Magnetic levitation vehicle nonlinear predictive control method and device based on PINN and medium

Abstract

The application discloses a magnetic levitation vehicle nonlinear prediction control method and device based on PINN and a medium, relates to the field of rail transit, and comprises the following steps: S1, constructing a dynamic model; S2, learning and approximating unknown dynamics and time-varying parameters in the dynamic model by using a physical information neural network; S3, designing an optimization cost function meeting input and output constraints of the system based on unknown dynamics of the dynamic model predicted by the physical information neural network; and S4, constructing a step-variable terminal constraint set to process input time delay. In the controller design and theoretical analysis process, the nonlinear dynamics form of the system is completely reserved, and a step-variable terminal constraint set suitable for input time delay is constructed, so that the controller can still maintain stability and dynamic performance in the case that the system state deviates from the equilibrium point significantly. The method effectively improves the running safety and control precision of the magnetic levitation vehicle in the face of complex working conditions such as parameter drift and time delay disturbance.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of rail transit technology, in particular to a control or regulation system, and specifically to a maglev vehicle nonlinear predictive control method based on PINN, equipment and medium. BACKGROUND

[0002] As an important development direction of future intelligent transportation, maglev vehicles have broad application prospects in urban rail transit and high-speed transportation due to their advantages such as contactless operation, low noise, and strong climbing ability. One of the core technologies is the electromagnetic suspension (EMS) system, which achieves vehicle suspension through electromagnetic force between electromagnets and the track, and needs to maintain stability within a very small suspension gap of 0-20 mm, which is extremely sensitive to external disturbances such as track irregularities and load changes.

[0003] However, the suspension system has strong nonlinear dynamic characteristics (such as the inverse square relationship between electromagnetic force and suspension gap), and during long-term service, the electromagnetic parameters (such as coil turns and magnetic pole area) will drift due to temperature fluctuations and material aging, resulting in unmodeled dynamics and parameter uncertainties in the system model. Traditional control methods that rely on accurate mathematical models (such as PID control and linear state feedback) cannot guarantee stability under complex conditions. Therefore, it is important to consider both unmodeled dynamics of the electromagnetic suspension system and input time delay caused by electromagnetic iron partial failure to ensure the safety of maglev vehicles in complex environments.

[0004] A maglev train suspension control method, device and storage medium are disclosed in Chinese patent CN118418746A, which constructs a track irregularity model and combines a tube-based model predictive control algorithm to output optimal current to adjust the suspension gap, thereby effectively improving the robustness of the system to random track irregularities. However, electromagnetic iron partial failure is a common abnormal condition in maglev train suspension systems, and current control methods mostly ignore the input time delay problem caused by electromagnetic iron partial failure, thereby reducing the accuracy of model-based control algorithms and worsening the dynamic tracking performance of the system, leading to suspension gap oscillation or control instability. SUMMARY

[0005] The present application overcomes the shortcomings of the prior art and provides a maglev vehicle nonlinear predictive control method based on PINN, equipment and medium.

[0006] To achieve the above-mentioned purpose, the technical solution adopted by the present application is as follows: In a first aspect, the present application provides a maglev vehicle nonlinear predictive control method based on PINN, comprising the following steps:

[0007] S1, constructing a dynamic model of the electromagnetic suspension system of the maglev vehicle;

[0008] S2, learning and approaching unknown dynamics and time-varying parameters in the dynamic model online by using a physical information neural network;

[0009] S3, designing an optimization cost function satisfying system input and output constraints based on unknown dynamics of the dynamic model predicted by the physical information neural network;

[0010] S4, constructing a step-by-step variable terminal constraint set to process input time delay to ensure the satisfaction degree of system state constraints and closed-loop stability.

[0011] In one preferred embodiment of the present application, in the step of S1, the dynamic model is constructed based on Newton's second law, and the equation is:

[0012]

[0013] wherein, , is the acceleration of gravity, is a time-varying external disturbance acting on the suspension system, including disturbance forces introduced by track irregularities or changes in vehicle load, is the mass of the single-point suspension system, is a time-varying parameter of the system, is the suspension gap between the electromagnet and the track, is the current passing through the suspension electromagnet coil.

[0014] In one preferred embodiment of the present application, in the step of S2, the training loss function of the physical information neural network includes a data fitting term and a physical loss term, and the physical loss term is realized by introducing system physical equation constraints, and the loss function expression is:

[0015]

[0016] wherein, is the data fitting term, is the physical loss term, is a weight parameter.

[0017] In one preferred embodiment of the present application, in the step of S2, after learning by the physical information neural network, the system dynamic model is discretized as:

[0018]

[0019] wherein, is the suspension gap state at the discrete time index k, is the current passing through the suspension electromagnet coil at time k, and the function characterizes the suspension gap ​​​and control input current The nonlinear relationship between them, where This is a discrete-time index.

[0020] In a preferred embodiment of the present invention, in step S3, the optimization cost function is defined as a quadratic function that includes the state tracking error in the prediction time domain and the control input energy consumption, and satisfies the feasible region constraints of the levitation gap and the control current, and its expression is:

[0021] ;

[0022] in, It predicts the time domain. Is The time step is predicted based on the discrete dynamics model. The predicted state of the time-lapse gap. It is the first The ideal state of the suspension gap at all times, It is the first Predicting and optimizing inputs at specific times. It is a positive definite weight matrix. P acts on the state tracking error term, Q acts on the control input term, and R acts on the terminal state term. Quadratic form operations are performed on the vectors within the parentheses. T is the matrix transpose symbol. This indicates a constraint condition, meaning the optimization problem must be solved within the feasible region constraints that satisfy the state variables and control inputs.

[0023] In a preferred embodiment of the present invention, the feasible region constraint includes: the suspension gap satisfies x min ≤ x ≤ x max The control current satisfies u min ≤ u ≤ u max .

[0024] In a preferred embodiment of the present invention, in step S4, the step-type variable terminal constraint set is an elliptic set. ,in, Represents the system state space; It is a weighted quadratic norm; c This represents the boundary constant that is dynamically adjusted based on the system's time delay characteristics, and satisfies the condition of the closed-loop system under the input time delay. Step-invariant set condition.

[0025] In a preferred embodiment of the present invention, the boundary constant of the elliptic set cThe spectral radius upper bound of the system matrix, the maximum value of input time delay and the dynamic adjustment of control input coefficient are used.

[0026] In a second aspect, the present application provides an electronic device, comprising: at least one processor and a memory connected in communication with the at least one processor;

[0027] The memory stores a computer program executed by the at least one processor, and the computer program is executed by the at least one processor to enable the at least one processor to perform the PINN-based maglev vehicle nonlinear predictive control method of any one of the above.

[0028] In a third aspect, the present application provides a computer readable storage medium storing computer instructions for enabling a processor to perform the PINN-based maglev vehicle nonlinear predictive control method of any one of the above when executed by the processor.

[0029] The present application solves the defects in the background art and has the following beneficial effects:

[0030] (1) The present application provides a PINN-based maglev vehicle nonlinear predictive control method, device and medium, which uses a physical information neural network to learn unknown parameters and structures of a maglev vehicle suspension system online, and embeds physical laws into the neural network training process so that the model can not only learn from data, but also strictly comply with system physical constraints, effectively improving data utilization efficiency, model generalization ability and prediction rationality. Compared with traditional data-driven neural network modeling methods, the present application effectively solves the defect of insufficient physical consistency, thereby further enhancing the adaptability of the controller under parameter perturbation and unmodeled dynamics.

[0031] (2) In the present application, a step-by-step variable terminal constraint set is designed to solve the input time delay problem caused by the partial failure of electromagnets. The constraint set can dynamically adjust the terminal constraint range according to the system time delay characteristics, thereby effectively ensuring the system state constraint satisfaction degree under the failure of electromagnets. Compared with existing model predictive control methods that ignore time delay or use fixed terminal sets, the proposed method effectively alleviates the state constraint violation problem caused by time delay, thereby ensuring the safe and stable operation of the suspension system under fault conditions.

[0032] (3) In the present application, by completely retaining the complete nonlinear dynamics form of the electromagnetic suspension system, the linearization approximation near the equilibrium point is avoided, so that the controller fully considers the real dynamic characteristics of the system in the design stage, and then the system state deviates from the equilibrium working point due to external disturbance or internal fault, and the controller still has stable tracking ability. Compared with the existing model predictive control method based on linearization model, the present application effectively overcomes the problem of control performance degradation caused by model mismatch, thereby improving the reliability and stability of the suspension control in the unbalanced state. BRIEF DESCRIPTION OF DRAWINGS

[0033] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed to be used in the embodiments or prior art description will be briefly introduced as follows. Obviously, the drawings in the following description are only some embodiments described in the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0034] Figure 1 is the loss function change diagram of PINN training of the present application embodiment 1;

[0035] Figure 2 is the system response diagram under static suspension of the present application embodiment 1;

[0036] Figure 3 is the system response diagram under random external disturbance of the present application embodiment 1;

[0037] Figure 4 The structure of the electronic device that can be used to implement the present application embodiment 1 is shown. DETAILED DESCRIPTION

[0038] The technical solutions in the embodiments of the present application will be described clearly and completely in the following description of the embodiments of the present application, obviously, the described embodiments are only some of the embodiments of the present application, not all. Based on the embodiments of the present application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the present application.

[0039] In the following description, many specific details are set forth in order to provide a thorough understanding of the present application, but the present application can also be implemented in other ways different from those described herein, therefore, the scope of protection of the present application is not limited by the specific embodiments disclosed below.

[0040] SUMMARY

[0041] In recent years, intelligent learning algorithms have been widely applied in nonlinear system control, such as neural networks, fuzzy logic and reinforcement learning methods are introduced to deal with system model uncertainty. Among them, neural networks show potential in system identification and adaptive control due to their highly parallel structure and fast convergence ability. However, traditional neural network methods rely heavily on a large amount of training data, and often lack embedding of the physical law of the system, resulting in difficulty in ensuring physical consistency and limited generalization ability in actual control. Therefore, the physical information neural network (PINN) is proposed, which significantly improves the data utilization efficiency and prediction rationality by introducing physical equations as constraints during training, and becomes a new way to solve the modeling and control problems of nonlinear systems.

[0042] Although intelligent algorithms such as PINN provide a new way to solve model uncertainty, and model predictive control (MPC) is widely used in maglev control because it can explicitly handle constraints, but traditional MPC needs to linearize the strong nonlinear dynamics of the electromagnetic suspension system at the equilibrium point, and design the controller through the approximate linear model. When the vehicle accelerates, brakes or encounters strong disturbances (such as sudden changes in track structure), the system state may deviate significantly from the equilibrium point, at which time the error between the linearized model and the actual nonlinear dynamics will accumulate rapidly, resulting in a decrease in control accuracy, a delay in dynamic response, and even causing suspension gap oscillation. Especially in the case of partial failure of electromagnets and input time delay, the linearized model cannot accurately reflect the real dynamic evolution of the system, further reducing the phase margin of the linearized MPC and increasing the risk of system instability.

[0043] To solve the above problems, the present application proposes a PINN-based nonlinear predictive control method for maglev vehicles, which retains the complete nonlinear dynamics of the system during controller design and theoretical analysis, avoids linearization approximation at the equilibrium point, and combines PINN to learn unknown dynamics and parameters of the dynamic model online, and designs a step-by-step variable terminal constraint set that adapts to input time delay. This method can ensure that the controller remains stable and dynamic performance even when the system state deviates significantly from the equilibrium point, effectively improving the running safety and control accuracy of maglev vehicles under complex working conditions such as parameter drift and time delay disturbance.

[0044] Embodiment 1: A PINN-based nonlinear predictive control method for maglev vehicles, comprising the following steps:

[0045] S1, constructing a dynamic model of the electromagnetic suspension system of the maglev vehicle;

[0046] S2, using a physical information neural network to learn and approximate unknown dynamics and time-varying parameters in the dynamic model online;

[0047] S3, unknown dynamics of the physics-informed neural network predicted dynamics model are designed to meet the optimization cost function that satisfies the system input and output constraints;

[0048] S4, a step-by-step variable terminal constraint set is constructed to process the input time delay to ensure the satisfaction of the system state constraint and the closed-loop stability.

[0049] In some specific embodiments, in the step of S1, the EMS type maglev train suspension system is a complex multi-point coupled system; the decoupling can be used to decompose the suspension system control problem into a single suspension magnet control problem by adopting the decentralized independent suspension control strategy and the magnet structure modularization idea.

[0050] According to Newton's second law, the dynamics equation of the electromagnet in the vertical direction is:

[0051] ;

[0052] wherein, , is the acceleration of gravity, is the time-varying external disturbance acting on the suspension system, including the disturbance force introduced by the track irregularity or the change of the vehicle load, is the mass of the single-point suspension system, is the time-varying parameter of the system, is the suspension gap between the electromagnet and the track, is the current passing through the suspension electromagnet coil.

[0053] In some specific embodiments, in the step of S2, the system parameters of the maglev train cannot be accurately obtained in general. And during the operation, the irregularity of the track and the change of the number of passengers will further change the value of , causing the uncertainty of the suspension system model, which will lead to the fact that the controller designed based on the dynamics model of the electromagnetic suspension system cannot ensure the asymptotic stability of the magnetic suspension system, and even may endanger the reliability of the suspension control. In order to improve the suspension control precision and ensure the smooth operation of the maglev train in complex environment, PINN is used to update the suspension system parameters online.

[0054] Further, in order to ensure that the fitting error of the system parameters is minimum, the following loss cost function is designed:

[0055] ;

[0056] wherein, is the data fitting term, is the physical loss term, is the weight parameter, and and The following definitions apply:

[0057] ;

[0058] ;

[0059] wherein, is the number of samples, is the number of sampling points in the physical domain, is the discrete time index, is the predicted output of the neural network under input , is the actual output of the physical system under input , represents the physical information loss variance, which can be expressed as:

[0060] ;

[0061] wherein, is the predicted parameter value of the PINN, f d is the physical equation residual term.

[0062] The weight parameter is in the range of [0.1, 1.0].

[0063] Further, after discretizing the system, the discrete dynamic equation is obtained:

[0064] ;

[0065] wherein, is the levitation gap state at discrete time index k, is the current passing through the electromagnetic coil of the levitation electromagnet at time k, the function characterizes the nonlinear relationship between the levitation gap and the control input current , wherein is the discrete time index.

[0066] In some specific embodiments, in the step of S3, considering the system input and output constraints, an optimization cost function is designed;

[0067] Specifically, MPC is an iterative control strategy that estimates the current state and obtains the optimal input vector by minimizing the cost function and satisfying the constraint conditions. For the discrete system model learned based on PINN obtained in the step of S2, the optimization cost function is defined as:

[0068] ;

[0069] wherein, is the prediction horizon, is the prediction horizon, is the predicted state of the levitation gap at time is the predicted state of the levitation gap at time is the ideal state of the levitation gap at time is the ideal state of the levitation gap at time is the predicted optimal input at time is the predicted optimal input at time is a positive definite weight matrix, P acts on the state tracking error term, Q acts on the control input term, R acts on the terminal state term, the quadratic form is performed on the vectors in the parentheses, T is the matrix transpose symbol, denotes the constraint condition, i.e. the optimization problem needs to be solved under the constraints of the feasible region of the state variable and the control input.

[0070] It can be understood that the constraint condition is specifically embodied as: denotes that the levitation gap (state variable) needs to satisfy x min ≤ x ≤ x max , to ensure that the vehicle is not in contact with the track and avoid levitation failure; denotes that the control current (input variable) needs to satisfy u min ≤ u ≤ u max , to prevent the coil from being burned out by too large current or levitation force from being insufficient due to too small current.

[0071] Further, based on the physical loss term and the physical information loss variance, the optimization cost function can be rewritten as a nonlinear programming convex problem:

[0072] ;

[0073] wherein, represents a non-convex optimization function.

[0074] It can be understood that for the discrete dynamic model obtained in the S2 step, a positive invariant set can usually be constructed to ensure that the system state trajectory converges after a finite step iteration and is always located within the set. However, when the system has input time delay, the time delay effect will destroy the synchronization between the system state and the controller output, so that the existence condition of the traditional invariant set is no longer established.

[0075] In some specific embodiments, in the step of S4, considering the system input time delay, a variable terminal constraint set is designed to ensure that the state constraint satisfaction degree under the partial failure of the electromagnet is met;

[0076] Specifically, for the discrete system model based on PINN learning obtained in step S2, it is assumed that there exists an elliptic set. Make Satisfy; among them, express n A real vector space, corresponding to the dimension of the system state; It is a weighted quadratic norm; c It represents a positive constant, defines the boundary size of the elliptic set, and determines the maximum allowable deviation range of the state.

[0077] If the matrix power norm inequality An elliptical domain with an origin is defined as a terminal constraint elliptic set. ;

[0078] Make It is the following closed-loop system Step-invariant set: ;

[0079] in, If it is a unitary matrix, then yes Schur decomposition, It is a diagonal matrix. It is a strictly upper triangular matrix; It is a relaxation parameter. ; Denotes the Frobenius norm of a matrix; It is the upper bound of the spectral radius; It is a system matrix used to describe the dynamic characteristics of a closed-loop system containing faults or disturbances. , A It is the nominal system matrix. B It is the input matrix. It is an external disturbance / modeling error. It is the input delay of the levitation system, and it meets the condition. , Input delay The maximum value; yes k - d The control input vector at each time step; yes k The system state vector at time t, i.e., the current state; c It is the boundary constant of the original elliptic set; These are the adjusted constraint constants; It controls the input coefficient; It is the smallest eigenvalue.

[0080] To further make the purposes and effects of the present application simple and easy to understand, the above control method is applied to the electromagnetic suspension module of the maglev vehicle, system parameters and simulation initial values are configured, a traditional MPC control method is selected for comparison, and the following three groups of simulations are performed in MATLAB / Simulink: model identification, static suspension and time-varying external disturbance.

[0081] Figure 1 is a loss function change graph of PINN training. In the simulation, with the increase of the number of training iterations, the standard deviation of the prediction error presents a gradual convergence trend, which verifies that the constructed PINN learner can effectively identify the unknown dynamics / parameters of the dynamic model and realize good parameter approximation performance. Figure 2 is a system response graph under static suspension. It can be known from the result that, in the case that the system has input time delay, the traditional MPC method will cause the system response to have obvious overshoot phenomenon, and the dynamic response speed of the system is reduced and the regulation time is significantly increased. In comparison, the proposed control method can effectively improve the dynamic performance of the system. Figure 2 Figure 3 is a system response graph under random external disturbance. It can be known from the result that, under the action of random external disturbance, the traditional MPC method has great dynamic fluctuation and significant steady-state suspension error. In comparison, the proposed control method has more stable system dynamic response and lower system energy consumption. The simulation results show that the design scheme of the present application has better performance than the traditional MPC control in static suspension and resisting time-varying external disturbance and the like.

[0082] wherein, in Figure 2 and Figure 3 , PINMPC represents a model predictive control method based on a physical information neural network (PINN), that is, the control algorithm proposed in the present application; MPC represents a traditional linearized model predictive control method.

[0083] Embodiment 2: Figure 4 shows an electronic device structure schematic diagram that can be used to implement Embodiment 1 of the present application. The electronic device 10 is intended to represent various forms of digital computers, such as laptops, desktops, workstations, personal digital assistants, servers, blade servers, mainframes, and other appropriate computers. The electronic device can also represent various forms of mobile devices, such as personal digital processors, cellular telephones, smart phones, wearable devices (such as helmets, glasses, watches, etc.), and other similar computing devices. The components shown herein, their connections and relationships, and their functions, are meant to be examples only, and are not intended to limit the implementations of the present application described and / or claimed in this document.

[0084] As Figure 4 ​As shown, the electronic device 10 includes at least one processor 11, and a memory, such as a Read-Only Memory (ROM) 12, a Random Access Memory (RAM) 13, etc., connected to the at least one processor 11 in communication. The memory stores a computer program executable by the at least one processor 11, and the computer program is executed by the at least one processor 11 to enable the at least one processor 11 to perform the method provided by the present application.

[0085] Further, the processor 11 can perform various appropriate actions and processes according to a computer program stored in the Read-Only Memory (ROM) 12 or a computer program loaded from the storage unit 18 into the Random Access Memory (RAM) 13. Various programs and data required for the operation of the electronic device 10 can also be stored in the RAM 13. The processor 11, the ROM 12, and the RAM 13 are connected to each other through a bus 14. An input / output (I / O) interface 15 is also connected to the bus 14.

[0086] Various components in the electronic device 10 are connected to the I / O interface 15, including an input unit 16, such as a keyboard, a mouse, etc., an output unit 17, such as various types of displays, a loudspeaker, etc., a storage unit 18, such as a magnetic disk, an optical disk, etc., and a communication unit 19, such as a network card, a modem, a wireless communication transceiver, etc. The communication unit 19 allows the electronic device 10 to exchange information / data with other devices through a computer network, such as the Internet, and / or various telecommunication networks.

[0087] Further, the processor 11 can be various general and / or special purpose processing components with processing and computing capabilities. Some examples of the processor 11 include, but are not limited to, a Central Processing Unit (CPU), a Graphics Processing Unit (GPU), various special-purpose Artificial Intelligence (AI) computing chips, various processors running machine learning model algorithms, a Digital Signal Process (DSP), and any appropriate processor, controller, microcontroller, etc. The processor 11 performs various methods and processes described above, such as the method of resource management for a database.

[0088] In some particular embodiments, the method of resource management of a database can be implemented as a computer program tangibly embodied in a computer readable storage medium, such as the storage unit 18. In some embodiments, parts or all of the computer program can be loaded onto the electronic device 10 via the ROM 12 and / or the communication unit 19. When the computer program is loaded onto the RAM 13 and executed by the processor 11, one or more steps of the method of resource management of a database described above can be performed. Alternatively, in other embodiments, the processor 11 can be configured to perform the method of resource management of a database by any other suitable means, for example by means of firmware.

[0089] Various implementations of the systems and techniques described above can be realized in digital electronic circuitry, integrated circuitry, a Field Programmable Gate Array (FPGA), an Application Specific Integrated Circuit (ASIC), a System on Chip (SOC), a Complex Programmable logic device (CPLD), computer hardware, firmware, software, and / or combinations thereof. These various implementations can include implementation in one or more computer programs that are executable and / or interpretable on a programmable system including at least one programmable processor, which can be special or general purpose, coupled to receive data and instructions from, and to transmit data and instructions to, a storage system, at least one input device, and at least one output device.

[0090] Computer programs used to implement the present methods can be written in any combination of one or more programming languages. These computer programs can be provided to a processor of a general purpose computer, special purpose computer, or other programmable data processing apparatus to produce a machine, such that the computer program running on the processor implements the functions / operations specified in the flowcharts and / or the block diagrams. The computer program can be executed entirely on a machine, partially on a machine, partially on a machine as part of a standalone software package, or entirely on a remote machine or server.

[0091] In the context of the present application, the computer readable storage medium stores computer instructions for causing a processor to implement the method of resource management of a database provided by the present application when executed. The computer readable storage medium can be a tangible medium which can contain or store the computer program for use by or in connection with an instruction execution system, apparatus, or device. The computer readable storage medium can include, but is not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any suitable combination of the foregoing. Alternatively, the computer readable storage medium can be a machine readable signal medium. More specific examples of the machine readable storage medium will include one or more lines of electrical connections, portable computer disks, hard disk drives, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or Flash memory), optical fibers, portable compact disc read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination of the foregoing.

[0092] To provide for interaction with a user, the systems and techniques described here can be implemented on an electronic device having a display device (e.g., a Cathode Ray Tube (CRT) or a Liquid Crystal Display (LCD) monitor) for displaying information to the user and a keyboard and a pointing device (e.g., a mouse or a trackball) by which the user can provide input to the electronic device. Other kinds of devices can be used to provide for interaction with a user as well; for example, feedback provided to the user can be any form of sensory feedback (e.g., visual feedback, auditory feedback, or tactile feedback); and input from the user can be received in any form, including acoustic, speech, or tactile input.

[0093] The systems and techniques described herein can be implemented in a computing system that includes a back end component (e.g., as a data server), or that includes a middleware component (e.g., an application server), or that includes a front end component (e.g., a user computer having a graphical user interface or a Web browser through which a user can interact with an implementation of the systems and techniques described herein), or any combination of such back end, middleware, or front end components. The components of the system can be interconnected by any form or medium of digital data communication (e.g., a communication network). Examples of communication networks include a local area network (LAN), a wide area network (WAN), the Internet, and a blockchain network.

[0094] Optionally, the computing system can include clients and servers. A client and server are generally remote from each other and typically interact through a communication network. The relationship of client and server arises by virtue of computer programs running on the respective computers and having a client-server relationship to each other. A server can be a cloud server, also known as a cloud computing server or cloud host, which is a host product in the cloud computing service system, to solve the defects of large management difficulty and weak business scalability in traditional physical host and virtual private server (VPS) services.

[0095] In light of the above, it should be appreciated that many modifications and variations to exemplary embodiments of the present application are possible in light of the above teachings. It is, therefore, to be understood that within the scope of the present application there is a full equivalency of all features between the claims and the specification. Moreover, any combination of the above-described elements in all possible variations thereof is encompassed by the application unless otherwise indicated herein or otherwise clearly contradicted by context.

[0096] Furthermore, it should be appreciated that a singular element of the present application can be implemented in a variety of ways and the examples described herein are merely representative of such. The present application should be given the broadest interpretation consistent with the principles of the application as set forth in the following claims.

Claims

1. A method for nonlinear predictive control of maglev vehicles based on PINN, characterized in that, The method comprises the following steps: S1, constructing a dynamic model of an electromagnetic suspension system of a maglev vehicle; S2, using a physical information neural network to learn and approximate unknown dynamics and time-varying parameters in the dynamic model online; S3, based on the unknown dynamics of the dynamic model predicted by the physical information neural network, designing an optimization cost function that meets the constraints of system input and output; S4, constructing a step-by-step variable terminal constraint set to process input time delay, so as to guarantee the satisfaction degree of system state constraints and closed-loop stability; In the step S1, the dynamic model of the single electromagnet suspension system is constructed based on Newton's second law, and the equation is: ； wherein, , is the gravitational acceleration, is the time-varying external disturbance acting on the levitation system, including disturbance forces introduced by track irregularities or vehicle load variations, is the mass of the single-point levitation system, is the time-varying parameter of the system, is the levitation gap between the electromagnet and the track, is the current through the electromagnetic coil of the levitation electromagnet; In the step S2, the training loss function of the physical information neural network includes a data fitting term and a physical loss term, and the physical loss term is realized by introducing a system physical equation constraint, and the loss function expression is: ; wherein, is a data fitting term, is a physical loss term, is a weight parameter; After learning by the physical information neural network, the system dynamic model is discretized as: ; where is a discrete time index is the levitation gap state at time is is the current through the levitation electromagnet coil at time characterizes the non-linear relationship between the levitation gap and the control input current where is a discrete time index.

2. The PINN-based maglev vehicle nonlinear predictive control method according to claim 1, characterized in that: In the step S3, the optimization cost function is defined as a quadratic function containing state tracking error and control input energy consumption in the prediction time domain, and meets the feasible region constraints of suspension gap and control current, and the expression is: ； in, It predicts the time domain. Is The time at which the discrete dynamics model predicts the first... The predicted state of the time-lapse gap. It is the first The ideal state of the suspension gap at all times, It is the first Predicting and optimizing inputs at specific times. It is a positive definite weight matrix. It applies to the state tracking error term. Acts on control input items, This operation is applied to the terminal state item, performing a quadratic form operation on the vector within the parentheses. T It is the matrix transpose symbol. This indicates the constraints, meaning the optimization problem must be solved within the feasible region constraints that satisfy the state variables and control inputs; It is a discrete-time index Predicted state of the suspension gap at time t. It is a discrete-time index Predicting and optimizing inputs at specific times.

3. The PINN-based maglev vehicle nonlinear predictive control method of claim 2, wherein: The feasible region constraint includes: the suspension gap satisfies x min ≤ x ≤ x max , the control current satisfies u min ≤ u ≤ u max .

4. The PINN-based maglev vehicle nonlinear predictive control method of claim 1, wherein: In the step of the S4, the step-variable terminal constraint set is an ellipse set wherein, represents a system state space; is a weighted quadratic norm; c represents a boundary constant dynamically adjusted according to a system time delay characteristic, and satisfies a step-invariant set condition of a closed-loop system under an input time delay. step-invariant set condition.

5. The PINN-based maglev vehicle nonlinear predictive control method of claim 4, wherein: The boundary constant of the ellipse set c By the upper bound of the spectral radius of the system matrix, the maximum value of the input delay and the dynamic adjustment of the control input coefficient.

6. An electronic device, comprising: The method comprises: At least one processor and a memory connected in communication with the at least one processor; The memory stores a computer program executed by the at least one processor, and the computer program is executed by the at least one processor to enable the at least one processor to execute the PINN-based nonlinear predictive control method for a maglev vehicle according to any one of claims 1-5.

7. A computer readable storage medium characterized in that, The computer readable storage medium stores computer instructions for enabling the processor to implement the PINN-based nonlinear predictive control method for a maglev vehicle according to any one of claims 1-5 when executed.

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