A confidence embedding model predictive control method, medium and device

Abstract

The application discloses a confidence embedding model predictive control method, medium and equipment, and belongs to the technical field of suspension control. The method establishes a dynamic equation of a suspension system, adopts an uncertainty quantification method driven by data and mechanism, uses original operation data of a maglev train and online measured suspension state information, learns modeling of dynamic characteristics of the suspension system under constraints of the dynamic equation, predicts distribution of state variables such as a suspension air gap, a vertical speed, an electromagnet current and the like at a future time, and obtains corresponding state prediction mean and prediction standard deviation. In model predictive control optimization, a nominal trajectory of the suspension system is constructed by using the predicted state mean, and a penalty term proportional to prediction uncertainty is added in a cost function; meanwhile, a confidence constraint is constructed based on the prediction standard deviation, so that dynamic constraint tightening of key physical variables such as the suspension air gap, the vertical speed and the coil current is realized. The application realizes real-time perception and adaptive closed-loop control of operation risks of the suspension system.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of control of maglev train suspension systems, and in particular to a confidence embedded model predictive control method for a maglev train system, a medium and equipment. BACKGROUND

[0002] Model predictive control (MPC) is an advanced control method based on rolling optimization, which realizes dynamic control and decision-making of the system by solving the optimization problem with constraints in a limited prediction time domain. Traditional MPC usually assumes that the system model is accurate and deterministic, and can obtain good control performance under ideal modeling conditions. However, in actual engineering applications, especially in maglev train suspension systems, the system dynamics often exhibit strong nonlinearity, high coupling, and sensitivity to parameter changes, and are also affected by multiple sources of uncertainty such as track irregularities, aerodynamic load changes, sensor noise, and electromagnetic parameter drift, making it difficult for traditional MPC to guarantee that the suspension gap constraints are met and the control stability under operation.

[0003] To cope with uncertainty, researchers have proposed robust model predictive control (RMPC) methods. There are mainly two implementation ideas for common RMPC: the first is the worst-case robust MPC (Min-Max RMPC), which formulates the optimization problem as "minimizing the maximum cost", that is, the controller still maintains constraint satisfaction under the worst case of all possible disturbances. Its advantages are rigorous theory and strong robustness, but due to the need for nested optimization of disturbances in the prediction domain, the computational complexity is extremely high, making it difficult to meet real-time control requirements; the second is the tube-based RMPC, which decomposes the system state into "nominal trajectory" and "error trajectory" to reduce computational complexity. The nominal trajectory evolves under the undisturbed model and is used for optimization calculation; the error trajectory is constrained within a fixed robust tube (or invariant set) under a given feedback gain. By shrinking the nominal trajectory in the constraint space, the actual state is always within the original constraint range even if it is disturbed. Although this method simplifies the solution process and ensures real-time performance, there are still two main problems:

[0004] (1) The robust tube and disturbance set are usually set by humans or obtained based on system linearization, making it difficult to accurately characterize the complex uncertainties such as track disturbances, aerodynamic loads, and electromagnetic parameter changes in maglev suspension systems;

[0005] (2) The robust tube remains fixed throughout the prediction time domain, making the control strategy conservative and difficult to dynamically adjust to the time-varying characteristics of uncertainty, thereby limiting the improvement of control performance under operating conditions. SUMMARY

[0006] The present application aims to overcome the following problems of conventional model predictive control (MPC) and robust model predictive control (RMPC) in dealing with uncertainties in the levitation system of a maglev train: difficulty in truly reflecting complex uncertainties such as track irregularities, changes in aerodynamic loads, and drifts in electromagnetic parameters, by relying on artificially set disturbance sets or approximate sets obtained based on linearization; high conservativeness of the robust tube, which remains fixed in the entire prediction horizon, and reduction of the dynamic performance of the levitation system; difficulty in dynamically adjusting to time-varying characteristics of uncertainties under operating conditions, and difficulty in balancing control accuracy and safety margin. To this end, the present application proposes a confidence-embedded model predictive control method for the levitation system of a maglev train, based on data-mechanism dual-driven uncertainty quantification, a medium, and equipment, to achieve quantitative characterization of uncertainties in the levitation system, adaptive risk-constrained shrinkage, and high-precision real-time control.

[0007] According to a first aspect of the present application, a confidence-embedded model predictive control method is provided, comprising the following steps:

[0008] (1) establishing a dynamic equation of the levitation system of a maglev train to describe the nonlinear coupling relationship between the levitation air gap, the vertical velocity, the electromagnetic coil current, and the electromagnetic force;

[0009] (2) based on the dynamic equation and multiple sets of state observation data, using a data-mechanism dual-driven uncertainty quantification method, obtaining the predicted mean and predicted standard deviation of the state of the levitation system in the future prediction horizon;

[0010] (3) constructing a confidence-embedded model predictive control optimization problem, wherein: the nominal trajectory of the levitation system is generated based on the predicted mean of the state, and is used for optimization calculation; the uncertainty penalty term is constructed based on the predicted standard deviation of the state, and is used to form dynamic constraint shrinkage based on confidence;

[0011] (4) solving the optimization problem to obtain the optimal levitation control input of the levitation system of a maglev train in the prediction horizon, and applying the first control input to the levitation actuator to realize real-time closed-loop control.

[0012] According to a second aspect of the present application, a computer-readable storage medium is provided, which stores a computer program, wherein the computer program is executed by a processor to implement the steps of the above-mentioned confidence-embedded model predictive control method.

[0013] According to a third aspect of the present application, a computer device is provided, comprising a memory and a processor, and a computer program capable of running on the processor is stored on the memory, wherein the processor implements the steps of the above-mentioned confidence-embedded model predictive control method when executing the computer program.

[0014] Compared with the prior art, the confidence embedded model predictive control method provided by the application directly predicts the state mean value and standard deviation of the suspension system through a data-mechanism dual-driven uncertainty quantification method, avoids the problems of strong dependence of traditional RMPC on a disturbance set and too many modeling assumptions, and constructs a nominal trajectory by using the predicted mean value, which can effectively reduce the deviation caused by model mismatch and improve the control accuracy of the maglev suspension system in a strong nonlinear working condition. The predicted standard deviation is introduced into the target function and the constraint condition at the same time, uncertainty quantification and risk sensitive adjustment are realized, and the controller can flexibly balance between performance optimization and safety confidence. The feasible region is defined by probability constraint dynamics, the geometric conservativeness problem of traditional Tube-based RMPC is avoided, and the constraint is automatically adjusted with the uncertainty. The application obtains the distribution of the system state in the prediction time domain through a networked physical information modeling framework (such as a Bayesian physical information neural network), realizes accurate quantification of uncertainty in a complex working condition, and is particularly suitable for a maglev suspension control scene with time-varying and strong coupling. In summary, the application can effectively balance performance, real-time performance and safety in maglev train suspension control, and has clear engineering application value.

[0015] Other features of the present application, and their advantages, will become apparent in the non-limiting description of the drawings in which: BRIEF DESCRIPTION OF DRAWINGS

[0016] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments of the application and, together with the description, serve to explain the principles of the application.

[0017] Figure 1 is a flow chart of a confidence embedded model predictive control method according to an embodiment of the application;

[0018] Figure 2 is a schematic diagram of a maglev train suspension system structure according to an embodiment of the application;

[0019] Figure 3 is a schematic diagram of a Bayesian physical information neural network modeling framework according to an embodiment of the application. DETAILED DESCRIPTION

[0020] Various exemplary embodiments of the present application will now be described in detail with reference to the accompanying drawings. It should be noted that the relative arrangement of the components and steps set forth in these embodiments, numerical expressions, and numerical values are not limiting to the scope of the present application unless otherwise specifically stated.

[0021] The following description of at least one exemplary embodiment is merely illustrative in nature and is in no way limiting to the scope of the application or its applications or uses.

[0022] Techniques, methods, and apparatus known to those of ordinary skill in the relevant art can not be discussed in detail herein, but should be considered as part of the specification.

[0023] In all of the examples shown and discussed herein, any specific values should be interpreted as merely exemplary and not limiting. Thus, other examples of the exemplary embodiments can have different values.

[0024] It should be noted that like reference numerals and letters in the various figures represent similar items, and thus further discussion of the same will not be repeated.

[0025] At present, the data-mechanism dual-driven uncertainty quantification method (such as Bayesian Physics-Informed Neural Networks (B-PINNs)) can drive network training together with historical data and real-time operation data by taking system dynamics equation as a constraint condition, thereby realizing learning of system dynamics law and quantification of prediction uncertainty, and providing statistical information support for state distribution of subsequent control optimization. Based on this, the confidence embedded model predictive control method proposed in the application introduces an uncertainty information and risk measurement mechanism in the traditional MPC optimization framework. The method uses the state mean value and standard deviation predicted by the uncertainty quantification method to construct dynamic risk constraints and penalty terms, and realizes data-mechanism dual-driven risk adaptive control.

[0026] In the application, the state prediction mean value and prediction standard deviation obtained by the uncertainty quantification method are used to construct dynamic nominal trajectory, probability constraint and uncertainty penalty term respectively, thereby realizing the data-mechanism dual-driven risk adaptive control strategy. Compared with the nominal trajectory obtained by the deterministic nominal model in the traditional robust MPC, the application takes the prediction mean value as the optimization benchmark, so that the optimization result is more consistent with the real running characteristics of the maglev train suspension system, and the control deviation caused by model mismatch can be significantly reduced. At the same time, the prediction standard deviation is used to construct the probability constraint and the dynamic penalty term, so that the controller can adaptively adjust the risk level according to the confidence requirement, and realize the balance between performance and safety.

[0027] Compared with the traditional RMPC, the application has the following advantages: no need to fix the disturbance set and robust tube construction, avoiding conservative geometric constraint assumption; using the prediction mean value instead of the nominal trajectory, improving the prediction accuracy and control flexibility; introducing a dynamic risk trade-off mechanism to realize performance optimization under the premise of guaranteeing confidence safety; having stronger adaptability and data self-learning ability for nonlinear and time-varying systems.

[0028] In a preferred embodiment, the magnetic levitation train suspension system is taken as the controlled object, the Bayesian physics-informed neural network is taken as the data-mechanism dual-driven uncertainty quantification method, and the specific implementation process of the confidence embedded model predictive control method proposed in the application is given. Referring to Figure 1 The confidence embedded model predictive control method of the application mainly includes the following steps.

[0029] 1. System modeling

[0030] Taking the magnetic levitation train suspension system structure of Figure 2 , a nonlinear dynamic model of the magnetic levitation train suspension system is established, the nonlinear relationship between the suspension force and the suspension gap, the number of turns of the electromagnet, the current and other parameters is considered, and the load mass, the number of turns of the electromagnet, the effective cross-sectional area and the like are introduced into the model as uncertain parameters. The constructed dynamic model can reflect the main dynamic characteristics of the suspension system and provide a basis for subsequent controller design. The nonlinear dynamic model can be established in the form of state space, and the state variables include but are not limited to the suspension gap, the speed, the current and the like.

[0031] For example, the discrete dynamic model of a single-point suspension system is constructed as follows:

[0032] (1)

[0033] wherein, is the suspension gap error, is the vertical motion speed of the suspension electromagnet, is the input current increment of the magnetic levitation electromagnet coil, is the system sampling interval time, is the steady-state current size, is the target suspension air gap size, is the load mass of the suspension electromagnet, is the aerodynamic disturbance force, is the differential of the track irregularity, and is the electromagnetic force coefficient.

[0034] 2. Uncertainty modeling

[0035] The uncertainty modeling is based on the data-mechanism dual-driven uncertainty quantification method, the future state of the magnetic levitation train suspension system is predicted, and the prediction mean and prediction standard deviation are obtained to describe the statistical distribution of the system state. The application can adopt various data-mechanism dual-driven uncertainty modeling frameworks, and the Bayesian physics-informed neural network (B-PINNs) is an optional implementation way. The following takes B-PINNs as an exemplary method to describe the uncertainty modeling process, but the application is not limited to this specific form.

[0036] In the construction of B-PINNs, the network usually includes a Bayesian neural network module, a physical information constraint module, and a Bayesian posterior inference module, etc. Among them: the Bayesian neural network module takes the historical state sequence and real-time measurement data of the levitation system as input, and outputs the prediction distribution of state quantities such as levitation air gap, speed, acceleration, and current. Through training combined with observation data, the network parameters form a posterior distribution, thereby characterizing the uncertainty of the prediction result. The physical information constraint module takes the nonlinear dynamics model of the levitation system as a constraint condition, calculates the physical residual between the network output and the dynamics equation, and includes the residual and the observation data in the likelihood function or the loss term. This module ensures that the prediction result conforms to the physical law, and improves the interpretability and reliability of the prediction under strong disturbance and strong nonlinearity. The Bayesian posterior inference module obtains the posterior distribution of the network parameters under the Bayesian framework by combining the prior distribution and the likelihood function constructed based on data and physical residual. By sampling the posterior parameters, the mean, variance or confidence interval of the state prediction can be obtained to reflect the prediction uncertainty of the levitation system.

[0037] The state quantity of the levitation system can be flexibly selected according to the control target, including but not limited to levitation gap, vertical speed, electromagnet coil current, acceleration, etc. Figure 3 The schematic structure of B-PINNs based on the above dynamics model is given, and the network input is the time sequence of system state variables , and the output is the predicted state of the levitation air gap, speed, acceleration, etc. The observation data can include the measurement set of the levitation air gap, current, acceleration, etc. , external disturbance data and boundary condition data , etc. In this framework, the network parameters have a prior distribution , and the posterior distribution is determined by the prior and the likelihood.

[0038] B-PINNs can output state prediction mean and uncertainty quantification results, such as state prediction standard deviation or confidence interval, that satisfy physical consistency under the conditions of noise, measurement error, sparse data, and parameter deviation, thereby providing a basis for subsequent risk measurement and control optimization.

[0039] In the confidence embedded model predictive control method of the application: the state prediction mean is used to generate a future prediction trajectory (i.e. nominal trajectory) to guide optimization calculation; the state prediction standard deviation is used to represent the prediction confidence, which is further used to construct a probability constraint and an uncertainty penalty term, thereby suppressing the prediction variance diffusion in the optimization process and realizing risk adaptive adjustment.

[0040] Finally, the constructed optimization problem is solved by a quadratic programming (QP) or nonlinear programming (NLP) solver to obtain the optimal control sequence in the prediction horizon. The controller adopts a receding horizon strategy, only the first step control input in the optimal sequence is applied to the magnetic levitation electromagnet, and then the optimization is re-executed according to the new state measurement in the next sampling period to realize real-time closed-loop control.

[0041] 3. Designing confidence embedded robust controller

[0042] The data-mechanism dual-driven uncertainty quantification method outputs the mean and standard deviation of the state variable at the next step by fusing the original data set, online measurement data and the nonlinear dynamics equation of the system. The predicted mean obtained by the data-mechanism dual-driven uncertainty quantification method is used as the nominal trajectory, and the state prediction standard deviation is used to construct the penalty term and the constraint condition in the cost function. The control law is solved based on finite time domain optimization to ensure that the suspension gap, electromagnetic force and current, etc. still satisfy the physical constraint conditions under uncertainty.

[0043] Specifically, applying the prediction results output by the data-mechanism dual-driven uncertainty quantification method to the confidence embedded model predictive control method includes:

[0044] 3.1. The state prediction mean obtained by the data-mechanism dual-driven uncertainty quantification method is used as the nominal trajectory, and the stage cost in the cost function of the confidence embedded model predictive control method obtained therefrom is:

[0045] (2)

[0046] Wherein is the state mean at time predicted by the uncertainty quantification method, is the target optimal input. is the state weight matrix, is the input weight matrix. Unlike the traditional robust MPC, which recursively obtains the nominal trajectory by determining the system model to calculate the stage cost, the obtained by the data-mechanism dual-driven uncertainty quantification method is obtained by fusing the original data set, online measurement data and the nonlinear dynamics equation of the system, and has been corrected by data, so as to make up for the model deviation. The state mean is used to replace the nominal trajectory in the traditional robust MPC;

[0047] 3.2. The standard deviation output by the data-mechanism dual-driven uncertainty quantification method is used to describe the uncertainty of the state prediction, so a penalty term is introduced in the cost function of the confidence embedded model predictive control method, which is equivalent to the penalty of the state prediction uncertainty. The penalty term is:

[0048] (3)

[0049] in The trace is a matrix representing the total variance (the sum of the variances of all states) and the coefficients. Control the severity of punishment. The time-based uncertainty quantification method driven by both data and mechanism is used to predict the time. The state covariance at time indicates that the uncertainty of the state is greater and the prediction confidence is lower when the variance is larger. This results in a larger penalty term and more conservative control, while a smaller variance indicates a more aggressive controller. Therefore, the "terminal state penalty" in traditional robust MPC is extended to "penalty for uncertainty across the entire prediction time domain," used for weighted calculation based on the state prediction variance within the prediction time domain.

[0050] 3.3. The data-mechanism dual-driven uncertainty quantification method, based on a combination of historical data, online measurement data, and system dynamics equations, can directly provide the distribution characteristics of future states, including the predicted mean and standard deviation, thereby characterizing the range to which future states may fall. Therefore, in the confidence-embedded model predictive control framework of this invention, there is no need to artificially assume a deterministic set of disturbances; instead, constraints can be constructed using the predicted standard deviation. These constraints can include deterministic and probabilistic forms, used to dynamically adjust the state safety margin and achieve adaptive risk control. The deterministic form is as follows:

[0051] (4)

[0052] in For the constraint direction matrix, To constrain the upper bound. When the system state is one-dimensional, the deterministic form is:

[0053] (5)

[0054] in This is a confidence coefficient, which can be adjusted according to the actual project requirements. It is the state standard deviation predicted by the uncertainty quantification method when the system state is 1-dimensional.

[0055] The probability form is:

[0056] (6)

[0057] That is: at least The probability satisfies the constraint.

[0058] When the system state is one-dimensional, the probability form is:

[0059] (7)

[0060] in The allowed probability of default is used to influence the degree of constraint tightening.

[0061] Constraints based on state distributions are in probabilistic form, allowing constraint definitions to be made within a set range of default probabilities.

[0062] In summary, the final form of the cost function of the proposed confidence embedding model predictive control method is:

[0063] (8)

[0064] in, i It controls the input sequence number. It is the predicted step size. k It is the current moment; k The optimization objective function at time step is ; The uncertainty quantification method predicts the result. The state mean of the step; To predict Step control input; It is the state weight matrix. It is the input weight matrix; The trace is a matrix representing the total variance (the sum of the variances of all states); the coefficients... Control the severity of punishment; For the constraint direction matrix, To constrain the upper bound; The allowed probability of default; To control the input feasible region, s.t Indicates constraints.

[0065] The above optimization problem is solved using a quadratic programming or nonlinear programming solver to obtain the optimal control sequence in the prediction time domain. The controller applies only the first step of the control input to the magnetic levitation electromagnetic coil, and re-executes the optimization based on the new state measurement in the next sampling period to achieve rolling control.

[0066] In summary, the confidence-embedded model predictive control method provided by this invention does not require artificially assumed deterministic perturbation sets. Instead, it utilizes the standard deviation obtained from the data-mechanism dual-drive uncertainty quantification method to construct constraints. Furthermore, it no longer relies on artificially set worst-case perturbation sets, but instead uses the uncertainty distribution obtained from the uncertainty quantification method. Through this uncertainty distribution, a penalty term is introduced into the cost function, and the constraint form is determined.

[0067] 4. Adaptive control based on real-time measurement updates

[0068] In the operation of maglev train suspension system, the system dynamics are influenced by many factors such as environmental temperature changes, vehicle load fluctuations, electromagnetic parameter drifts, and track irregularities, thus showing obvious time-varying characteristics and uncertainties. In order to continuously maintain the accurate characterization of the system state and uncertainties by the controller, the present invention introduces an adaptive control mechanism based on real-time measurement update in the control execution phase, so that the control model and control law can be automatically adjusted with the changes of the system operating state.

[0069] Specifically includes the following steps:

[0070] (1) Real-time measurement data acquisition

[0071] At the end of each sampling period, the system real-time acquires the key state quantities of the suspension module, including the suspension air gap, the electromagnetic coil current, the coil end voltage, and the necessary speed or acceleration measurement data. These real-time measurement data are used to reflect the actual response of the system under the current working condition, and as input information for correcting the model prediction bias.

[0072] (2) Model posterior update (Bayesian physics information neural network online learning)

[0073] After obtaining new observation data, the data-mechanism dual-driven uncertainty quantification model (such as the Bayesian physics information neural network implementation form) used in the present invention inputs the real-time measurement data and the corresponding control input into the model as new incremental samples, and updates the posterior distribution of the network parameters online through the Bayesian backpropagation or variational inference algorithm. After this update step, the model will automatically correct its estimation of the system dynamics according to the latest observation data, so that the mean of the state prediction is closer to the actual evolution process of the system, and the prediction standard deviation more accurately reflects the uncertainty level of the system under the current working condition. Through this online learning mechanism, the present invention can ensure that the uncertainty model remains effective in long-term operation, thus avoiding the problem of gradual performance degradation of traditional fixed model MPC under system parameter drift or external condition changes.

[0074] (3) Dynamic prediction and control law correction

[0075] After the model posterior update is completed, the application regenerates the state distribution information in the next prediction time domain based on the updated model, including the prediction mean and the prediction standard deviation, and automatically corrects the optimization objective and the constraint definition of the control law accordingly. The prediction mean is used to construct the nominal state trajectory of the next time domain, so that the control decision can accurately capture the true evolution trend of the system, while the prediction standard deviation is used to describe the uncertainty level of the system state under different working conditions, and dynamically adjusts the tightening amplitude of the state constraint and the action strength of the uncertainty penalty term. When the prediction standard deviation increases, the controller automatically enhances the safety margin, so that the constraint condition is more conservative to ensure safety; on the contrary, when the prediction standard deviation decreases, the constraint is appropriately relaxed, so that the controller can adopt a more aggressive optimal control strategy to improve performance. Through this dynamic risk adjustment mechanism based on confidence, the application realizes the real-time balance between performance and safety.

[0076] (4) Rolling optimization execution

[0077] Based on the updated prediction results, the controller reconstructs the finite time domain optimization problem in each sampling period, and uses the quadratic programming or nonlinear programming solver to solve the optimal control sequence in the time domain. In the obtained control sequence, the controller only applies the optimal control input at the first time to the suspension electromagnet coil, and the remaining control input will be recalculated according to the updated system state and model information at the next sampling time. With the help of the rolling optimization mechanism of "prediction-optimization-execution-update", the application realizes adaptive closed-loop control in the time-varying environment of the system, so that the controller can continuously maintain the sensitivity and adaptability to the change of complex working conditions.

[0078] Through the above adaptive mechanism, the application can realize online perception and correction of model uncertainty and external disturbance, thereby maintaining high stability and low risk operation of the suspension system under nonlinear and time-varying working conditions. Compared with the traditional fixed model MPC, the mechanism significantly improves the long-term adaptability, dynamic robustness and prediction reliability of the control. In summary, the application based on the data-mechanism dual-driven uncertainty quantification method proposes a confidence embedded model predictive control method. The method uses the prediction results of the uncertainty quantification model for the future state of the system to obtain the state prediction mean and state prediction standard deviation information, and accordingly constructs dynamic risk constraints and risk penalty objectives in control optimization, realizing a data-driven risk adaptive control strategy that takes into account control performance and operational safety. Under this control framework, the controller replaces the nominal trajectory in the traditional robust MPC with the predicted state mean, and uses the predicted standard deviation to represent the confidence level of the state prediction and the system uncertainty, thereby realizing the probabilistic modeling and dynamic adaptive adjustment of the control constraints and optimization objectives. In this way, the control system can adaptively balance performance and safety according to the confidence level, significantly reducing the conservatism caused by the fixed disturbance set and robust tube construction in traditional RMPC or Tube-based RMPC. In addition, the application realizes dynamic correction and self-learning of the control model for the system operating state through an adaptive updating mechanism based on real-time measurement data, thereby maintaining excellent robustness and long-term stability under nonlinear, time-varying and external disturbance conditions.

[0079] The application can be widely applied to precise suspension control, robot actuators, unmanned systems, energy conversion devices and other scenarios, and has significant engineering application value in improving control accuracy, reducing risk and enhancing system adaptability. The application can be a system, a method and / or a computer program product. The computer program product can include a computer readable storage medium having computer readable program instructions loaded thereon for causing a processor to implement various aspects of the application.

[0080] A computer readable storage medium can be a tangible device that can retain and store instructions for use by an instruction execution device. The computer readable storage medium can be, for example, but is not limited to, an electronic storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any suitable combination of the foregoing. A non-exhaustive list of more specific examples of the computer readable storage medium includes the following: a portable computer diskette, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or Flash memory), a static random access memory (SRAM), a portable compact disc read-only memory (CD-ROM), a digital versatile disk (DVD), a memory stick, a floppy disk, a mechanically encoded device such as punch-cards or raised structures in a groove having instructions recorded thereon, and any suitable combination of the foregoing. A computer readable storage medium, as used herein, is not to be construed as being transitory signals per se, such as radio waves or other freely propagating electromagnetic waves, electromagnetic waves propagating through a waveguide or other transmission media (e.g., light pulses passing through a fiber-optic cable), or electrical signals transmitted through a wire.

[0081] Computer readable program instructions described herein can be downloaded to respective computing / processing devices from a computer readable storage medium or to an external computer or external storage device via a network, for example, the Internet, a local area network, a wide area network and / or a wireless network. The network can comprise copper transmission cables, optical transmission fibers, wireless transmission, routers, firewalls, switches, gateway computers and / or edge servers. A network adapter card or network interface in each computing / processing device receives computer readable program instructions from the network and forwards the computer readable program instructions for storage in a computer readable storage medium within the respective computing / processing device.

[0082] Computer program instructions for carrying out methods of the present application can be implemented in assembly language, instruction set architecture (ISA) instructions, machine instructions, machine dependent instructions, microcode, firmware instructions, state-setting data, or any combination thereof. These computer program instructions can be supplied to a computer, or other programmable data processing apparatus, to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions / acts specified in the flowchart and / or block diagram block or blocks. These computer program instructions can also be stored in a computer readable storage medium that can direct a computer, a programmable data processing apparatus, and / or other devices to function in a particular manner, such that the computer readable storage medium having instructions for causing a computer, programmable data processing apparatus, and / or other devices to implement the functions / acts specified in the flowchart and / or block diagram block or blocks.

[0083] According to an embodiment of the present application, the flowcharts and block diagrams of methods, apparatuses and computer program products shown in the specification are merely used to show the architecture, functions or operation modes of the system. Each block in the flowcharts or block diagrams can be implemented by computer readable program instructions, and the single block or the combination of blocks can be executed by the processor in the general purpose computer, special purpose computer or other programmable data processing apparatus to produce the computing apparatus that implements the specific functions after executing the instructions.

[0084] The computer readable program instructions 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 instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions / acts specified in the flowchart and / or block diagram block or blocks. These computer readable program instructions can also be stored in a computer readable storage medium that can direct a computer, a programmable data processing apparatus, and / or other devices to function in a particular manner, such that the computer readable storage medium having instructions for causing a computer, programmable data processing apparatus, and / or other devices to implement the functions / acts specified in the flowchart and / or block diagram block or blocks.

[0085] The computer readable program instructions can also be loaded onto a computer, other programmable data processing apparatus, or other device to cause a series of operational steps to be performed on the computer, other programmable data processing apparatus, or other device to produce a computer implemented process such that the instructions which execute on the computer, other programmable data processing apparatus, or other device implement the functions / acts specified in the flowchart and / or block diagram block or blocks.

[0086] The computer program product of the present application can be a computer program product which implements the methods of the present application. This implementation can be done in the form, for example, of a computer program, which can be stored on a CD-ROM, and / or a floppy disc, and / or can be available for downloading over the internet. The program codes can be implemented in the object-oriented, script-based, downloadable, and / or applet programming languages.

[0087] Embodiments of the application have been described above, with the understanding that these embodiments are illustrative only and are not restrictive in nature. Many modifications and variations of the disclosed embodiments are possible in light of the above teachings. The terminology used herein is for the purpose of describing the particular embodiments only and is not intended to limit the scope of the embodiments disclosed herein. It is therefore contemplated to cover any and all modifications and variations of this application that fall within the scope of the appended claims.

Claims

1. A confidence-embedded model predictive control method, characterized by, The method comprises the following steps: establishing a dynamic equation of a levitation system of a maglev train, the dynamic equation describing a dynamic coupling relationship between a levitation air gap, a vertical motion speed, an electromagnet coil current, and a levitation force; based on the dynamic equation and a plurality of sets of state observation data of the levitation system, using a data-mechanism dual-driven uncertainty quantification method to obtain state prediction mean values and state prediction standard deviations of states of the levitation system at each time in a future prediction time domain; constructing a model prediction control optimization problem for the levitation system of the maglev train, wherein: the state prediction mean values are used to generate a nominal trajectory of the levitation system; the state prediction standard deviations are used to set an uncertainty-related penalty term in a cost function and to construct a confidence-based state constraint; wherein the cost function is set as: wherein k is the time instant, is k the cost function at time instant, is the prediction step, is the state prediction mean at step , is the predicted control input at step , is the state weight matrix, is the input weight matrix, denotes the trace of a matrix, is the penalty term, with coefficient used to control the degree of uncertainty penalty of the suspension system based on the prediction covariance, is the state covariance at step predicted.

2. The method of claim 1, wherein, constraint conditions of the cost function include a confidence tightening constraint constructed based on the state prediction mean values and state prediction covariances, the constructed constraint conditions include a deterministic form and a probabilistic form, and are used to dynamically adjust a state safety margin and implement risk adaptive control, wherein the deterministic form is: the probabilistic form is: wherein, is a constraint direction matrix, is a constraint upper bound, is an allowed violation probability, is a confidence coefficient, used to dynamically adjust the safety margin according to the prediction uncertainty.

3. The method of claim 1, wherein, the state observation data include an original running data set of the levitation system of the maglev train and online measured levitation state data.

4. The method of claim 3, wherein, the original running data set includes: levitation air gap state quantities, vertical speed state quantities, and electromagnet coil current state quantities of the levitation system of the maglev train in a historical running process; and levitation state output quantities simulated by a nonlinear dynamic model of the levitation system of the maglev train under conditions of uncertain parameters, changes in aerodynamic load, or track irregularity excitation.

5. The method of claim 1, wherein, the state prediction mean values and the state prediction standard deviations are obtained by a data-mechanism dual-driven uncertainty quantification method; wherein the uncertainty quantification method takes the dynamic model of the levitation system of the maglev train as a physical constraint, and takes the original running data set and the online measured data as joint training data; the uncertainty quantification method uses a Bayesian physical information neural network, or uses an uncertainty modeling method capable of simultaneously utilizing data and physical mechanism constraints.

6. A computer-readable storage medium having stored thereon a computer program, characterized in that, The computer program, when executed by a processor, implements the steps of the method according to any one of claims 1 to 5.

7. A computer device comprising a memory and a processor, having stored on the memory a computer program capable of running on the processor, characterized in that, The processor, when executing the computer program, implements the steps of the method according to any one of claims 1 to 5.

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