A hybrid model predictive control acceleration method and system for high-dimensional space

Abstract

The application provides a high-dimensional space-oriented hybrid model predictive control acceleration method and system, and belongs to the technical field of traffic control; the method comprises the following steps: a segmented affine model for describing a target section of an expressway is constructed, and sampling is performed in the state space of the segmented affine model; a dataset is constructed by solving a hybrid model predictive control problem for multiple state samples; multiple tuples most similar to the state of the current segmented affine model are selected from the dataset based on a K nearest neighbor algorithm, corresponding optimal integer solutions are extracted, and a potential integer solution set is determined; according to the potential integer solution set, corresponding logical constraints in the hybrid model predictive control problem are removed, and a reduced optimization problem is generated; a current control input is determined by solving the optimization problem, and the obtained control input is applied to the segmented affine model. The application can optimize the solving speed of high-dimensional space-oriented calculation, and thus significantly improves the timeliness of traffic control.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of traffic control, and particularly relates to a high-dimensional space-oriented hybrid model predictive control acceleration method and system. BACKGROUND

[0002] The statements in this section merely provide background information related to the present application and do not necessarily constitute prior art.

[0003] As a typical hybrid system, the piecewise affine model has unique piecewise linear characteristics and can accurately approximate various complex system dynamics, and is therefore widely used in the field of traffic control. Therefore, the hybrid model-based predictive control method has unique advantages in the control field, which can comprehensively consider the continuous dynamics and discrete events of the system, and realize efficient prediction and optimal control of the future behavior of the system through optimization under the premise of meeting various constraint conditions.

[0004] However, with the significant increase in traffic flow, the scale of intelligent traffic control also increases, resulting in an increase in the system modes of the hybrid model used to solve traffic control problems, and the scale of the mixed integer programming problem converted from the online control problem also increases exponentially, which makes the solving process extremely complex and difficult, greatly limiting the practical application of such control methods in high-dimensional system space, and limiting the timeliness of peak traffic control. SUMMARY

[0005] To overcome the above shortcomings of the prior art, the present application provides a high-dimensional space-oriented hybrid model predictive control acceleration method and system, which can optimize the solving speed of high-dimensional space-oriented calculation, and thus significantly improve the timeliness of traffic control.

[0006] To achieve the above object, one or more embodiments of the present application provide the following technical solutions:

[0007] The first aspect of the present application provides a high-dimensional space-oriented hybrid model predictive control acceleration method.

[0008] A high-dimensional space-oriented hybrid model predictive control acceleration method comprises:

[0009] A piecewise affine model for describing a target section of an expressway is constructed, and sampling is performed in the state space under the constructed piecewise affine model; a data set is constructed by solving a hybrid model predictive control problem for a plurality of state samples obtained by sampling, wherein the state samples are traffic density;

[0010] selecting multiple tuples from the built dataset based on a K-Nearest Neighbor algorithm, the multiple tuples being most similar to a current state of the piecewise affine model, extracting corresponding optimal integer solutions and determining a set of potential integer solutions; wherein each tuple contains a traffic density value and a corresponding discrete congestion level;

[0011] based on the set of potential integer solutions, removing corresponding logical constraints in a hybrid model predictive control problem, generating a reduced optimization problem, and determining a current control input by solving the optimization problem and applying the determined control input to the piecewise affine model.

[0012] Further, sampling in a state space of the piecewise affine model includes: using a Markov Monte Carlo sampling method to uniformly sample in a convex polyhedron formed by the state space of the piecewise affine model; wherein the state space of the piecewise affine model corresponds to traffic states in each sub-section within a target section of the highway.

[0013] Further, the Markov Monte Carlo sampling method includes: selecting an arbitrary point in a target distribution from the convex polyhedron and randomly selecting a direction from a unit hypersphere; taking an intersection of the direction and the convex polyhedron, and randomly selecting a new sampling point in a line segment formed by the intersection; wherein the convex polyhedron is composed of multiple sub-spaces, each sub-space corresponding to a traffic state of a complete section, i.e., each sub-space is composed of states of multiple sub-sections included in the target section of the highway.

[0014] Further, the unit hypersphere has the same spatial dimension as the target distribution.

[0015] Further, the K-Nearest Neighbor algorithm selects multiple tuples from the dataset based on a distance metric, the distance metric using Euclidean distance; wherein each tuple contains a congestion level corresponding to a traffic density, i.e., a discrete congestion level value of a corresponding sub-section in the future under optimal control.

[0016] Further, removing corresponding logical constraints in the hybrid model predictive control problem includes: selecting a mode that has never been activated from the multiple nearest neighbors in the set of potential integer solutions, and removing a logical constraint corresponding to the mode; wherein the logical constraint corresponds to a discrete congestion level condition that will not occur in each sub-section of the target section of the highway in the future.

[0017] Further, the control input is applied to the piecewise affine model, including: when solving the reduced optimization problem, if an optimal integer solution is obtained, applying the first term of the sequence in the optimal integer solution to the piecewise affine model; if the reduced optimization problem is not solvable, solving the optimization problem before reduction, and putting a tuple composed of the model state and the corresponding optimal integer solution into the dataset; wherein the optimal integer solution represents a discrete congestion degree value of each sub-road segment in the future under the optimal control of the target road segment of the highway.

[0018] The second aspect of the application provides a hybrid model predictive control acceleration system for a high-dimensional space.

[0019] A hybrid model predictive control acceleration system for a high-dimensional space, comprising:

[0020] The dataset generation module is configured to: construct a piecewise affine model for describing the target road segment of the highway, and sample in the state space under the constructed piecewise affine model; and construct a dataset by solving a hybrid model predictive control problem for a plurality of state samples obtained by sampling; wherein the state sample is traffic density.

[0021] The optimization problem scale reduction module is configured to: select a plurality of tuples most similar to the current piecewise affine model state from the constructed dataset based on a K-nearest neighbor algorithm, extract corresponding optimal integer solutions and determine a set of potential integer solutions; wherein each tuple contains a traffic density value and a discrete congestion degree corresponding thereto; remove the corresponding logical constraints in the hybrid model predictive control problem according to the set of potential integer solutions, generate a reduced optimization problem, and determine the current control input by solving the optimization problem, and apply the obtained control input to the piecewise affine model.

[0022] The third aspect of the application provides a computer readable storage medium having a program stored thereon, the program being executed by a processor to implement the steps of the hybrid model predictive control acceleration method for a high-dimensional space according to the first aspect of the application.

[0023] The fourth aspect of the application provides an electronic device comprising a memory, a processor, and a program stored on the memory and executable on the processor, wherein the processor executes the program to implement the steps of the hybrid model predictive control acceleration method for a high-dimensional space according to the first aspect of the application.

[0024] The above one or more technical solutions have the following beneficial effects:

[0025] The application solves a hybrid model predictive control problem by constructing a data set through a plurality of state samples obtained by sampling, selects a plurality of tuples most similar to a state of a segmented affine model currently used to describe a target section of the expressway from the data set based on a K nearest neighbor algorithm to determine a potential integer solution set, wherein each tuple contains a traffic density value and a discrete congestion degree corresponding thereto, and finally generates a reduced optimization problem by removing corresponding logical constraints in the hybrid model predictive control problem according to the potential integer solution set. Therefore, the application can optimize the solving speed for high-dimensional space calculation, and further significantly improve the timeliness of traffic control.

[0026] Advantages of the additional aspects of the application will be partially given in the following description, partially become obvious from the following description, or be known by the practice of the application. BRIEF DESCRIPTION OF DRAWINGS

[0027] The accompanying drawings, which form a part of the specification, are included to provide a further understanding of the application and are incorporated herein by reference. The illustrations are shown for the purpose of enabling those skilled in the art to

[0028] Figure 1 A flowchart of a high-dimensional space-oriented hybrid model predictive control acceleration method in the embodiment one of the application. DETAILED DESCRIPTION

[0029] It should be noted that the following detailed description is exemplary in nature and is intended to provide further description of the application. Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which the application belongs.

[0030] It should be noted that the terms used herein are only for the purpose of describing specific embodiments and are not intended to limit the exemplary embodiments according to the application.

[0031] In the case of no conflict, the embodiments in the application and the features in the embodiments can be combined with each other.

[0032] The general idea of the application is that the application provides a high-dimensional space-oriented hybrid model predictive control acceleration method, which uses a data-driven machine learning method to fully mine the optimal integer solution features of the control problem from historical data, thereby greatly reducing the feasible solution space and improving the solving speed.

[0033] Embodiment one

[0034] The embodiment discloses a high-dimensional space-oriented hybrid model predictive control acceleration method.

[0035] As Figure 1As shown, a high-dimensional space-oriented hybrid model predictive control acceleration method comprises the following steps:

[0036] Step S1, a piecewise affine model for describing a target section of an expressway is constructed, and sampling is performed in a state space under the constructed piecewise affine model; a dataset is constructed by solving a hybrid model predictive control problem for a plurality of state samples obtained through sampling; wherein the state samples are traffic densities;

[0037] Step S2, a plurality of tuples most similar to a current piecewise affine model state are selected from the constructed dataset based on a K-nearest neighbor algorithm, corresponding optimal integer solutions are extracted, and a set of potential integer solutions is determined; wherein each tuple contains a traffic density value and a discrete congestion degree corresponding thereto; according to the set of potential integer solutions, corresponding logical constraints in the hybrid model predictive control problem are removed, and a reduced optimization problem is generated; a current control input is determined by solving the optimization problem, and the obtained control input is applied to the piecewise affine model.

[0038] Based on the above process, the application can optimize the solving speed for high-dimensional space calculation, and thus significantly improve the timeliness of traffic control. In order to facilitate the understanding of the technical scheme of the application, the specific implementation method in the technical scheme of the application will be further explained and described below.

[0039] In step S1, a piecewise affine model for describing a target section of an expressway is constructed, and sampling is performed in a state space under the constructed piecewise affine model; a dataset is constructed by solving a hybrid model predictive control problem for a plurality of state samples obtained through sampling; wherein the state samples are traffic densities. The following method can be used to achieve this:

[0040] Step S1-1, standardization of the piecewise affine model.

[0041] Suppose the system state is , the input is , the output is , and the time step is ; wherein represents the set of real numbers, , and represent the dimensions of the system state, the input, and the output, respectively. Thus, the piecewise affine model can be represented as:

[0042] ;

[0043] ;

[0044] wherein and represent the piecewise affine model in the i-th a state matrix of the zth partition and an input matrix of the zth partition, an output matrix of the zth partition of the piecewise affine model; an output matrix of the zth partition of the piecewise affine model; a system state at the zth time instant, a system output at the zth time instant, a system output at the zth time instant, a system input at the zth time instant. a zth constant vector for system state update; a zth constant vector for system output, the coefficients represent the dynamic characteristics of the model on the zth partition. a zth constant vector for system state update; a zth constant vector for system output, the coefficients represent the dynamic characteristics of the model on the zth partition. a zth constant vector for system output, the coefficients represent the dynamic characteristics of the model on the zth partition. a zth constant vector for system output, the coefficients represent the dynamic characteristics of the model on the zth partition. a zth constant vector for system output, the coefficients represent the dynamic characteristics of the model on the zth partition. a zth partition of the piecewise affine model, usually represented as a polytope, which is defined as:

[0045] ;

[0046] wherein, a zth partition matrix, a zth partition vector; , a zth partition vector; , a zth partition vector; a zth partition matrix, a zth partition vector;

[0047] Step S1-2, standardization of the hybrid model predictive control problem.

[0048] Generally, the hybrid model predictive control problem for the piecewise affine model can be expressed as the following optimization problem:

[0049] ;

[0050] , ;

[0051] relevant equality and inequality constraints, ;

[0052] relevant equality and inequality constraints, ;

[0053] and joint equality and inequality constraints of​ ;

[0054] where, denotes the number of control horizons, denotes the optimization objective function.

[0055] By introducing logical variables and auxiliary variables through Big-M method, the model can be dynamically represented as the following constraints:

[0056] ;

[0057] ;

[0058] ;

[0059] where, denotes a large enough constant. The logical variable , denotes whether the system state at time belongs to the th partition. Therefore, when the system state belongs to the partition , i.e.:

[0060] ;

[0061] ;

[0062] Therefore, at time , the control problem is converted into a mixed integer programming problem. Let the logical variable denotes the mode of the model at time (only a vector composed of 0 and 1). Let the matrix denotes all the logical variables in the mixed integer programming problem. The dimension of this matrix is , and the sum of each row variable is 1, for example:

[0063] ;

[0064] where, denotes an example of the matrix . The dimension of this matrix is , i.e. , . However, for a complex piecewise affine model, the number of modes can reach dozens or even hundreds. Assuming that this problem is a mixed integer linear programming problem, in the worst case, it needs to exhaust combinations to solve this optimization problem, i.e. to solve linear programming problem. Therefore, as the control horizon increases, the size of the optimization problem grows exponentially, making it difficult to solve the optimization problem within a specified time, and unable to meet the needs of real-time control.

[0065] Therefore, according to the nature of the hybrid model predictive control, for any initial system state , there is an optimal integer solution, i.e. the values of all logical variables in , if the value of the matrix is given, the optimization problem will degenerate into a linear programming problem, and the optimal integer solution can be obtained in polynomial time.

[0066] Step S1-3, standardization of the hybrid model predictive control problem.

[0067] In this embodiment, the data set is a collection of tuples composed of the initial system state and its corresponding optimal integer solution, denoted as ; where the superscript represents the data number in the data set , and there are pieces in total. Due to its "rolling horizon" characteristic, model predictive control will solve the same optimization problem multiple times (only the initial state is different), so the historical solving results can be used as one of the sources of the data set. However, this data source cannot cover the state space, so it is necessary to generate data to fill the data set. According to the nature of the piecewise affine system, its state space is a convex polyhedron. Therefore, uniform sampling needs to be performed within the polyhedron to obtain new , and then solve the optimization problem to obtain the optimal integer solution, thereby obtaining a new set of data . Generally speaking, sampling in a low-dimensional convex polyhedron can use the reject sampling method. However, when the dimension of the convex polyhedron is too high, the efficiency of the reject sampling method is extremely low.

[0068] Therefore, the algorithm adopts a more advanced hit-and-run (HAR) sampling method in Markov Chain Monte Carlo (MCMC) sampling method. This method aims to construct a Markov chain whose stationary distribution matches the target distribution, so as to efficiently explore the high-dimensional space. The steps of this sampling method are as follows: first, select an arbitrary point in the target distribution; then, randomly select a direction from the unit hyper-sphere (the same spatial dimension as the target distribution); finally, take the intersection of the direction and the polyhedron, and randomly select a new sampling point in the line segment formed by the intersection. Repeat this step to obtain multiple sampling points. The convex polyhedron is composed of multiple subspaces, and each subspace corresponds to the traffic state of a complete road section, that is, each subspace is composed of the state combination of multiple sub-road sections contained in the target road section of the highway.

[0069] This sampling method has the possibility of reaching any position in the polyhedron in a single operation, and as the number of samplings increases, the sampling points will gradually cover all the state space.

[0070] In step S2, based on the K-nearest neighbor algorithm, a plurality of tuples most similar to the current segmented affine model state are selected from the built data set, the corresponding optimal integer solution is extracted, and a set of potential integer solutions is determined; according to the set of potential integer solutions, the corresponding logical constraints in the hybrid model predictive control problem are removed, and a reduced optimization problem is generated; the current control input is determined by solving the optimization problem, and the obtained control input is applied to the segmented affine model. Wherein, the congestion degree corresponding to the traffic density contained in each tuple, that is, the discrete congestion degree value of the future corresponding sub-road section under the optimal control condition.

[0071] 1) Given the data set , the model of the current state of the optimization problem , and select the hyperparameter K;

[0072] 2) Let , find K nearest neighbors from the data set , the distance metric uses Euclidean distance, so as to obtain K tuples ; wherein each tuple contains a traffic density value and a discrete congestion degree corresponding thereto.

[0073] 3) Let represent the sum of the optimal integer solutions of the K nearest neighbors. The sum is the "or" operation of each element:

[0074] ;

[0075] Wherein, the subscript represents the matrix ​of the first row of the matrix column. Note that the sum of the elements of each row of the matrix is greater than or equal to 1.

[0076] 4) Select all elements in which the element is 0, these represent the modalities that the model has never been activated in the K neighbors.

[0077] 5) Remove the corresponding logical constraints, that is, remove the three groups of constraints introduced by the Big-M method in step S1-2 through the logical variables and auxiliary variables; from the original optimization problem in step S1-2, obtain the reduced optimization problem. Among them, the logical constraints correspond to the discrete congestion degree situations that will not appear in each future sub-section of the highway target section.

[0078] 6) Solve the reduced optimization problem, if the optimal integer solution is obtained, apply the first item of the optimal sequence to the piecewise affine model; if it is not solvable, solve the original optimization problem, and put the tuple composed of the model state and its optimal integer solution into the data set . Among them, the optimal integer solution represents the discrete congestion degree value of each future sub-section under the optimal control of the highway target section.

[0079] Embodiment Two

[0080] The embodiment discloses a hybrid model predictive control acceleration system for high-dimensional space.

[0081] A hybrid model predictive control acceleration system for high-dimensional space, comprising:

[0082] A data set generation module is configured to: construct a piecewise affine model for describing a highway target section, sample in the state space under the constructed piecewise affine model; and construct a data set by solving a hybrid model predictive control problem for a plurality of state samples obtained by sampling; wherein the state sample is traffic density.

[0083] An optimization problem scale reduction module is configured to: select a plurality of tuples most similar to the current piecewise affine model state from the constructed data set based on a K-nearest neighbor algorithm, extract corresponding optimal integer solutions and determine a set of potential integer solutions; wherein each tuple contains a traffic density value and a discrete congestion degree corresponding thereto; remove the corresponding logical constraints in the hybrid model predictive control problem according to the set of potential integer solutions, generate a reduced optimization problem; determine the current control input by solving the optimization problem, and apply the obtained control input to the piecewise affine model.

[0084] Embodiment Three

[0085] An object of the embodiment is to provide a computer-readable storage medium.

[0086] A computer-readable storage medium having stored thereon a computer program which, when executed by a processor, implements the steps of the method for accelerating a hybrid model predictive control oriented to a high-dimensional space according to any one of the preceding embodiments.

[0087] Embodiment Four

[0088] An object of the embodiment is to provide an electronic device.

[0089] An electronic device comprising a memory, a processor, and a program stored in the memory and executable on the processor, wherein the processor implements the steps of the method for accelerating a hybrid model predictive control oriented to a high-dimensional space according to any one of the preceding embodiments when executing the program.

[0090] The steps involved in the devices of the above embodiments two, three and four correspond to the method of embodiment one, and the specific embodiments can be seen from the relevant description of embodiment one. The term "computer-readable storage medium" should be understood as including a single medium or multiple media of one or more instruction sets; it should also be understood as including any medium capable of storing, encoding or carrying a set of instructions for execution by a processor and causing the processor to perform any one of the methods of the present application.

[0091] Those skilled in the art should understand that each module or step of the present application described above can be implemented by a general-purpose computer device, alternatively, they can be implemented by program codes executable by a computing device, so that they can be stored in a storage device for execution by a computing device, or they can be made into individual integrated circuit modules, or a plurality of modules or steps among them can be made into a single integrated circuit module. The present application is not limited to any specific combination of hardware and software.

[0092] Although the specific embodiments of the present application are described above in combination with the accompanying drawings, it is not a limitation on the scope of protection of the present application, and those skilled in the art should understand that various modifications or variations made by those skilled in the art on the basis of the technical solutions of the present application without creative labor are still within the scope of protection of the present application.

Claims

1. A method for accelerating predictive control of hybrid models in high-dimensional spaces, characterized in that, include: A piecewise affine model is constructed to describe the target road segment of a highway. Sampling is performed within the state space of the constructed piecewise affine model, including: uniform sampling within the convex polyhedron formed by the state space of the piecewise affine model using the Markov Monte Carlo sampling method; wherein, the state space of the piecewise affine model corresponds to the traffic state within each sub-segment of the target road segment of the highway; a dataset is constructed by solving the hybrid model predictive control problem on multiple sampled state samples; wherein, the state sample is traffic density. The implementation of the Markov Monte Carlo sampling method includes: selecting any point within the target distribution from the convex polyhedron, and randomly selecting a direction from the unit hypersphere; taking the intersection point of the direction and the convex polyhedron, and randomly selecting a new sampling point from the line segment formed by the intersection point; wherein, the convex polyhedron is composed of multiple subspaces, each subspace corresponding to the traffic state of a complete road segment, that is, each subspace is composed of the state of multiple sub-segments included in the highway target road segment; Based on the K-nearest neighbor algorithm, multiple tuples that are most similar to the current piecewise affine model state are selected from the constructed dataset, the corresponding optimal integer solutions are extracted, and the potential integer solution set is determined; where each tuple contains a traffic density value and a corresponding discrete degree of congestion; Based on the set of potential integer solutions, the corresponding logical constraints in the hybrid model predictive control problem are removed to generate a reduced optimization problem; wherein, removing the corresponding logical constraints in the hybrid model predictive control problem includes: selecting multiple nearest neighbor modes from the set of potential integer solutions that have never been activated, and removing the logical constraints corresponding to these modes; wherein, the logical constraints correspond to discrete congestion levels that will not occur in each sub-segment of the target highway segment in the future; The current control input is determined by solving this optimization problem, and the obtained control input is applied to the piecewise affine model. That is, when solving the reduced optimization problem, if the optimal integer solution is obtained, the first term of the sequence in the optimal integer solution is applied to the piecewise affine model; if the reduced optimization problem is unsolvable, the optimization problem before reduction is solved, and the tuple consisting of the model state and the corresponding optimal integer solution is placed into the dataset; wherein, the optimal integer solution represents the discrete congestion level value of each sub-segment in the future under the optimal control condition of the target road segment of the highway.

2. The method for accelerating predictive control of hybrid models in high-dimensional spaces as described in claim 1, characterized in that, The unit hypersphere has the same spatial dimension as the target distribution.

3. A hybrid model predictive control acceleration system for high-dimensional spaces, employing the hybrid model predictive control acceleration method as described in any one of claims 1-2, characterized in that, include: The dataset generation module is configured to: construct a piecewise affine model to describe the target road segment of the highway; sample within the state space of the constructed piecewise affine model; and construct a dataset by solving a hybrid model predictive control problem on multiple sampled state samples; wherein the state sample is traffic density. The optimization problem size reduction module is configured to: select multiple tuples from the established dataset that are most similar to the current piecewise affine model state based on the K-nearest neighbor algorithm, extract the corresponding optimal integer solutions, and determine the potential integer solution set; wherein, each tuple contains a traffic density value and a corresponding discrete congestion degree; according to the potential integer solution set, remove the corresponding logical constraints in the hybrid model predictive control problem to generate the reduced optimization problem; determine the current control input by solving the optimization problem, and apply the obtained control input to the piecewise affine model.

4. A computer-readable storage medium having a program stored thereon, characterized in that, When executed by the processor, the program implements the steps of the hybrid model predictive control acceleration method for high-dimensional space as described in any one of claims 1-2.

5. An electronic device, comprising a memory, a processor, and a program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps in the hybrid model predictive control acceleration method for high-dimensional space as described in any one of claims 1-2.

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