A switching control method of urban traffic network signals

Abstract

The application discloses a kind of switching control methods of urban traffic network signal, belong to intelligent traffic control technical field;Including the following steps: obtaining state space model parameter, maximum time lag upper bound and the expected residence time of each mode, and setting attenuation coefficient and jump coefficient;According to the historical traffic flow turning data of each period, generate multiple candidate switching probability matrix of each period respectively, and obtain long-term time proportion in combination with expected residence time;Feasibility is verified by linear matrix inequality group, and solution matrix is retained and no solution matrix is eliminated;The candidate matrix verified in each period is simulated respectively, and the one that makes the traffic flow recovery free time shortest in this period is selected as the optimal switching probability matrix of this period, and the corresponding optimal matrix control signal switching is selected according to current period in actual operation;The application generates and selects the optimal mechanism by multiple candidate schemes, which can effectively alleviate traffic congestion and improve road network traffic efficiency.

Description

Technical Field

[0001] This invention relates to the field of intelligent traffic control technology, and in particular to a method for switching control of urban traffic network signals. Background Technology

[0002] Signal switching control methods for urban traffic networks are a key intelligent traffic control technology aimed at regulating the dynamic characteristics of vehicle queuing at multiple intersections in urban traffic networks. Since state variables such as the number of vehicles queuing and the turning ratio in a traffic system have non-negative characteristics at any given time, and are affected by traffic light cycles and traffic flow propagation delays, urban traffic networks are essentially typical discrete-time positive switching systems.

[0003] In existing technologies, the Modal Dependent Average Dwell Time (MDADT) switching method is a common scheme in the control strategy of such systems. This method, by matching corresponding average dwell times for different subsystems within a defined framework, can optimize the analysis results to some extent compared to traditional schemes. However, existing deterministic switching methods often rely on relatively strict idealized assumptions in practical applications, making them difficult to adapt to the complex and variable conditions of urban traffic networks. In particular, traditional switching system theories generally require the existence of at least one stable subsystem as a prerequisite for stability. When the traffic network is congested at all times and all timing modes are unstable, this method fails due to the lack of a "stable anchor point." Summary of the Invention

[0004] The purpose of this invention is to provide a method for switching control of urban traffic network signals. Through a multi-candidate scheme generation and optimization mechanism, it can effectively alleviate traffic congestion and improve the efficiency of road network traffic.

[0005] To address the aforementioned technical problems, embodiments of the present invention provide a method for switching control of urban traffic network signals, comprising the following steps: The state-space model parameters, maximum time delay upper bound, and expected dwell time of each timing mode of the urban traffic network under multiple preset traffic signal timing modes are obtained, and the attenuation coefficient for controlling the dissipation speed of traffic flow and the jump coefficient for controlling the fluctuation amplitude of traffic flow during the switching process are set. Based on historical traffic flow turning data for each time period, multiple candidate switching probability matrices are generated for each time period; the long-term time proportion of each timing mode is obtained based on the candidate switching probability matrices and the expected dwell time. Multiple matrix inequalities are constructed based on the state-space model parameters, the upper bound of the maximum time delay, and the jump coefficient to constrain the decay rate of the system energy function along the vehicle queue state during the duration of a single timing mode. Scalar inequalities are constructed based on the long-term time proportion, decay coefficient, and jump coefficient to constrain the overall stability of each timing mode after weighting by time proportion during long-term operation. The system of linear matrix inequalities composed of matrix inequalities and scalar inequalities is solved. If a feasible solution exists for the unknown positive definite matrix in the system of linear matrix inequalities, the current candidate switching probability matrix passes the feasibility verification and is retained; otherwise, it is eliminated. For each time period, the switching rules corresponding to each candidate switching probability matrix that has passed the feasibility verification for that time period are simulated, and the one that makes the traffic flow return to normal in the shortest time period is selected as the optimal switching probability matrix for that time period. In actual operation, the switching of traffic signal timing modes at each intersection is controlled according to the optimal switching probability matrix corresponding to the current time period and the expected dwell time of each timing mode.

[0006] In some optional embodiments, the specific steps for controlling the switching of traffic signal timing modes at each intersection based on the optimal switching probability matrix corresponding to the current time period and the expected dwell time of each timing mode are as follows: In actual operation, the optimal switching probability matrix corresponding to the current time period is selected from the optimal switching probability matrices corresponding to each time period. The continuous running time of the current timing mode is monitored in real time. If the continuous running time is less than the preset minimum dwell time limit, the switching action is prohibited. If the continuous running time has reached the minimum dwell time limit, random sampling is performed according to the probability distribution of the corresponding row of the current timing mode in the currently selected optimal switching probability matrix to determine the next timing mode and perform the switching, while resetting the timer. The minimum dwell time limit is a preset constant, determined according to the minimum control cycle of the traffic signal controllers at each intersection and the minimum green light time for pedestrian crossing, to ensure that the actual dwell time of each timing mode is not less than the minimum control cycle of the traffic signal controllers and meets the minimum green light time requirement for pedestrian crossing. The actual dwell time of each timing mode fluctuates randomly around the expected dwell time, and the long-term average value of the actual dwell time approaches the expected dwell time.

[0007] In some optional embodiments, the plurality of matrix inequalities are constructed as follows: The time delay interval defined by the upper bound of the maximum time delay is divided into: M Divide the data into equal-length segments and construct the corresponding matrix inequalities for each segment; for any timing mode... and arbitrary segmented index The positive definite matrix to be solved and For unknown quantities, combined with the system matrix Time delay coefficient matrix and jump coefficient Construct the following matrix inequality: ; And transition constraints between adjacent segments: ; At the same time, an energy decay constraint is constructed for the time delay term itself: ; And construct jump constraints at the timing mode switching time: ; in, For the first The timing mode is in the first A state weighting matrix for each time-delay segment. For the first The timing mode is in the first The time-delay state weighting matrix of each time-delay segment, both of which are positive definite matrices to be solved; This is a matrix showing the proportion of vehicle transfers between intersections at the current moment. This is a matrix representing the contribution ratio of vehicles at delayed times to the current state of each intersection. This is the jump coefficient, used to control the upper bound of the energy jump in the vehicle queuing state at the moment of timing mode switching; This is the attenuation coefficient, used to control the attenuation magnitude of the time delay energy at the switching moment; For time-delay interval segmented index, M The total number of segments, The timing mode before the switch. The timing mode after the switch is defined; the above matrix inequalities together constitute a constraint on the rate of decay of the system energy function along the vehicle queue state during the duration of a single timing mode.

[0008] In some optional embodiments, the scalar inequality is constructed as follows: Based on the long-term time proportion of each timing mode. The attenuation coefficient The jump coefficient and the expected dwell time for each timing mode Construct the following scalar inequality: ; in, For the first The percentage of time each timing mode takes into account during long-term operation. The attenuation coefficient is... For the first The expected dwell time for each timing mode. The jump coefficient, This represents the total number of timing modes; A negative number indicates the energy decay effect during the duration of a single timing mode; A positive number indicates the energy jump effect at the moment of timing mode switching; the scalar inequality is used to constrain that after each timing mode is weighted according to its long-term time proportion, the sum of the attenuation effect must be greater than the sum of the jump effect, so as to ensure the overall stability of the urban transportation network in long-term operation.

[0009] In some optional embodiments, the switching probability matrix is ​​used to characterize the transition relationship between various timing modes. Each timing mode can only switch to other modes at any time, and can reach any timing mode after a finite number of switches. For each time period, multiple candidate switching probability matrices are generated based on the historical traffic flow turning data of that time period, and the sum of the elements in each row of each candidate switching probability matrix is ​​equal to one, and the diagonal elements are zero. The switching probability matrix is ​​updated periodically based on actual operating data, and feasibility verification and simulation optimization are re-executed to adapt to changes in traffic flow.

[0010] In some optional embodiments, the specific steps for obtaining the long-term time proportion of each timing mode based on the candidate handover probability matrix and the expected dwell time are as follows: Solve the stationary distribution equation for the current candidate switching probability matrix, i.e., the stationary distribution vector multiplied by the candidate switching probability matrix equals the stationary distribution vector itself, and the sum of all elements in the stationary distribution vector equals one, to obtain the stationary distribution corresponding to the candidate switching probability matrix; then multiply the stationary distribution component of each timing mode by the expected dwell time of the corresponding timing mode and divide by the sum of the products of all timing modes to obtain the time proportion of each timing mode in long-term operation.

[0011] In some optional embodiments, the timing modes of the state space model include stable subsystems and unstable subsystems; when all timing modes are unstable when run individually, the method can still determine the optimal switching probability matrix that makes the system stable by generating multiple candidate switching probability matrices and performing feasibility verification and simulation optimization of linear matrix inequalities one by one, thereby achieving stable convergence of the number of vehicles queuing at each intersection.

[0012] In some optional embodiments, the state space model is a discrete-time positive switching system model, and the parameters of the state space model include a system matrix and a time delay coefficient matrix. The state equation of the discrete-time positive switching system model is used to describe the dynamic evolution of the number of vehicles queuing at each intersection under different timing modes, and the expression is: the number of vehicles queuing at each intersection at the next time step is equal to the number of vehicles at each intersection after proportional transfer at the current time step plus the number of vehicles at each intersection at the delayed time step contributed proportionally by the delay. The system matrix is ​​used to characterize the transfer ratio of vehicles between intersections at the current time step, and the time delay coefficient matrix is ​​used to characterize the contribution ratio of vehicles at the delayed time step to the current state of each intersection. All elements of the system matrix and the time delay coefficient matrix are non-negative numbers, and the sum of the elements in each column of each matrix is ​​equal to one.

[0013] In some optional embodiments, the step of simulating the switching rules corresponding to each candidate switching probability matrix that has passed the feasibility verification for each time period is as follows: For each time period, the switching rules corresponding to each candidate switching probability matrix that has passed the feasibility verification for that time period are used as control inputs. Traffic flow numerical simulations are performed on the urban traffic network for that time period to simulate the dynamic change process of the number of vehicles queuing at each intersection under the control of each switching rule. The time required for the number of vehicles queuing at each intersection to converge to the equilibrium state is taken as the time for traffic flow to return to normal for that time period.

[0014] The signal switching control method for urban traffic networks provided by this invention has at least the following beneficial effects: This invention generates candidate switching probability matrices in different time periods, verifies the feasibility of linear matrix inequalities, selects the best option through simulation, and uses a random switching mechanism based on transition probabilities. This ensures that the final selected switching rule can maintain system stability even when there is congestion throughout the day and each timing mode is unstable when running alone. It achieves stable convergence of the number of vehicles queuing at each intersection, effectively alleviates traffic congestion, and improves the efficiency of road network traffic. Attached Figure Description

[0015] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this invention, illustrate exemplary embodiments of the invention and are used to explain the invention, but do not constitute an undue limitation of the invention. In the drawings:

[0016] Figure 1 This is a flowchart of a signal switching control method for an urban traffic network according to an embodiment of the present invention; Figure 2 This is a schematic diagram of vehicle travel trajectories at an intersection provided according to an embodiment of the present invention; Figure 3This is a schematic diagram of conventional handover and TP-based handover according to an embodiment of the present invention; Figure 4 This is provided according to an embodiment of the present invention. , and A schematic diagram showing the distribution of dwell time; Figure 5 This is a schematic diagram of the corresponding state trajectories of three modes under TP-based switching according to an embodiment of the present invention; Figure 6 This is a schematic diagram of the state trajectory and corresponding switching signal of a discrete-time positive switching system after adopting the switching control method of the present invention, according to an embodiment of the present invention. Detailed Implementation

[0017] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below in conjunction with specific embodiments and corresponding drawings. Obviously, the described embodiments are only a part of the embodiments of this invention, and not all of them. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention.

[0018] One embodiment of the present invention relates to a switching control method for urban traffic network signals. The implementation details of the switching control method for urban traffic network signals in this embodiment are described in detail below. The following implementation details are provided for ease of understanding and are not necessary for implementing this solution.

[0019] The specific process of the urban traffic network signal switching control method in this embodiment can be described as follows: Figure 1 As shown, it includes: Step 101: Obtain the state space model parameters, maximum time delay upper bound, and expected dwell time of the urban traffic network under multiple preset traffic signal timing modes, and set the attenuation coefficient for controlling the dissipation speed of traffic flow and the jump coefficient for controlling the fluctuation amplitude of traffic flow during the switching process. Step 102: Based on the historical traffic flow turning data for each time period, generate multiple candidate switching probability matrices for each time period; obtain the long-term time proportion of each timing mode based on the candidate switching probability matrices and the expected dwell time. Step 103: Construct multiple matrix inequalities based on the state-space model parameters, the upper bound of the maximum time delay, and the jump coefficient to constrain the decay rate of the system energy function along the vehicle queuing state during the duration of a single timing mode; construct scalar inequalities based on the long-term time proportion, decay coefficient, and jump coefficient to constrain the overall stability of each timing mode after weighting by time proportion during long-term operation; solve the linear matrix inequalities system composed of matrix inequalities and scalar inequalities. If the unknown positive definite matrix in the linear matrix inequality system has a feasible solution, the current candidate switching probability matrix passes the feasibility verification and is retained; otherwise, it is eliminated. Step 104: For each time period, simulate the switching rules corresponding to each candidate switching probability matrix that has passed the feasibility verification for that time period, and select the one that makes the traffic flow return to normal in the shortest time period as the optimal switching probability matrix for that time period; In actual operation, control the switching of traffic signal timing modes at each intersection according to the optimal switching probability matrix corresponding to the current time period and the expected dwell time of each timing mode.

[0020] Specifically, this invention addresses the engineering challenge of inherently unstable traffic patterns in urban transportation networks during a single time period by proposing a mode-dependent average residence time switching control method based on transition probability. By modeling urban intersection traffic flow as a discrete-time positive switching system, and utilizing the transition probability matrix to characterize the stochastic characteristics of vehicle turning ratios at different road intersections, combined with the Lyapunov-Krasovskii functional theory to derive sufficient conditions for system stability, the invention ultimately achieves exponentially stable operation of the entire transportation network even when all traffic subsystems are unstable. This effectively solves the all-time congestion problem that traditional traffic control methods cannot address.

[0021] The following provides a detailed description of the modeling process of the discrete-time positive switching traffic control system in the embodiments of the present invention.

[0022] Intersection vehicle trajectory diagram as follows Figure 2 As shown in the figure, the specific driving paths of vehicles from different directions when turning left, turning right, and going straight at an intersection are illustrated.

[0023] Define state vector , among which This indicates the number of vehicles at the corresponding intersection.

[0024] Real-time transfer relationships between vehicles at intersections are represented by a matrix. , It is expressed in the following form: ; Indicates leaving the intersection Vehicles entering the intersection The proportions. These proportions satisfy the normalization condition: for any row , This condition ensures the complete distribution of vehicle traffic flow.

[0025] Traffic control systems can be modeled as follows: ; Traffic control systems are relatively complex, and reality is not always ideal. Differences in the turning ratios of vehicles in different lanes can have varying degrees of impact on subsequent traffic conditions. Therefore, time-varying delay terms... It was introduced and analyzed.

[0026] The following section introduces the time delay matrix. It describes time The influence of previous historical states on the current state takes the following form: ; Indicates past state The proportion of the influence exerted on the current state, of which Indicates a time delay. Specifically, Description of the impact on the intersection Leave the intersection before the current state's delay time. The proportion of vehicles. This is similar to... However, it involves manipulating past states to capture lag effects in traffic propagation (e.g., delays due to signal cycles or congestion). It also satisfies the normalization condition, that is, .

[0027] Then, the traffic control system can be represented as follows: ; Based on the above analysis, consider the following form of discrete-time positive-switching traffic control system. ; Where the state vector . Switching signals , To switch sequences, Indicates switching signal No. The second visit The dwell time of each subsystem Indicates the first At the next switching moment, time-varying time delay satisfy , positive integer and It is known. It is the initial function.

[0028] Definition 5.1 For any initial conditions and arbitrary switching signals ,in If the solution of the discrete-time switching system (5.1) is... satisfy If so, then system (5.1) is called a positive system.

[0029] Lemma 5.1 For If and only if and The system (5.1) is positive.

[0030] Definition 5.2 For switching signals ,if and Duration of stay and If it is an uncorrelated random positive variable, then the switching signal... With the transition probabilities shown below from Mode switch model ,in , , ,and This type This is called TP-based MDADT handover.

[0031] Duration of stay The mathematical expectation is expressed as , ,in It is a positive number.

[0032] Note 5.1 When , This indicates that the subsystem's dwell time handover has transitioned from MDADT handover to ADT handover. It is worth noting that ADT handover implies that the continuous handover interval between subsystems is not less than a constant. The dwell time used in this technology It is a random variable and does not need to be greater than a constant. .

[0033] Traditional handover and TP-based handover diagrams are shown below. Figure 3 As shown, the figure illustrates the probability transition between two dwell time switching modes, involving three modes ( , and Subgraph (i) shows ADT and MDADT handovers, indicating that the handover probabilities between subsystems are consistent (i.e., ...). Subgraph (ii) depicts TP-based handover, indicating that handover probabilities between subsystems may be inconsistent (i.e., ).

[0034] Note 5.2 ADT (MDADT) handover requires that the average time interval between any two consecutive handover events be no less than a constant. ( Clearly, TP-based MDADT switching also satisfies this average constraint, and its dwell time is a random variable with probabilistic characteristics.

[0035] Assumption 5.1 Assume that all subsystems of system (5.1) are unstable, that is, None of them are Schur matrices. Based on the time-delay insensitivity of discrete-time positive systems, the above assumptions can be reasonably made without loss of generality.

[0036] Assumption 5.2 Assumption of the TP matrix It is irreducible, and its stationary distribution is .

[0037] It should be noted that the stationary distribution in assumption 5.2 must not only satisfy the existence condition, but also the ergodicity condition. Ergodicity theory is crucial to the validity of Lemma 5.2.

[0038] If the matrix If it is irreducible, then there exists a unique stationary distribution such that... ; Lemma 5.2 Let To satisfy the TP-based MDADT handover under Definition 5.2 and Assumption 5.1, the following equation holds. ; in . It refers to the interval Inside Total runtime.

[0039] Definition 5.3 If for any , Then the positive switching system (5.1) is almost necessarily exponentially stable.

[0040] For a given Duration of stay ,in , .

[0041] Assumption ,and Then the interval Classified as Equal length segments Its length is .

[0042] set up Construct a matrix function of the following form. ; for It can be deduced that ; here .

[0043] Theorem 5.1 Consider system (5.1). If assumption 5.1 holds, for any given switching signal... , and normal numbers Assuming that positive constants exist , satisfy ,matrix ,and , such that for any And for any The following inequalities hold. ; ; ; ; ; Then system (5.1) meets the switching signal of MDADT switching based on TP. The following is almost certainly an index of stability.

[0044] Proof: For the subsystem The discretized copositive Lyapunov-Krasovskii functional is as follows: ; Easy to obtain ; when It can be obtained through calculation difference ; Based on the conditions, we can obtain ; when It can be deduced that... ; This means that for any : ; Obviously ; Based on the above formula, we can obtain ; Combining the inequalities, we can obtain ; Take the logarithm of both sides of the inequality, then divide by... We can obtain the following inequality ; in, For the first Mode in interval The number of times it is activated within.

[0045] By Lemma 5.2, and with the ergodicity guarantee of the switching signal, we have ; Combining the above equations, we can obtain... ; because and Therefore, the result can be obtained. ; According to definition 5.3, it is clear that system (5.1) is almost necessarily exponentially stable, thus proving the point.

[0046] Note 5.3 If Assumption 5.1 does not hold, then the corresponding statement in Theorem 5.1... It becomes This corresponds to a positive switching system where all subsystems are stable, further reducing the research difficulty. Therefore, the research method proposed in this study is more general.

[0047] The above system of linear matrix inequalities can be solved using the algorithms in Table 1.

[0048] Table 1 Solution parameters Algorithm The effectiveness of the method of the present invention will be verified through a specific example below.

[0049] For system (5.1), consider time-varying delays. At this time, the lag fluctuates between 0 and 0.4. The system parameters of system (5.1) with the following three modes are taken.

[0050] The system matrix and time delay coefficient matrix for Mode 1 are as follows: ; The system matrix and time delay coefficient matrix for Mode 2 are as follows: ; The system matrix and time delay coefficient matrix for Mode 3 are as follows: ; Assume the expected value of the length of stay satisfies the following conditions: , , When the subsystem When activated, the dwell time takes the value according to the mathematical expectation. , and A uniform distribution centered on the subsystem. When the subsystem enters mode... ,model The dwell time is automatically determined by probability sampling from the above distribution, thus reflecting the randomness of the dwell time.

[0051] Corresponding to , and The diagram showing the distribution of dwell time is as follows: Figure 4 As shown, the figure corresponds to , and The plot shows the residence time distribution. The horizontal axis represents residence time length, and the vertical axis represents probability density. The residence time of pattern 1 is concentrated around 0.67, pattern 2 around 1.5, and pattern 3 around 1.4.

[0052] Using the algorithm in Table 1 above, the transition probability matrix can be calculated: ; The matrix satisfies the irreducibility condition of assumption 5.2 and has a stationary distribution. Given , , .set up Solving the linear matrix inequality in Theorem 5.1, we can obtain:

[0053] ; The initial parameters are selected as follows , They are three independent random positive variables that satisfy a uniform distribution with a variance of 0.3.

[0054] The corresponding state trajectory diagrams for the three modes under TP-based switching are shown below. Figure 5 As shown in the figure, the state trajectories of the three discrete-time subsystems are displayed when they are run individually. It can be clearly seen from the figure that all three modes diverge when run individually, indicating that all three modes are unstable when run individually.

[0055] The schematic diagram of the state trajectory and corresponding switching signal of the discrete-time positive switching system after adopting the switching control method of the present invention is shown below. Figure 6 As shown in the figure, it can be clearly seen that the state of system (5.1) always remains non-negative (i.e., it is a positive system), and it achieves almost inevitable exponential stability under TP-based MDADT switching control, with the number of vehicles queuing at the three intersections rapidly converging to the zero equilibrium point. This proves that the method proposed in Theorem 5.1 is effective.

[0056] In summary, this invention addresses the core challenge of instability in all subsystems, a problem that traditional deterministic switching methods cannot solve. It innovatively proposes a mode-dependent average dwell time (TP-MDADT) stochastic switching control method. First, a mathematical model of a discrete-time positive switching system with time-varying delays is established, clarifying the definition and characteristics of TP-MDADT switching. Second, based on co-positive Lyapunov-Krasovskii functional theory and the ergodicity of stochastic processes, a sufficient condition for the system to be almost necessarily exponentially stable is rigorously derived, and a linear matrix inequality criterion solvable using the MATLAB LMI toolbox is provided. Finally, numerical simulation experiments verify the effectiveness of this method. The results show that, when all subsystems diverge when running independently, the switching strategy designed in this invention enables the system to converge rapidly to the zero equilibrium point.

[0057] This invention breaks through the existing switching system theory's premise of "at least one stable subsystem," expands the theoretical boundary of stability analysis for positive switching systems, and proposes a method that has the advantages of easy engineering implementation, strong robustness, and wide applicability. It can provide new theoretical support and technical solutions for practical engineering problems such as urban traffic congestion control, multi-agent collaboration, and industrial process control.

[0058] The steps of the various methods described above are only for clarity. In practice, they can be combined into one step or some steps can be split into multiple steps. As long as they include the same logical relationship, they are all within the protection scope of this invention. Adding insignificant modifications or introducing insignificant designs to the algorithm or process, without changing the core design of the algorithm and process, are also within the protection scope of this invention.

[0059] Another embodiment of the present invention relates to a computer-readable storage medium storing a computer program. When executed by a processor, the computer program implements the method embodiments described above.

[0060] That is, those skilled in the art will understand that all or part of the steps in the methods of the above embodiments can be implemented by a program instructing related hardware. This program is stored in a storage medium and includes several instructions to cause a device (which may be a microcontroller, chip, etc.) or processor to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0061] Those skilled in the art will understand that the above embodiments are specific embodiments for implementing the present invention, and in practical applications, various changes can be made to them in form and detail without departing from the spirit and scope of the present invention.

Claims

1. A method for switching control of signals in an urban traffic network, characterized in that, The method includes: The state-space model parameters, maximum time delay upper bound, and expected dwell time of each timing mode of the urban traffic network under multiple preset traffic signal timing modes are obtained, and the attenuation coefficient for controlling the dissipation speed of traffic flow and the jump coefficient for controlling the fluctuation amplitude of traffic flow during the switching process are set. Based on historical traffic flow turning data for each time period, multiple candidate switching probability matrices are generated for each time period; the long-term time proportion of each timing mode is obtained based on the candidate switching probability matrices and the expected dwell time. Multiple matrix inequalities are constructed based on the state-space model parameters, the upper bound of the maximum time delay, and the jump coefficient to constrain the decay rate of the system energy function along the vehicle queue state during the duration of a single timing mode. Scalar inequalities are constructed based on the long-term time proportion, decay coefficient, and jump coefficient to constrain the overall stability of each timing mode after weighting by time proportion during long-term operation. The system of linear matrix inequalities composed of matrix inequalities and scalar inequalities is solved. If a feasible solution exists for the unknown positive definite matrix in the system of linear matrix inequalities, the current candidate switching probability matrix passes the feasibility verification and is retained; otherwise, it is eliminated. For each time period, the switching rules corresponding to each candidate switching probability matrix that has passed the feasibility verification for that time period are simulated, and the one that makes the traffic flow return to normal in the shortest time period is selected as the optimal switching probability matrix for that time period. In actual operation, the switching of traffic signal timing modes at each intersection is controlled according to the optimal switching probability matrix corresponding to the current time period and the expected dwell time of each timing mode.

2. The urban traffic network signal switching control method as described in claim 1, characterized in that, The specific steps for controlling the switching of traffic signal timing modes at each intersection based on the optimal switching probability matrix corresponding to the current time period and the expected dwell time of each timing mode are as follows: In actual operation, the optimal switching probability matrix corresponding to the current time period is selected from the optimal switching probability matrices corresponding to each time period according to the current time period. The system monitors the continuous running time of the current timing mode in real time. If the continuous running time is less than the preset minimum dwell time, the switching action is prohibited. If the continuous running time has reached the minimum dwell time limit, random sampling is performed based on the probability distribution of the corresponding row of the current timing mode in the currently selected optimal switching probability matrix to determine the next timing mode and execute the switch, while resetting the timer. The minimum dwell time limit is a preset constant, determined based on the minimum control cycle of the traffic signal controllers at each intersection and the minimum green light time for pedestrian crossing, to ensure that the actual dwell time of each timing mode is not lower than the minimum control cycle of the traffic signal controllers and meets the minimum green light time requirement for pedestrian crossing. The actual dwell time of each timing mode fluctuates randomly around the expected dwell time, and the long-term average value of the actual dwell time approaches the expected dwell time.

3. The urban traffic network signal switching control method as described in claim 1, characterized in that, The multiple matrix inequalities are constructed as follows: The time delay interval defined by the upper bound of the maximum time delay is divided into: M Divide the data into equal-length segments and construct the corresponding matrix inequalities for each segment; for any timing mode... and arbitrary segmented index The positive definite matrix to be solved and For unknown quantities, combined with the system matrix Time delay coefficient matrix and jump coefficient Construct the following matrix inequality: ； And transition constraints between adjacent segments: ； At the same time, an energy decay constraint is constructed for the time delay term itself: ； And construct jump constraints at the timing mode switching time: ； in, For the first The timing mode is in the first A state weighting matrix for each time-delay segment. For the first The timing mode is in the first The time-delay state weighting matrix of each time-delay segment, both of which are positive definite matrices to be solved; This is a matrix showing the proportion of vehicle transfers between intersections at the current moment. This is a matrix representing the contribution ratio of vehicles at delayed times to the current state of each intersection. This is the jump coefficient, used to control the upper bound of the energy jump in the vehicle queuing state at the moment of timing mode switching; This is the attenuation coefficient, used to control the attenuation magnitude of the time delay energy at the switching moment; For time-delay interval segmented index, M The total number of segments, The timing mode before the switch. The timing mode after the switch is defined; the above matrix inequalities together constitute a constraint on the rate of decay of the system energy function along the vehicle queue state during the duration of a single timing mode.

4. The urban traffic network signal switching control method as described in claim 1, characterized in that, The scalar inequality is constructed as follows: Based on the long-term time proportion of each timing mode. The attenuation coefficient The jump coefficient and the expected dwell time for each timing mode Construct the following scalar inequality: ； in, For the first The percentage of time each timing mode takes into account during long-term operation. The attenuation coefficient is... For the first The expected dwell time for each timing mode. The jump coefficient, This represents the total number of timing modes; A negative number indicates the energy decay effect during the duration of a single timing mode; A positive number indicates the energy jump effect at the moment of timing mode switching; the scalar inequality is used to constrain that after each timing mode is weighted according to its long-term time proportion, the sum of the attenuation effect must be greater than the sum of the jump effect, so as to ensure the overall stability of the urban transportation network in long-term operation.

5. The urban traffic network signal switching control method as described in claim 1, characterized in that, The switching probability matrix is ​​used to characterize the transition relationship between each timing mode. Each timing mode can only switch to other modes at any time, and can reach any timing mode after a finite number of switching. For each time period, multiple candidate switching probability matrices are generated based on the historical traffic flow turning data for that time period. The sum of the elements in each row of each candidate switching probability matrix is ​​equal to one, and the diagonal elements are zero. The switching probability matrix is ​​updated periodically based on actual operating data, and feasibility verification and simulation optimization are re-executed to adapt to changes in traffic flow.

6. The urban traffic network signal switching control method as described in claim 1, characterized in that, The specific steps for obtaining the long-term time proportion of each timing mode based on the candidate handover probability matrix and the expected dwell time are as follows: Solve the stationary distribution equation for the current candidate switching probability matrix, i.e., the stationary distribution vector multiplied by the candidate switching probability matrix equals the stationary distribution vector itself, and the sum of all elements in the stationary distribution vector equals one, to obtain the stationary distribution corresponding to the candidate switching probability matrix; then multiply the stationary distribution component of each timing mode by the expected dwell time of the corresponding timing mode and divide by the sum of the products of all timing modes to obtain the time proportion of each timing mode in long-term operation.

7. The urban traffic network signal switching control method as described in claim 1, characterized in that, The timing modes of the state-space model include stable subsystems and unstable subsystems. When all timing modes are unstable when run individually, the method can still determine the optimal switching probability matrix that makes the system stable by generating multiple candidate switching probability matrices and verifying the feasibility of linear matrix inequalities and performing simulation optimization on each one, thus achieving stable convergence of the number of vehicles queuing at each intersection.

8. The urban traffic network signal switching control method as described in claim 1, characterized in that, The state space model is a discrete-time positive switching system model. The parameters of the state space model include the system matrix and the time delay coefficient matrix. The state equation of the discrete-time positive switching system model is used to describe the dynamic evolution of the number of vehicles queuing at each intersection under different timing modes. The expression is: the number of vehicles queuing at each intersection at the next time is equal to the number of vehicles at each intersection after proportional transfer at the current time plus the number of vehicles at each intersection contributed by the delay ratio at the delayed time. The system matrix is ​​used to characterize the proportion of vehicles transferring between intersections at the current time, and the time delay coefficient matrix is ​​used to characterize the proportion of vehicles contributing to the current state of each intersection at the delayed time. All elements of the system matrix and the time delay coefficient matrix are non-negative, and the sum of the elements in each column of each matrix is ​​equal to one.

9. The urban traffic network signal switching control method as described in claim 1, characterized in that, The following steps are taken to simulate the switching rules corresponding to each candidate switching probability matrix that has passed the feasibility verification for each time period: For each time period, the switching rules corresponding to each candidate switching probability matrix that has passed the feasibility verification for that time period are used as control inputs. Traffic flow numerical simulations are performed on the urban traffic network for that time period to simulate the dynamic change process of the number of vehicles queuing at each intersection under the control of each switching rule. The time required for the number of vehicles queuing at each intersection to converge to the equilibrium state is taken as the time for traffic flow to return to normal for that time period.

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