Iterative fault-tolerant control method for traffic signal considering initial disturbance and signal light failure

Abstract

The application discloses a traffic signal iterative fault-tolerant control method considering initial disturbance and signal lamp failure, and specifically comprises the following steps: establishing a road network state space equation according to a traffic flow model; defining a signal lamp failure model and designing an iterative learning fault-tolerant control law; judging whether a signal lamp in the road network fails according to the vehicle operation law at the intersection and the cumulative vehicle number of the vehicle queue, and switching the iterative learning fault-tolerant control law according to the judgment result; judging whether the signal lamp in the road network fails, and controlling the signal in the road network under the influence of the initial state disturbance in the road network; and resetting the green light duration of each phase of the signal lamp according to the signal lamp green light duration increment obtained by the iterative learning fault-tolerant control, so that the vehicle queue lengths at each intersection in the road network tend to be balanced. The method guarantees that the remaining normal working signal lamps in the road network coordinate and control the vehicle flow direction in the road network when the signal lamp fails.

Description

Technical Field

[0001] This invention relates to the field of traffic control technology, and specifically to an iterative fault-tolerant control method for traffic signals that takes into account initial disturbances and traffic light malfunctions. Background Technology

[0002] With the rapid increase in the number of motor vehicles in cities, road traffic issues have become a focus of social concern. At urban road intersections, traffic signals are generally used to control vehicle flow, and traffic lights are the core equipment for operating these signals, playing a crucial role in directing and managing vehicle flow at intersections. However, traffic lights operate in harsh environments and are subject to prolonged, uninterrupted operation, making them highly susceptible to various malfunctions. The usual handling of traffic light malfunctions is simply downgrading to flashing yellow lights. During a traffic light failure, vehicle flow at the intersection is disorderly, potentially causing traffic congestion, chaos, and even accidents. Even after the traffic lights are repaired, the congestion generated during the failure period is difficult to alleviate in the short term and may even spread to surrounding areas. Adopting a fault-tolerant control strategy can better coordinate vehicle flow within the road network during traffic light failures, preventing large queues of vehicles from accumulating at intersections with malfunctioning traffic lights.

[0003] For a specific area within a city, from a macroscopic perspective, its daily traffic flow exhibits similar spatiotemporal distribution characteristics and repetitive operation. Iterative learning control (ILC) can be used to solve the tracking control problem of repetitive systems operating within a finite interval. It does not rely on an exact system model, aims for complete tracking, is easy to implement, and can obtain control inputs that can track the desired output trajectory using previous tracking errors and control information, thereby improving control quality. It is suitable for traffic control with repetitive characteristics. Combining fault-tolerant control strategies with iterative learning control not only enables the output to quickly track the desired output trajectory by utilizing the system's previous state information, but also ensures stable system operation even in the presence of faults, improving system robustness.

[0004] In practical system applications, the initial state of a system is often arbitrary and does not necessarily equal a fixed state. Such arbitrary initial state disturbances acting on the controlled system can weaken the control performance or even lead to unpredictable results. Therefore, studying the effect of initial state disturbances on control performance is crucial. Most existing urban traffic signal control methods operate under the condition that the initial state is exactly equal to the expected initial state, meaning the initial state is strictly repeated, without considering the impact of arbitrary initial state disturbances in actual urban traffic system operation. Initial state disturbances not only affect the control performance of traffic signal controllers but may also further exacerbate existing traffic congestion; this is also the most realistic scenario in practical system applications. Summary of the Invention

[0005] The purpose of this invention is to provide an iterative fault-tolerant control method for traffic signals that takes into account initial disturbances and traffic light malfunctions. It adopts an iterative learning fault-tolerant control strategy for urban traffic signals to ensure that when a traffic light malfunctions, the remaining normally functioning traffic lights in the road network coordinate to control the flow of vehicles in the road network. After the malfunctioning traffic light is repaired, it can quickly alleviate the congestion at the intersection, prevent the congestion from spreading, and make the queue length of vehicles in each lane tend to be balanced.

[0006] The technical solution adopted in this invention is an iterative fault-tolerant control method for traffic signals that considers initial disturbances and traffic light malfunctions. Specifically, it includes: Step 1) Selecting the road network of the traffic area to be studied and establishing the road network state space equation based on the traffic flow model; Step 2) Defining the traffic light malfunction model, constructing the road network state space equation considering input disturbances and traffic light malfunctions, and designing an iterative learning fault-tolerant control law and a correction term to compensate for the influence of initial state disturbances; Step 3) Determining whether there are traffic light malfunctions in the road network based on the vehicle operation patterns at intersections and the cumulative number of vehicles in queues, and switching the iterative learning fault-tolerant control law based on the determination result; Step 4) Determining whether there are traffic light malfunctions in the road network through Step 3), controlling the traffic signals in the road network under the influence of initial state disturbances, and resetting the green light duration of each phase of the traffic lights based on the green light duration increment obtained from the iterative learning fault-tolerant control, so that the vehicle queue lengths at each intersection in the road network tend to be balanced.

[0007] The invention is further characterized in that,

[0008] Step 1 specifically involves: Step 1.1) Constructing the road network state space equations based on the "store-and-forward" traffic flow model. The specific process is as follows: Assume two adjacent intersections are j... p and j p-1 Let p = 1, 2, ..., N, and z be the road segment connecting the intersection. Then the queuing equation for the vehicles is as follows:

[0009]

[0010] In the formula, Indicates the intersection at time k. p The queue length of vehicles at the i-th entrance lane, i = 1, 2, 3, 4; ΔT is the control period; and They represent the intersection at time k and j respectively. p Vehicle arrival rate and vehicle dispersal rate at the i-th entrance lane, vehicle dispersal rate In the formula, Indicates the intersection at time k. p The green light time corresponding to the i-th approach lane phase; Indicates intersection j p The saturation flow rate of the i-th approach lane; T represents the signal cycle of the traffic lights at the intersection, and the vehicle arrival rate. In the formula, q i (k) represents the input flow rate of inlet channel i at time k. For vehicles passing through the intersection j p-1 The turning rate of the vehicle entering road segment z;

[0011] Let T = ΔT, and rearrange formula (1) to obtain the intersection j p The vehicle queuing equation for the i-th entrance lane is:

[0012]

[0013] Step 1.2) Write the vehicle queuing equation (2) in 1.1) for all intersection approach lanes, and obtain the vehicle queuing equation for the entire road network at time k+1 as follows:

[0014] X(k+1)=AX(k)+BU(k)+ξ(k) (3)

[0015] In the formula, X(k) is the state vector, representing the queue length of vehicles in all approach lanes of the intersection at time k; U(k) is the control vector, representing the green light time of the corresponding phase of all approach lanes of the intersection at time k; ξ(k) is the initial state disturbance vector in the road network at time k; A is the state matrix, which is the identity matrix; B is the input matrix, whose elements are determined by factors such as the period, saturation flow, and turning rate of each intersection in the road network.

[0016] Intersections within a road network typically have four approach lanes in each direction. The difference in queue lengths between adjacent approach lanes at time k is chosen as the output Y(k). For any intersection j within the road network... p Its output at time k Represented as:

[0017]

[0018] In the formula, Indicates the intersection at time k. p Output of inlet channel 1; Indicates the intersection at time k. p Output of Inlet 2; Indicates the intersection at time k. p The output of inlet channel 3; Indicates the intersection at time k. p The output of inlet channel 4; Indicates the intersection at time k. p The vehicle queue length at all approach lanes; η(k) is the output error generated by the data acquisition equipment at time k. The above output equations are written for all intersections in the road network, resulting in the output equation for the entire road network at time k:

[0019] Y(k)=CX(k)+η(k))(5)

[0020] In the formula, N is the number of intersections; C is the output matrix. The state-space equation of the road network at time k+1 is as follows:

[0021]

[0022] Step 2 specifically includes: Step 2.1), let u F (k) represents the output signal of the traffic light malfunction at time k. The traffic light malfunction model is defined as u. F (k)=M a U(k), where matrix M a It's a traffic light malfunction signal, M a =diag(m a1 ,m a2 ,…,m aN ); and 0≤m ap ≤1, p=1,2,…N, when m ap =0 indicates that the p-th traffic light is completely faulty; 0 < m ap <1 indicates a partial fault in the p-th traffic light; when m ap When m = 1, it indicates that the p-th indicator light is working normally; in the fault signal, m ap The value is a random number in the range (0,1), i.e., m ap =rand(0,1], Substituting the traffic light fault model expression into the road network state-space equation obtained in step 1, we obtain the road network state-space equation at time k+1 considering initial state disturbances and traffic light faults as follows:

[0023]

[0024] In the formula, X F(k) represents the queue length of all approach lanes at the intersection within the road network at time k when a traffic light malfunction occurs; Y F (k) represents the difference in vehicle queue lengths at adjacent approach lanes at all intersections within the road network at time k when a traffic light malfunction occurs; ξ F (k) is the input state disturbance vector within the road network at time k when a traffic light malfunction occurs; η F (k) represents the output error generated by the data acquisition device at time k when there is a signal light malfunction;

[0025] 2.2) For the state-space equation of a road network considering input disturbances and traffic light malfunctions, the tracking error of the road network is defined as:

[0026] e n (k)=y d (k)-y n (k) (8)

[0027] In the formula, y d (k) represents the desired output within the road network at time k, y n (k) represents the actual output within the road network at time k during the nth iteration; the D-type iterative learning control law is u n+1 (k)=u n (k)+Le n (k+1), where L is the learning gain matrix; u n (k) is the control input at time k of the nth iteration, which corresponds to the green light duration increment of the traffic lights at each intersection; e n (k) is the tracking error at time k in the nth iteration, and n = 1, 2, ..., N1, where N1 is the maximum number of iterations.

[0028] 2.3) Introducing the correction term into the D-type iterative learning control law, considering the elimination of interference caused by different initial state disturbances on traffic signal control when k=0, we obtain an iterative learning control algorithm for urban traffic signals that can reduce the impact of different initial state disturbances when there is no traffic light failure, namely iterative learning control law 1:

[0029] u n+1 (k)=u n (k)+Le n (k+1)+r(k)θ n (9)

[0030] In the formula, r(k)θ n Here is the correction term for the design; r(k) is the impulse function, which has the following form:

[0031]

[0032] In the formula, L is the iterative learning gain matrix; θn It is a term related to the initial state perturbation in the nth iteration, and is θ. n =B T (BB T ) -1 A(x n (0)-x n+1 (0))+Le n (0), where B T x is the transpose of the input matrix B; n (k), (k=0,1,2,…,K) represents the queue length of all approach lanes at the intersection at time k of the nth iteration; u n (k) represents the control input at time k of the nth iteration, corresponding to the green light duration increment of each intersection in the road network at time k of the nth iteration. When a traffic light in the road network malfunctions and after the malfunction is repaired, the iterative learning fault-tolerant control algorithm for dealing with traffic light malfunctions is obtained by introducing state feedback into the iterative learning control, namely, iterative learning fault-tolerant control law 2:

[0033] u n+1 (k)=u n (k)+L1[x n+1 (k)-x n (k)]+L2e n (k+1)+r(k)φ n (11)

[0034] Where L1 and L2 are both iterative learning fault-tolerant gain matrices; u n (k) represents the control input at time k of the nth iteration, corresponding to the green light duration increment at each intersection within the road network at time k of the nth iteration; x n (k), (k=0,1,2,…) represents the queue length of all approach lanes at the intersection at time k in the nth iteration; φ n It is a term related to the initial state perturbation in the nth iteration, and is...

[0035] Step 3 is as follows: Step 3.1) Based on the vehicle operation patterns and the cumulative number of vehicles in the queue in the road network, a critical value for the queue length at an intersection is set. When the difference in queue length at a certain intersection at time k is greater than the difference in queue length at time k-1 under the control of iterative learning control law 1, and exceeds the critical value, it indicates that the traffic light at that intersection is malfunctioning, and it is necessary to switch to iterative learning fault-tolerant control law 2 for signal control. When the fluctuation of the difference in queue length at the intersection does not exceed the critical value, it indicates that no traffic light is malfunctioning, and iterative learning control law 1 can be used to control the traffic signal indefinitely. Step 3.2) When the queue length at a certain intersection in the road network exceeds the critical value for half or more of the time in one iteration, it indicates that the traffic light at that intersection is in a malfunctioning state. When the queue length gradually decreases to below the critical value after exceeding the critical value for a long time under the control of iterative learning fault-tolerant control law 2, it indicates that the traffic light malfunction has been repaired. In step 3.1), the average value of the vehicle queue length difference after the vehicle queue length difference in the road network has stabilized is taken, and three times the size of this average value is taken as the critical value.

[0036] Step 4 specifically involves: Step 4.1) In the first iteration, the existing fixed timing scheme of the traffic lights at intersections in the road network is used. Then, based on whether there are any traffic light malfunctions in the road network as determined in Step 3), starting from the second iteration, the corresponding control law in Step 2.3) is selected based on the determined road network conditions to obtain a new control input u. n (k) represents the green light duration increment at each intersection within the road network at time k in the nth iteration, used to re-time the intersection traffic lights; where u n (k)∈[u min (k),u max (k)], where u min (k) and u max (k) represents the limiting control input u n (k) minimum and maximum values; Step 4.2) When no signal light malfunctions, the control input u at time k of the nth iteration is obtained according to the iterative learning control law 1. n (k) is the green light duration increment, which is added to the green light duration at time k of the previous iteration to obtain the green light duration at time k of the nth iteration. The newly obtained green light duration replaces the corresponding green light duration in the previous iteration to set the green light duration for each phase of the intersection. The actual queue length of each lane is adjusted by adjusting the number of vehicles at the intersection within the road network. 4.3) If a signal light at an intersection malfunctions, the control input u at time k of the nth iteration is obtained according to the iterative learning fault-tolerant control law 2. n(k) is the green light duration increment, which is added to the green light duration at time k of the previous iteration to obtain the green light duration at time k of the nth iteration. The newly obtained green light duration replaces the corresponding green light duration in the previous iteration. The green light duration of the remaining non-faulty traffic lights is set to reduce the number of vehicles entering the intersection with the faulty traffic light and coordinate the actual number of vehicles queuing in each lane of the road network. 4.4) When the faulty traffic light is repaired, all traffic lights in the road network are re-timed under the action of the iterative learning fault-tolerant control law 2. In each control cycle, the phase green light ratio of each signal cycle remains unchanged. At the current control cycle, the green light increment is calculated based on the tracking error and control input in the previous control cycle. The green light increment is added to the green light duration in the previous iteration to obtain the new green light duration. The new green light duration is then substituted into the current control cycle to adjust the green light ratio in the current control cycle.

[0037] The beneficial effects of this invention are as follows: The method constructs a system state-space expression that considers input disturbances and traffic light malfunctions. It employs an iterative learning fault-tolerant control strategy for urban traffic signals, ensuring that when a traffic light malfunctions, the remaining normally functioning traffic lights in the road network coordinate to control vehicle flow. After the malfunctioning traffic light is repaired, it quickly alleviates congestion at the intersection, prevents its spread, and balances the queue lengths of vehicles in each lane. Simultaneously, an initial state correction term is introduced into the signal control law to address the current urban traffic control system's failure to consider the impact of arbitrary initial state disturbances. This invention considers the impact of initial operating state disturbances on subsequent signal control in actual urban road networks, as well as the problem of quickly alleviating congestion after traffic light malfunctions and repairs. Combining iterative learning control with fault-tolerant control for traffic signal control further improves the system's robustness. Attached Figure Description

[0038] Figure 1 This is a schematic flowchart of the method of the present invention;

[0039] Figure 2 This is a schematic diagram of the road segment traffic flow model of the method of the present invention;

[0040] Figure 3 A simplified diagram of the road network structure for the selected urban area;

[0041] Figure 4 This shows how the overall error of the road network changes with the number of iterations.

[0042] Figure 5 This shows how the error at the faulty traffic light intersection changes with the number of iterations.

[0043] Figure 6 This shows how vehicle queuing time changes with the number of iterations within the road network.

[0044] Figure 7 This shows how the number of vehicle stops within the road network changes with the number of iterations.

[0045] Figure 8 This shows how vehicle delay times within the road network change with the number of iterations. Detailed Implementation

[0046] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0047] Example 1

[0048] This invention proposes an iterative fault-tolerant control method for traffic signals that considers initial disturbances and traffic light malfunctions, such as... Figure 1 As shown, it includes the following steps:

[0049] Step 1) Select the road network of the traffic area to be studied, and establish the state space equation of the road network based on the traffic flow model;

[0050] Step 1.1) Model urban traffic flow based on the "store-and-forward" traffic flow model. The basic idea of ​​the model is to calculate the actual flow rate of vehicles leaving a road segment within a cycle using the average flow rate. For example... Figure 2 As shown, the road network state space equation is constructed based on the "store-and-forward" traffic flow model. The specific process is as follows: Assume two adjacent intersections are j p and j p-1 Let p = 1, 2, ..., N, and z be the road segment connecting the intersection. Then the queuing equation for the vehicles is as follows:

[0051]

[0052] In the formula, Indicates the intersection at time k. p The queue length of vehicles at the i-th entrance lane, i = 1, 2, 3, 4; ΔT is the control period; and They represent the intersection at time k and j respectively. p Vehicle arrival rate and vehicle dispersal rate at the i-th entrance lane, vehicle dispersal rate In the formula, Indicates the intersection at time k. p The green light time corresponding to the i-th approach lane phase; Indicates intersection j p The saturation flow rate of the i-th approach lane; T represents the signal cycle of the traffic lights at the intersection, and the vehicle arrival rate. In the formula, q i (k) represents the input flow rate of inlet channel i at time k. For vehicles passing through the intersection j p-1 The turning rate of the vehicle entering road segment z;

[0053] Let T = ΔT, and rearrange formula (1) to obtain the intersection j p The vehicle queuing equation for the i-th entrance lane is:

[0054]

[0055] Step 1.2) Write the vehicle queuing equation (2) in 1.1) for all intersection approach lanes, and obtain the vehicle queuing equation for the entire road network at time k+1 as follows:

[0056] X(k+1)=AX(k)+BU(k)+ξ(k) (3)

[0057] In the formula, X(k) is the state vector, representing the queue length of vehicles at all approach lanes of the intersection at time k; U(k) is the control vector, representing the green light time of the corresponding phase for all approach lanes of the intersection at time k; ξ(k) is the initial state disturbance vector within the road network at time k, and the changes between two adjacent disturbances are bounded, with the upper bound being a constant b. d Because the number of vehicles entering an intersection typically does not meet the expected number, it is affected by factors such as traffic accidents and pedestrians crossing the road. A is the state matrix, which is an identity matrix; B is the input matrix, whose elements are determined by factors such as the period, saturation flow, and turning rate of each intersection in the road network. Figure 3 Taking the road network in China as an example:

[0058]

[0059] The purpose of intersection signal control is to ensure that the queue lengths of vehicles in each lane are balanced, preventing uneven queue lengths from causing insufficient green light time in one phase while other phases experience long queues, thus leading to traffic congestion. Intersections within a road network typically have four approach lanes in each direction. The difference in queue lengths between adjacent approach lanes at time k is chosen as the output Y(k). For any intersection j within the road network... p Its output at time k Represented as:

[0060]

[0061] In the formula, Indicates the intersection at time k. p Output of inlet channel 1; Indicates the intersection at time k. p Output of Inlet 2; Indicates the intersection at time k. p The output of inlet channel 3; Indicates the intersection at time k. p The output of inlet channel 4; Indicates the intersection at time k. p The vehicle queue length at all approach lanes; η(k) is the output error generated by the data acquisition equipment at time k. The above output equations are written for all intersections in the road network, resulting in the output equation for the entire road network at time k:

[0062] Y(k)=CX(k)+η(k) (5)

[0063] In the formula, N is the number of intersections; C is the output matrix. The state-space equation of the road network at time k+1 is as follows:

[0064]

[0065] Step 2) Define the traffic light fault model and substitute it into the road network state space equation obtained in Step 1 to construct a road network state space equation that considers input disturbances and traffic light faults. At the same time, design an iterative learning fault-tolerant control law and a correction term to compensate for the influence of initial state disturbances.

[0066] Step 2.1) Construct the road network state-space equations considering initial state disturbances and traffic light malfunctions. Specifically, let u F (k) represents the output signal of the traffic light malfunction at time k. The traffic light malfunction model is defined as u. F (k)=M a U(k), where matrix M a It's a traffic light malfunction signal, M a =diag(m a1 ,m a2 ,…,m aN ); and 0≤m ap ≤1, p=1,2,…N, when m ap =0 indicates that the p-th traffic light is completely faulty; 0 < m ap <1 indicates a partial fault in the p-th traffic light; when m ap When m = 1, it indicates that the p-th traffic light is working normally. In reality, after a traffic light malfunctions, it will downgrade to flashing yellow, temporarily losing its function of guiding traffic flow. At this time, vehicles from all four intersections will pass through the intersection simultaneously. In practice, for the entire road network, there will always be vehicles passing through the intersection, but its capacity will not reach the capacity when the traffic lights are working normally. Therefore, in the faulty signal, m... ap The value is a random number in the range (0,1), i.e., m ap =rand(0,1], Substituting the traffic light fault model expression into the road network state-space equation obtained in step 1, we obtain the road network state-space equation at time k+1 considering initial state disturbances and traffic light faults as follows:

[0067]

[0068] In the formula, X F (k) represents the queue length of all approach lanes at the intersection within the road network at time k when a traffic light malfunction occurs; Y F (k) represents the difference in vehicle queue lengths at adjacent approach lanes at all intersections within the road network at time k when a traffic light malfunction occurs; ξ F (k) is the input state disturbance vector within the road network at time k when a traffic light malfunction occurs; η F (k) represents the output error generated by the data acquisition device at time k when there is a signal light malfunction;

[0069] 2.2) For the state-space equation of a road network considering input disturbances and traffic light malfunctions, the tracking error of the road network is defined as:

[0070] e n (k)=y d (k)-y n (k) (8)

[0071] In the formula, y d (k) represents the desired output within the road network at time k, y n (k) represents the actual output within the road network at time k during the nth iteration; the D-type iterative learning control law is u n+1 (k)=u n (k)+Le n (k+1), where L is the learning gain matrix; u n (k) is the control input at time k of the nth iteration, which corresponds to the green light duration increment of the traffic lights at each intersection; e n (k) is the tracking error at time k in the nth iteration, where n = 1, 2, ..., N1, and N1 is the maximum number of iterations. For a system with the desired initial state, the iterative learning control law exhibits good convergence. However, for arbitrary initial states in iterative learning control, the convergence speed of this control algorithm is not good. Therefore, it is necessary to consider reducing the influence of initial state disturbances during iteration, so that the system can converge quickly under any initial state.

[0072] 2.3) To ensure the system converges quickly to the desired output under any initial state, a correction term is introduced into the D-type iterative learning control law. Considering the elimination of interference from different initial state disturbances on traffic signal control when k=0, an iterative learning control algorithm for urban traffic signals that can reduce the impact of different initial state disturbances when there is no traffic light malfunction is obtained, namely, iterative learning control law 1:

[0073] u n+1 (k)=u n(k)+Le n (k+1)+r(k)θ n (9)

[0074] In the formula, r(k)θ n Here is the correction term for the design; r(k) is the impulse function, which has the following form:

[0075]

[0076] In the formula, L is the iterative learning gain matrix; θ n It is a term related to the initial state perturbation in the nth iteration, and is θ. n =B T (BB T ) -1 A(x n (0)-x n+1 (0))+Le n (0), where B T x is the transpose of the input matrix B; n (k), (k=0,1,2,…,K) represents the queue length of all approach lanes at the intersection at time k of the nth iteration; u n (k) represents the control input at time k of the nth iteration, corresponding to the green light duration increment at each intersection within the road network at time k of the nth iteration. When a traffic light malfunctions within the road network and after the malfunction is repaired, by introducing state feedback into the iterative learning control, an iterative learning fault-tolerant control algorithm for dealing with traffic light malfunctions is obtained, namely, iterative learning fault-tolerant control law 2:

[0077] u n+1 (k)=u n (k)+L1[x n+1 (k)-x n (k)]+L2e n (k+1)+r(k)φ n (11)

[0078] Where L1 and L2 are both iterative learning fault-tolerant gain matrices; u n (k) represents the control input at time k of the nth iteration, corresponding to the green light duration increment at each intersection within the road network at time k of the nth iteration; x n (k), (k=0,1,2,…) represents the queue length of all approach lanes at the intersection at time k in the nth iteration; φ n It is a term related to the initial state perturbation in the nth iteration, and is...

[0079] Step 3) Based on the vehicle operation pattern at the intersection and the cumulative number of vehicles in the queue, determine whether there is a traffic light malfunction in the road network, and switch the iterative learning fault-tolerant control law according to the judgment result; Step 3.1) Based on the vehicle operation pattern in the road network and the cumulative number of vehicles in the queue, set a critical value for the queue length of a road intersection (usually under the action of iterative learning control and after multiple iterations, the difference in queue length in the road network will tend to stabilize and gradually converge to a value, so take the average value of the stable queue length difference, and use 3 times the size of this average value as the critical value). When the difference in vehicle queue length at a certain intersection at time k is greater than the difference in vehicle queue length at time k-1 under the control of iterative learning control law 1, and exceeds the critical value, it indicates that the traffic light at that intersection is malfunctioning, and it is necessary to switch to iterative learning fault-tolerant control law 2 for signal control; when the fluctuation of the difference in vehicle queue length at the intersection does not exceed the critical value, it indicates that no traffic light is malfunctioning, and iterative learning control law 1 can be used to control the traffic signal indefinitely; in step 3.2), when the vehicle queue length at a certain intersection in the road network exceeds the critical value for half or more of the time in one iteration, it indicates that the traffic light at that intersection is in a malfunctioning state; when the vehicle queue length gradually decreases to below the critical value after exceeding the critical value for a long time under the control of iterative learning fault-tolerant control law 2, it indicates that the traffic light malfunction has been repaired at this time.

[0080] Step 4) Based on Step 3), determine whether there is a fault in the traffic lights within the road network. Under the influence of the initial state disturbance within the road network, implement signal control within the road network. Reset the green light duration of each phase of the traffic lights according to the green light duration increment obtained from iterative learning fault-tolerant control, so that the vehicle queue lengths at each intersection within the road network tend to be balanced. Step 4.1) The first iteration uses the original fixed timing scheme of the traffic lights at the intersections in the road network. Then, based on whether there is a fault in the traffic lights within the road network as determined in Step 3), starting from the second iteration, select the corresponding control law from Step 2.3) to obtain a new control input u based on the determined road network conditions. n (k) represents the green light duration increment at each intersection within the road network at time k of the nth iteration. This increment is used to re-time the intersection traffic lights. Considering factors such as signal cycle and pedestrian crossings, the green light duration at intersections should be within a reasonable range; that is, the control input needs to meet the actual traffic conditions. Where u n (k)∈[u min (k),u max (k)], where u min (k) and u max (k) represents the limiting control input u n (k) minimum and maximum values; Step 4.2) When no signal light malfunctions, the control input u at time k of the nth iteration is obtained according to the iterative learning control law 1.n (k) is the green light duration increment, which is added to the green light duration at time k of the previous iteration to obtain the green light duration at time k of the nth iteration. The newly obtained green light duration replaces the corresponding green light duration in the previous iteration to set the green light duration for each phase of the intersection. The actual queue length of each lane is adjusted by adjusting the number of vehicles at the intersection within the road network. 4.3) If a signal light at an intersection malfunctions, the control input u at time k of the nth iteration is obtained according to the iterative learning fault-tolerant control law 2. n (k) is the green light duration increment. This increment is added to the green light duration at time k in the previous iteration to obtain the green light duration at time k in the nth iteration. The newly obtained green light duration replaces the corresponding green light duration in the previous iteration. The green light durations of the remaining non-faulty traffic lights are set to reduce the number of vehicles entering the intersection with the faulty traffic light and coordinate the actual number of vehicles queuing in each lane of the road network. 4.4) When the faulty traffic light is repaired, all traffic lights in the road network are re-timed under the action of the iterative learning fault-tolerant control law 2. In each control cycle, the phase green light ratio of each signal cycle remains unchanged. At the current control cycle, the green light increment is calculated based on the tracking error and control input in the previous control cycle. The green light increment is added to the green light duration in the previous iteration to obtain the new green light duration. The new green light duration is then substituted into the current control cycle to adjust the green light ratio in the current control cycle.

[0081] Principle: The basic idea of ​​iterative learning control is that for a system that runs repeatedly over a finite time interval, by repeatedly trying to control the same trajectory, the control input is continuously corrected using the error information measured in the previous one or several runs of the system, so that the output trajectory of the system can track the desired trajectory over the entire time interval.

[0082] (1) For iterative learning control law 1, it is used when there is no traffic light failure in the road network. The state-space equation of the road network at this time is as follows:

[0083]

[0084] And there exists a bounded desired control input u at time k. d (k) enables the road network (12) to completely track the desired output y at time k within the time interval [0,K]. d (k), that is

[0085]

[0086] In the formula, x d (k) is the desired state vector within the road network at time k.

[0087] Lemma 1: ||u d(k)-sat[u n (k)]||≤||u d (k)-u n (k)|| (13)

[0088] Among them, sat[u n [(k)] is the saturation function controlling the input at time k in the nth iteration, i.e.:

[0089]

[0090] Quoted from [Zhongsheng Hou,Jianxin Xu,Jinwen Yan.An iterative learning approach for density control of freeway traffic flow via ramp metering[J].Transportation Research Part C, 2008,16(1):71-97.]

[0091] Iterative learning control law 1 is revised to: when considering input constraints.

[0092] u n+1 (k)=sat[u n (k)]+Le n (k+1)+r(k)θ n (15)

[0093] For any given control input u n (k)∈[u min (k),u max (k)], k∈[0,K], the state vector of the road network at time k during the nth and n+1th iterations. n (k) and x n+1 (k), that is, the solutions to the state equations in the state space equation (12) of the road network at the nth and n+1th iterations are respectively:

[0094]

[0095]

[0096] In the formula, j (j = 0, 1, 2, ..., k-1) represents the index of the control input value after the summation symbol changes as it changes, ξ n (k) is the initial state disturbance vector within the road network at time k of the nth iteration, which can be obtained according to equations (16) and (17):

[0097]

[0098] Substituting the iterative learning control law 1 for input constraints, i.e., equation (15), into equation (18) and simplifying, we get:

[0099]

[0100] According to equation (10) and θ n Substituting the expression into equation (19), we get:

[0101]

[0102] The error portion can be simplified to the following form:

[0103]

[0104] Substituting equation (21) into (20) and simplifying, we get:

[0105]

[0106] From the definition of tracking error and equation (12), we can obtain:

[0107]

[0108] Substituting equation (22) into equation (23) and simplifying, we get:

[0109]

[0110] Taking the norm of both sides of equation (24), we get:

[0111]

[0112] Lemma 2: Introduce the λ-norm, i.e. Where λ > 0, a > 1, and f(k) is an arbitrary function. (Adapted from [Yan Fei, Tian Fuli, Shi Zhongke. Iterative learning approach for traffic signal control of urban road networks[J]. IET Control Theory & Applications, 2017, 11(4):466-475.])

[0113] The state perturbation changes between two adjacent iterations are bounded, with an upper bound of a constant b. d ,Right now

[0114] ||ξ n+1 (k)-ξ n (k)||≤b d (26)

[0115] Furthermore, the change in output perturbation between two adjacent iterations is bounded, and its bound is a constant b. η ,Right now

[0116] ||η n+1 (k)-η n (k)||≤b η (27)

[0117] remember:

[0118] Substituting equations (26), (27), and (28) into equation (25), we get:

[0119]

[0120] Multiply both sides of equation (29) by a -λk (a>1), and taking the supremum, we get:

[0121]

[0122] From equation (30) and the definition of λ-norm, we get:

[0123]

[0124] Simplifying the above equation, we get:

[0125]

[0126] According to equation (32), when λ→∞, we have

[0127] ||e n+1 (k)|| λ ≤ρ||e n (k)|| λ +γcKb d +b η (33)

[0128] Where ρ=||I-CBL||, c=||C||. Rearranging equation (33), we get:

[0129]

[0130] Furthermore, after multiple iterations, as the number of iterations n→∞, we can obtain the following from the above formula:

[0131]

[0132] From equation (35), we can deduce that when ρ=||I-CBL||<1, we have:

[0133]

[0134] And when the change in output perturbation between two consecutive iterations and the change in state perturbation between two consecutive iterations are both 0, i.e., b d →0,b η When →0, we have:

[0135]

[0136] The above proof shows that when there is an initial state disturbance in the road network, as the number of iterations increases, the tracking error in the road network will converge to a bound, and the influence of the initial state disturbance can be eliminated at the initial time k=0 of each iteration.

[0137] (2) For iterative learning fault-tolerant control law 2, it is used after a traffic light fault occurs in the road network and the fault is repaired. The state-space equation of the road network at this time is as follows:

[0138]

[0139] The iterative learning fault-tolerant control law 2 is revised to consider input constraints and is now:

[0140] u n+1 (k)=sat[u n (k)]+L1[x n+1 (k)-x n (k)]+L2e n (k+1)+r(k)φ n (39)

[0141] For any given control input u n (k)∈[u min (k),u max (k)], k∈[0,K], the state vector of the road network at time k during the nth and n+1th iterations. n (k) and x n+1 (k), that is, the solutions to the state equations in the state space equation (38) of the road network at the nth and n+1th iterations are respectively:

[0142]

[0143]

[0144] From equations (40) and (41), we can obtain:

[0145]

[0146] Substituting equation (39) into (42) and simplifying, we get:

[0147]

[0148] The error portion can be simplified to the following form:

[0149]

[0150] From the definition of tracking error and equation (38), we can obtain:

[0151]

[0152] Substituting equations (43) and (44) into equation (45), we get

[0153]

[0154] The length of vehicle queues at each intersection is constrained by the length and width of the road, meaning that there is also a state constraint for equation (38), namely ||x n (k)-x d (k)||≤b x .

[0155] Taking the norm of both sides of equation (46), we get

[0156]

[0157] From equations (13), (26), (27), (28), and (47), we obtain

[0158]

[0159] Multiply both sides of equation (48) by a -λk (a>1), and taking the supremum, we obtain

[0160]

[0161] From equation (49) and the definition of λ-norm, we get

[0162]

[0163] From equation (50), we can further obtain:

[0164]

[0165] According to equation (51), when λ→∞, we have

[0166] ||e n+1 (k)|| λ ≤ρ||e n (k)|| λ +γcKb d +δb x +b η(52)

[0167] Where ρ=||I-CBM a L2||,δ=2γ||CBM a L1||, c=||C||.

[0168] Arrange equation (52) to obtain

[0169]

[0170] And after multiple iterations, we can obtain the following from the above formula:

[0171]

[0172] From equation (54), it can be concluded that when ρ=||I-CBM a When L2||<1, we have

[0173]

[0174] That is, we get:

[0175] The above proof demonstrates that when there is a bounded state perturbation within the road network, the tracking error within the road network will converge to a bound as the number of iterations increases. When the state vector x during the iteration process... n (k) at control input u n Under the influence of (k), it gradually approaches the desired state x. d When (k), and when the change in output perturbation between two adjacent iterations and the change in state perturbation between two adjacent iterations are both 0, i.e., b d →0,b η When →0, we have:

[0176] The above proof shows that when there are traffic light malfunctions and state disturbances in the road network, as the number of iterations increases, under the action of the iterative learning fault-tolerant control law 2, the tracking error in the road network will converge to a bound.

[0177] Experimental Results of Iterative Learning Fault-Tolerant Control Law 2: The experimental results are shown in the figure, which only compares the results of various indicators of the road network under the action of Iterative Learning Fault-Tolerant Control Law 2 after the traffic lights in the road network have failed and after the failures have been repaired. The error in the road network is the difference between adjacent approach lanes at each intersection. To better reflect the characteristics of peak traffic flow in road segments, the input traffic flow trend is set to gradually increase first, reach the peak, and then gradually decrease. The input traffic flow uses random input that does not exceed the set value to simulate the impact of random initial disturbances on the input traffic flow. The set values ​​of input traffic flow and road segment numbers in the road network are shown in Table 1. To better simulate the randomness in the actual road network, the number of random seeds in the road network in the simulation experiment is shown in Table 2. The random seed is the initial random number generator in the simulation. Different random numbers result in different arrival patterns of vehicles. The number of lanes and their numbers in each road segment are shown in Table 3. The simulation duration is 7200s; the left-turn, straight-ahead, and right-turn steering ratios of vehicles at all intersections are set to 1:2:1; during the simulation... Figure 3 Intersection 9 is a fault signal intersection.

[0178] Results Comparison Figure 4-8 In the fixed timing control scheme (FT), the green light duration ratio for the four directions is 1:1:1:1; the iterative learning control scheme adopts the D-type iterative learning control law in step 2.2), which is u. n+1 (k)=u n (k)+Le n (k+1).

[0179] Table 1. Road network input flow (veh / h)

[0180]

[0181] Table 2 Random Seed Settings

[0182]

[0183] Table 3 Number of lanes per road section

[0184]

[0185] Figure 4-5 In this context, ILC stands for Iterative Learning Control and ILFTC stands for Iterative Learning Fault-Tolerant Control. By comparing the two methods, when a traffic light in the road network malfunctions and is repaired, the ILFTC method can converge the error in the road network to a smaller value more quickly than the ILC method, making the number of vehicles queuing in each lane more balanced and avoiding large-scale congestion caused by traffic light malfunctions. Figure 6-8In this context, FT stands for Fixed Timing Control, ILC stands for Iterative Learning Control, and ILFTC stands for Iterative Learning Fault-Tolerant Control. By comparing the three methods, when a traffic light in the road network malfunctions and the malfunction is repaired, the ILFTC method can control the performance indicators of the road network, such as vehicle queuing time, number of stops, and delay time, to a lower level compared to the FT and ILC methods, thereby reducing vehicle delays and improving road traffic efficiency.

[0186] Example 2

[0187] The iterative fault-tolerant control method for traffic signals considering initial disturbances and traffic light malfunctions is as follows: Step 1) Select the road network of the traffic area to be studied and establish the road network state space equation based on the traffic flow model; Step 2) Define the traffic light malfunction model, construct the road network state space equation considering input disturbances and traffic light malfunctions, and design an iterative learning fault-tolerant control law and a correction term to compensate for the impact of initial state disturbances; Step 3) Determine whether there are any traffic light malfunctions in the road network based on the vehicle operation patterns at intersections and the cumulative number of vehicles in queues, and switch the iterative learning fault-tolerant control law according to the judgment result; Step 4) Based on the judgment in Step 3) whether there are any traffic light malfunctions in the road network, control the traffic signals in the road network under the influence of initial state disturbances, and reset the green light duration of each phase of the traffic lights according to the green light duration increment obtained from the iterative learning fault-tolerant control, so that the vehicle queue length at each intersection in the road network tends to be balanced.

[0188] Example 3

[0189] Based on Example 2, Step 1 specifically includes: Step 1.1) Constructing the road network state space equation according to the "store-and-forward" traffic flow model. The specific process is as follows: Assume two adjacent intersections are j p and j p-1 Let p = 1, 2, ..., N, and z be the road segment connecting the intersection. Then the queuing equation for the vehicles is as follows:

[0190]

[0191] In the formula, Indicates the intersection at time k. p The queue length of vehicles at the i-th entrance lane, i = 1, 2, 3, 4; ΔT is the control period; and They represent the intersection at time k and j respectively. p Vehicle arrival rate and vehicle dispersal rate at the i-th entrance lane, vehicle dispersal rate In the formula, Indicates the intersection at time k. p The green light time corresponding to the i-th approach lane phase; Indicates intersection j p The saturation flow rate of the i-th approach lane; T represents the signal cycle of the traffic lights at the intersection, and the vehicle arrival rate. In the formula, q i (k) represents the input flow rate of inlet channel i at time k. For vehicles passing through the intersection j p-1 The turning rate of the vehicle entering road segment z;

[0192] Let T = ΔT, and rearrange formula (1) to obtain the intersection j p The vehicle queuing equation for the i-th entrance lane is:

[0193]

[0194] Step 1.2) Write the vehicle queuing equation (2) in 1.1) for all intersection approach lanes, and obtain the vehicle queuing equation for the entire road network at time k+1 as follows:

[0195] X(k+1)=AX(k)+BU(k)+ξ(k) (3)

[0196] In the formula, X(k) is the state vector, representing the queue length of vehicles in all approach lanes of the intersection at time k; U(k) is the control vector, representing the green light time of the corresponding phase of all approach lanes of the intersection at time k; ξ(k) is the initial state disturbance vector in the road network at time k; A is the state matrix, which is the identity matrix; and B is the input moment.

[0197] An intersection within the road network has four approach lanes in each direction. The difference in queue lengths between adjacent approach lanes at time k is chosen as the output Y(k). For any intersection j within the road network... p Its output at time k Represented as:

[0198]

[0199] In the formula, Indicates the intersection at time k. p Output of inlet channel 1; Indicates the intersection at time k. p Output of Inlet 2; Indicates the intersection at time k. p The output of inlet channel 3; Indicates the intersection at time k. p The output of inlet channel 4; Indicates the intersection at time k. pThe vehicle queue length at all approach lanes; η(k) is the output error generated by the data acquisition equipment at time k. The above output equations are written for all intersections in the road network, resulting in the output equation for the entire road network at time k:

[0200] Y(k)=CX(k)+η(k) (5)

[0201] In the formula, N is the number of intersections; C is the output matrix. The state-space equation of the road network at time k+1 is as follows:

[0202]

Claims

1. An iterative fault-tolerant control method for traffic signals considering initial disturbances and signal light malfunctions, characterized in that, Specifically: Step 1) Select the road network of the traffic area to be studied, and establish the state space equation of the road network based on the traffic flow model; Step 1 is as follows: Step 1.1) Construct the road network state space equations based on the "store-and-forward" traffic flow model. The specific process is as follows: Assume two adjacent intersections are... and , The road section connecting the intersection is z The queuing equation for vehicles is as follows: （1） In the formula, express k Intersection No. i The length of the queue for vehicles entering the port. ; To control the cycle; and They represent k Intersection First i Vehicle arrival rate and vehicle dispersal rate at each entrance lane; vehicle dispersal rate In the formula, express k Intersection Corresponding to the i The green light time for each phase of the entrance lane; Indicates an intersection No. i The saturation flow rate of each inlet channel; T This indicates the signal cycle and vehicle arrival rate of the traffic lights at the intersection. In the formula, express k Import Channel i Input flow, For vehicles passing through the intersection The turning rate of the vehicle entering road segment z; make Simplify formula (1) to obtain the intersection No. i The vehicle queuing equation for each entrance lane is as follows: (2); Step 1.2) Write the vehicle queuing equation (2) in 1.1) for all intersection approach lanes, and obtain the vehicle queuing equation for the entire road network at time k+1 as follows: （3） In the formula, X(k) Let be the state vector, representing k Queue lengths for vehicles at all approach lanes of the intersection; U(k) For control vectors, representing k The green light duration for all approach lanes at the intersection, corresponding to the corresponding phase; for k The initial state perturbation vector within the road network at time t. A It is a state matrix, which is an identity matrix; B It is the input moment; The intersection within the road network has four approach lanes in each direction. The choice is to... k The difference in vehicle queue length between adjacent approach lanes at the intersection is used as the output. Y(k) For any intersection within the road network ,That k Output at time Represented as: （4） In the formula, express k Intersection Output of inlet channel 1; express k Intersection Output of Inlet 2; express k Intersection The output of inlet channel 3; express k Intersection The output of inlet channel 4; , ,express k Intersection The length of vehicle queues at all entrance lanes; for k The output error generated by the time-based data acquisition equipment is used to write the output equations for all intersections in the road network, resulting in the output equation for the entire road network at time k: （5） In the formula, N is the number of intersections; C is the output matrix. The state-space equation of the road network at time k+1 is as follows: （6）； Step 2) Define the traffic light fault model, construct the road network state space equation that considers input disturbances and traffic light faults, and design an iterative learning fault-tolerant control law and a correction term to compensate for the influence of initial state disturbances. Step 2 is as follows: Step 2.1) Let express k The output signal of a traffic light malfunction is defined as follows: , where the matrix It's a signal light malfunction. ;and ,when Time indicates the first p All traffic lights are completely faulty; Indicates the first p One of the traffic lights is malfunctioning; when When, it indicates the first p All traffic lights are working normally; fault signal is present. A random number whose value is in the range (0,1). Substituting the traffic light fault model expression into the road network state-space equation obtained in step 1, we obtain the road network state-space equation at time k+1 considering initial state disturbances and traffic light faults as follows: （7） In the formula, When indicating a traffic light malfunction k Queue length of vehicles at all approach lanes of intersections within the road network at any given time; When indicating a traffic light malfunction k The difference in queue length between adjacent approach lanes at all intersections within the road network at any given time; When there is a traffic light malfunction k The input state disturbance vector within the road network at any given time; When there is a traffic light malfunction k Output error generated by real-time data acquisition equipment; 2.2) For the state-space equation of a road network considering input disturbances and traffic light malfunctions, the tracking error of the road network is defined as: （8） In the formula, for k The expected output within the time-limited road network. For the first n During the next iteration k The actual output within the road network at any given time; the D-type iterative learning control law is... ,in, L It is the learning gain matrix; It is the first n iteration k The control input at any given time corresponds to the increment of the green light duration for each intersection signal light; It is the first n iteration k The tracking error at any given time, and , This represents the maximum number of iterations. 2.3) Introduce the correction term into the D-type iterative learning control law, considering... k When the initial state is zero, the interference caused by different initial state disturbances on traffic signal control is eliminated, resulting in an iterative learning control algorithm for urban traffic signals that can reduce the impact of different initial state disturbances when there is no traffic light failure, namely iterative learning control law 1: （9） In the formula, For the correction items in the design; r ( k Let ) be the impulse function, and its form is: （10） In the formula, L The gain matrix is ​​learned iteratively; Is with the first n The terms related to the initial state perturbation in the next iteration are: ,in, For the input matrix B Transpose of; For the first n iteration k Queue lengths for vehicles at all approach lanes of the intersection; For the first n iteration k The control input at time , corresponding to the n iteration k The increment of green light duration at each intersection within the road network at any given time; When a traffic light malfunctions within the road network and after the malfunction is repaired, an iterative learning fault-tolerant control algorithm for handling traffic light malfunctions is obtained by introducing state feedback into the iterative learning control, namely, iterative learning fault-tolerant control law 2: （11） in, All are fault-tolerant gain matrices learned iteratively; For the first n iteration k The control input at time , corresponding to the n iteration k The increment of green light duration at each intersection within the road network at any given time; For the first n iteration k Queue lengths for vehicles at all approach lanes of the intersection; Is with the first n The terms related to the initial state perturbation in the next iteration are: ; Step 3) Based on the vehicle operation pattern at the intersection and the cumulative number of vehicles in the queue, determine whether there is a traffic light malfunction in the road network, and perform iterative learning to switch the fault-tolerant control law based on the judgment result. Step 4) Based on Step 3), determine whether the traffic lights in the road network are faulty. Under the influence of the initial state disturbance in the road network, perform signal control in the road network. According to the green light duration increment of the traffic lights obtained by iterative learning fault-tolerant control, reset the green light duration of each phase of the traffic lights so that the vehicle queue length at each intersection in the road network tends to be balanced.

2. The iterative fault-tolerant control method for traffic signals considering initial disturbances and signal light malfunctions according to claim 1, characterized in that, Step 3 specifically involves: Step 3.1) Based on the vehicle operation patterns in the road network and the cumulative number of vehicles in queues, set a critical value for the queue length at an intersection. Under the control of iterative learning control law 1, a certain intersection... k The difference in vehicle queue length at any given time is greater than k If the difference in vehicle queue length at time -1 exceeds the critical value, it indicates that the traffic light at the intersection is malfunctioning and needs to be switched to iterative learning fault-tolerant control law 2 for signal control. When the fluctuation of the difference in the length of the vehicle queue at the intersection does not exceed the critical value, it indicates that there is no malfunction of the traffic lights, and the iterative learning control law 1 can be used to control the traffic signals indefinitely. Step 3.2) When the queue length of vehicles at an intersection in the road network exceeds the critical value for half or more of the time in one iteration, it indicates that the traffic light at that intersection has been in a faulty state. When the queue length of vehicles exceeds the critical value for a long time and then gradually decreases to below the critical value under the action of the iterative learning fault-tolerant control law 2, it indicates that the traffic light fault has been repaired at this time.

3. The traffic signal iterative fault-tolerant control method considering initial disturbances and traffic light malfunctions according to claim 2, characterized in that, In step 3.1), the average value of the vehicle queue length difference after the vehicle queue length difference in the road network has stabilized is taken, and three times the size of this average value is taken as the critical value.

4. The iterative fault-tolerant control method for traffic signals considering initial disturbances and signal light malfunctions according to claim 2, characterized in that, Step 4 is as follows: Step 4.1) In the first iteration, the existing fixed timing scheme of the traffic lights at intersections in the road network is used. Then, based on whether there are any traffic light malfunctions in the road network as determined in Step 3), starting from the second iteration, the corresponding control law in Step 2.3) is selected to obtain new control inputs based on the determined road network conditions. That is, the first n iteration k The green light duration increments at each intersection within the road network are used to re-time the intersection traffic lights; among which... In the formula and These are the limits of control input. The minimum and maximum values; Step 4.2) When no signal light malfunctions, the first step is to obtain the result according to the iterative learning control law 1. n iteration k Time control input That is, the green light duration increment, which is then correlated with the previous iteration. k The sum of the green light durations at each moment gives the first... n iteration k The green light duration at each moment is determined, and the newly obtained green light duration is used to replace the corresponding green light duration in the previous iteration to set the green light duration for each phase of the intersection. The actual queue length of each lane is adjusted by adjusting the number of vehicles at the intersection within the road network. 4.3) If a traffic light at an intersection malfunctions, the fault-tolerant control law 2, obtained from iterative learning, yields the... n iteration k Time control input That is, the green light duration increment, which is then correlated with the previous iteration. k The sum of the green light durations at each moment gives the first... n iteration k The green light duration at each moment is determined, and the newly obtained green light duration is used to replace the corresponding green light duration in the previous iteration. The green light duration of other non-faulty traffic lights is set to reduce the number of vehicles entering the intersection with faulty traffic lights and coordinate the actual number of vehicles queuing in each lane of the road network. 4.4) After the faulty traffic light is repaired, all traffic lights in the road network are re-timed under the action of the iterative learning fault-tolerant control law 2. In each control cycle, the phase green light ratio of each signal cycle remains unchanged. At the current control cycle, the green light increment is calculated based on the tracking error and control input in the previous control cycle. The green light increment is added to the green light duration in the previous iteration to obtain the new green light duration. The new green light duration is then substituted into the current control cycle to adjust the green light ratio in the current control cycle.

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