarchical traffic signal control method for urban road network based on iterative learning control. The simulation results show that the algorithm can achieve better control effect and can solve the problem of urban traffic congestion more effectively than traditional traffic control methods.


---

## Body

## 1. Introduction

Traffic signal control is an effective method to change urban road traffic conditions and improve road capacity. Because the current transportation system has the characteristics of complexity, variability, uncertainty, and strong randomness, it is difficult to create an accurate mathematical model [1, 2]. The current control of traffic signals at intersections is to divide the day into several time periods, and the cycle length is fixed in each time period. However, due to the strong randomness of the traffic flow of the road section, the phased traffic congestion is unavoidable, and it cannot be based on specific conditions. It will make real-time adjustments [3]. If the green signal ratio of each phase can be controlled to respond to changes in traffic flow in real time, the waiting time of vehicles will be minimized.Iterative learning control [4, 5] is a control method for repetitive motion processes. At the same time and place, the traffic flow at the intersection will appear to be approximately repetitive. Ding [6] changed the traffic conditions and selection behaviors in the area according to different road network conditions, established a combined feedforward feedback iterative learning control model, and effectively controlled system interference. Simulation analysis is used to improve the accuracy of tracking error, but the selected traffic model is relatively simple and cannot be applied to complex urban intersections. Jing [7] took the traffic density of main and auxiliary roads as the control target, and the macro-traffic flow model proposed simplifies the store-and-forward model. Iterative learning is applied between the main and auxiliary roads to achieve equilibrium control in local sections, so that the equilibrium control error converges, but the disadvantage is that the model ignores the impact of changing lanes on traffic conditions and cannot be applied to traffic intersections in daily life. In [8], for the entrance of expressway, PD type iterative control law was used to control the traffic flow diffusion model, and then the center of gravity method was used to model and adjust the iterative learning gain, so that the output of the system has better tracking performance. The disadvantage is that it uses 3 types of traffic flow models which are all macroscopic traffic flow models, which will affect the accuracy of the results under microscopic characteristics. Zhou et al. [9] came up with the method of iterative learning control for green signal ratio of single intersection with fixed period. Luo [10] researched iterative control algorithm for descriptor systems. Lv et al. [11] accelerated the control of random initial state errors through iterative learning control. References [12–17] present the urban intersections, roads, signals verifications, and optimizations problem. Li and Li [18] gave the green wave signal setting and simulation analysis of bus lane. Xiao [19] researched on control group decision and dynamic optimization of arterial round intersection. Wang [20] modelled the traffic control signal optimization. Ge and Zhou [21] worked on the dual-layer hierarchical control solution for traffic signal.Since iterative learning control is mainly applied to fast intersections with relatively fixed traffic flow and relatively simple vehicle conditions, there are few studies on applying iterative learning control to daily intersection traffic light control. This article first uses the iterative learning control method to determine the best effective green light time for each phase and finally verifies the green signal ratio of a certain road section through simulation. The simulation results show that the control method can effectively reduce the queuing phenomenon of vehicles and play a great role in improving the traffic efficiency. After the introduction and literature review, Section2 presents the principle of iterative learning control algorithm. Section 3 discusses the timing of traffic signals. In Section 4, the iterative learning was used to design the timing scheme. In Section 5, the simulation research was carried out. Finally, Section 6 concludes the study.


## 2. The Principle of Iterative Learning Control Algorithm

Assumingt within a certain period of time, the controlled object undergoes multiple iterations from the initial state xk0; according to the algorithm, the expected value ydt and the result value of the dynamic process are superimposed continuously. When the number of downscaling approaches infinity, the control of the system will fail. The input function is(1)ukt⟶udt.The control output function of the system is(2)ykt⟶ydt.When it runs tok times, its expression is(3)xkt=fxkt,ukt,ykt=gxkt,ukt.Assuming that the expected valueydt of the system is set within the finite time of 0,T, the obtained input signal ukt makes the output signal ykt infinitely approach the output value ydt. The error accuracy of system tracking is(4)ekt=ydt−ykt.If the number of iterations isk⟶∞, the tracking error of the system is(5)limk⟶∞ekt=0.


## 3. Timing of Traffic Signals

The point control method is often adopted for the signal lights of a single intersection. This article uses the British TRRL method to optimize the signal timing of the current intersection. The number of phases and periods of the point are obtained based on field survey samples, and then the green light duration of each phase is determined separately. This signal timing optimization scheme can minimize the traffic delay time at the intersection, reasonably allocate the traffic flow of each phase to make the control system operate in an orderly manner, and then perform error corrections according to the actual situation to find the most ideal timing plan.


### 3.1. Optimal Period of Traffic Signal

The formula for calculating the optimal period of signal control is(6)C0=1.5L+51−Y,(7)L=∑il+I−A,where C0 is the size of the period, L is the time wasted for the system, l is the delay time for signal activation, A is the time for the yellow light, I is the time interval of the signal, i is the number of phases, and Y is the traffic ratio.Among them, the calculation formula of the flow ratio is as follows:(8)Y=∑i=1nYi,Yi=qiSi,where Yi is the flow ratio of the phase, qi is the traffic flow i of phase, and Si is the flow threshold of the phase.


### 3.2. The Best Effective Green Signal Time

According to the obtained signal period, the time of the green signal in each phase needs to be allocated reasonably. Because the green light time is affected by the delay of traffic flow, the traffic flow ratio and the green light signal ratio show a linear relationship; then:(9)g1g2=Y1Y2,where g1 is the effective time of the first phase green signal, g2 is the effective time of the second phase green signal, Y1 is the flow ratio of the first phase, and Y2 is the flow ratio of the second phase.From this, it can be deduced that the relational formula with multiple intersection phases is(10)gi∑i=1ngi=Yi∑i=1nYi.Then, the time of each phase of the green light is(11)gi=YiYC0−L.The green signal ratio of each phase is(12)λi=giC0.The traffic saturation of each phase is(13)xi=maxYiλI.This article will take the traffic intersection in a certain area as the research object, as shown in Figure1. After investigating the traffic situation at this intersection, the time lost for each phase is 3.2 s, the saturated flow is 103 veh/h, and the time for all red lights is 2.3 s.Figure 1
Intersection of Guangzhi Road and Nanhua Road.After the actual investigation, the traffic intersection signal light data are statistically analyzed. We optimize the statistical data as parameters, such as the original traffic signal timing plan shown in Table1 and the traffic data traffic flow statistics in Table 2.Table 1
The original timing plan of traffic lights.
ProjectPhase 1Phase 2Phase 3Cycle120120120Phase time711824Red light time4610393Green light time701826Yellow light time333Table 2
Traffic statistics.
Traffic directionTurn leftStraightTurn rightTotal trafficTraffic volumeNumber of lanesTraffic volumeNumber of lanesTraffic volumeNumber of lanesNorth import8012141161310South import95139612421733West import881681761232East import2651661741405The timing design adopted for the two-phase and three-phase signal control is shown in Figures2 and 3. The figures assume that the critical saturation flows of the three phases are 600, 300, and 100, respectively. According to formulae (6)–(13), the optimal cycle length, green signal ratio, and saturation are different. The calculation result of the green signal time of the phase is shown in Table 3.Figure 2
Timing design adopted for two-phase signal control.Figure 3
Timing design adopted for three-phase signal control.Table 3
Time allocation plan after the intersection signal optimization.
ProjectPhase 1Phase 2Phase 3Go straight on Guangzhi Road + turn rightTurn left on Guangzhi RoadNanhua Road passMaximum flow ratio of each phase0.390.110.27Total flow ratioY0.75Lost timeL16Optimal cycleC114Total effective green time100Effective green time for each phase501635Yellow light333Red light629679Green signal ratio of each phase0.430.130.32Saturation of each phase0.890.780.91In summary, after the preliminary optimization of the signal lights, the timing scheme with the least delay is derived, and the saturation of each phase is relatively uniform, which further shortens the whole cycle time, ensures the passage of vehicles, and increases the flow per unit time to maximize the application of green light time.


## 3.1. Optimal Period of Traffic Signal

The formula for calculating the optimal period of signal control is(6)C0=1.5L+51−Y,(7)L=∑il+I−A,where C0 is the size of the period, L is the time wasted for the system, l is the delay time for signal activation, A is the time for the yellow light, I is the time interval of the signal, i is the number of phases, and Y is the traffic ratio.Among them, the calculation formula of the flow ratio is as follows:(8)Y=∑i=1nYi,Yi=qiSi,where Yi is the flow ratio of the phase, qi is the traffic flow i of phase, and Si is the flow threshold of the phase.


## 3.2. The Best Effective Green Signal Time

According to the obtained signal period, the time of the green signal in each phase needs to be allocated reasonably. Because the green light time is affected by the delay of traffic flow, the traffic flow ratio and the green light signal ratio show a linear relationship; then:(9)g1g2=Y1Y2,where g1 is the effective time of the first phase green signal, g2 is the effective time of the second phase green signal, Y1 is the flow ratio of the first phase, and Y2 is the flow ratio of the second phase.From this, it can be deduced that the relational formula with multiple intersection phases is(10)gi∑i=1ngi=Yi∑i=1nYi.Then, the time of each phase of the green light is(11)gi=YiYC0−L.The green signal ratio of each phase is(12)λi=giC0.The traffic saturation of each phase is(13)xi=maxYiλI.This article will take the traffic intersection in a certain area as the research object, as shown in Figure1. After investigating the traffic situation at this intersection, the time lost for each phase is 3.2 s, the saturated flow is 103 veh/h, and the time for all red lights is 2.3 s.Figure 1
Intersection of Guangzhi Road and Nanhua Road.After the actual investigation, the traffic intersection signal light data are statistically analyzed. We optimize the statistical data as parameters, such as the original traffic signal timing plan shown in Table1 and the traffic data traffic flow statistics in Table 2.Table 1
The original timing plan of traffic lights.
ProjectPhase 1Phase 2Phase 3Cycle120120120Phase time711824Red light time4610393Green light time701826Yellow light time333Table 2
Traffic statistics.
Traffic directionTurn leftStraightTurn rightTotal trafficTraffic volumeNumber of lanesTraffic volumeNumber of lanesTraffic volumeNumber of lanesNorth import8012141161310South import95139612421733West import881681761232East import2651661741405The timing design adopted for the two-phase and three-phase signal control is shown in Figures2 and 3. The figures assume that the critical saturation flows of the three phases are 600, 300, and 100, respectively. According to formulae (6)–(13), the optimal cycle length, green signal ratio, and saturation are different. The calculation result of the green signal time of the phase is shown in Table 3.Figure 2
Timing design adopted for two-phase signal control.Figure 3
Timing design adopted for three-phase signal control.Table 3
Time allocation plan after the intersection signal optimization.
ProjectPhase 1Phase 2Phase 3Go straight on Guangzhi Road + turn rightTurn left on Guangzhi RoadNanhua Road passMaximum flow ratio of each phase0.390.110.27Total flow ratioY0.75Lost timeL16Optimal cycleC114Total effective green time100Effective green time for each phase501635Yellow light333Red light629679Green signal ratio of each phase0.430.130.32Saturation of each phase0.890.780.91In summary, after the preliminary optimization of the signal lights, the timing scheme with the least delay is derived, and the saturation of each phase is relatively uniform, which further shortens the whole cycle time, ensures the passage of vehicles, and increases the flow per unit time to maximize the application of green light time.


## 4. Timing Scheme Design Based on Iterative Learning

At each intersection, there isi that presents the phase, suppose the arrival rate of the first phase vehicle is qi, the waiting distance for this vehicle is xi, saturated traffic flow rate si, the arrival rate of phase i is di, and the effective time when the green light is on is gi. The ultimate goal of the traffic control signal light is to reduce the length of the vehicle queue and pass as many vehicles as possible within a certain period of time, so as to achieve the purpose of intelligent control. For this reason, in a certain signal period, the length of the queue becomes the state quantity of the system, and the dynamic state equation of the system is(14)xit+1=xit+C0dit+1−sigit.Among them, for the time when the green light is on, the constraint condition is(15)∑i=13git=C0−Lgimin≤gik≤gimax,where gimin is the minimum time for the green light to turn on (15 s); gimax is the maximum time of the first phase (90 s); and L is the total time lost while waiting for the vehicle (15 s).Control the signal lights to realize that the queue length of each entry vehicle is in a balanced state, that is, control the queue length of different phases. If the queue length is uneven, the green light time will not be fully utilized, which will cause traffic congestion. Therefore, the queuing length difference of each phase becomes the output of this article, and a reference phase needs to be selected here. In this article, the reference phase selects phase 1. Taking the difference between the other two phases and the queue length of phase 1 as the system outputyt, the system output is(16)yt=y2,1t,y3,1tT=x2t−x1t,x3t−x1tT=−110−101x1t,x2t,x3tT=cxt,where xt=x1t,x2t,x3tT; y2,1t is the output of phase 2; and y3,1t is the output of phase 3.From this, it can be calculated that the queuing length of vehicles at the intersection is(17)xt+1=xt+C0dt+1−sgt,where dt=d1t,d2t,d3tT, gt=g1t,g2t,g3tT, s=diags1,s2,s3. dit is the traffic flow for phase i and, git is the time when the green light of phase i. It is the time when the green light of phase i is on.According to the above expression, the vehicle queue length is determined by the vehicle queue lengthx (t + 1) of the current signal cycle, the traffic demand d (t + 1) of the next cycle, and the time g when the green light is on in the current cycle. x(t) and d(t) jointly decided the cycle.According to formula (16), the green time g1t of phase 1 can be obtained from the green time of the other two phases, so formula (17) can be changed to(18)xt+1=xt+C0dt+1−sgt−s1c1,0.0T.In the formula (18), c1, c, and l indicate the period, size of the signal, and the time lost in queuing, respectively.(19)s=−s1−s1s200s3.After introducing the number of iterations, formula (18) can be changed to(20)xkt+1=xkt+C0dkt+1−sgkt−s1c1,0.0T,where k is the number of iterations.Because of the large and unstable traffic flow at traffic intersections, the traffic flow has strong repetitiveness. Therefore, this paper adopts iterative learning control to control the periodic signal at each intersection, so as to draw the corresponding laws according to the calculation results.Assume that in iterative control, the vehicle queue length satisfies the following conditions:(21)xk0=x00.If the traffic volume at the intersection remains constant within a given period, then:(22)dkt=d0t.The resulting timing plan for the intersection is(23)gk+1t=gkt+αyd−ykk+1.where yd is the expected queuing difference and α is the iterative learning gain matrix.If the queuing length at the intersection controlled by traffic lights is close to balance, the phase queuing length at each intersection requiresyd=0.


## 5. Simulation Research

This paper takes the intersection composed of Nanhua East Road and Guangzhi Road as the object of simulation study. There are 3 phases in the intersection. The arrival rates of each phase are, respectively, 0.52 veh/s, 0.16 veh/s, and 0.24 veh/s, and the saturation flow rate of each phase is 0.27 veh/s. The learning gain is −0.83, the loss time of each phase is 2 s, the signal period is 114 s, and the green light time of the three phases is 51 s, 15 s, and 34 s. Considering the complexity of the actual situation, while optimizing the model, the green light time and queue length obtained by MATLAB simulation should be integer values. The simulation results are shown in Figures4–6.Figure 4
Queue length difference of iterative learning control.Figure 5
Error caused by the number of iterations.Figure 6
Green light time of each phase after iteration under iterative learning control.From the simulation results of Figures4 and 5, it can be seen that after the number of iterations exceeds 15 times, the difference and error of the queue length almost approach zero, and the timing of the entire traffic signal system is in a uniform distribution state.Figure6 shows the time curve of the three-phase green traffic signal lights. After adopting the iterative learning control signal, the green light time of each phase is adjusted in real time according to the specific traffic volume, and reasonable time allocation is carried out, which proves the effectiveness and reliability of the algorithm.


## 6. Conclusion

In this paper, the controlled object is the traffic light at intersections. The reasonable signal period is determined according to the TRRL method timing plan, and then based on the idea of iterative learning control law, a method to control signal lights is constructed to avoid the establishment of a complex traffic flow model. It can use very few priors. We use real-time traffic flow data to control the traffic lights at intersections. The experimental results of iterative learning control show that the control method of this algorithm is reasonable and can be changed according to the changes of traffic flow. It has the effect of adaptive adjustment and improves the traffic efficiency. The optimization effect of the iterative algorithm is far better than the traditional timed and fixed cycle traffic system. It can adaptively adjust the cycle length and the green light time of each phase. It can pass more vehicles at the same time without additional equipment. Support and additional costs can reduce people’s unnecessary waiting time, thereby saving people’s travel time and improving work efficiency. However, the scope of application of this article has certain limitations. When there are few or many vehicles at the intersection, the adjustment effect is not obvious.



---

*Source: 5027412-2022-02-08.xml*