Confidence embedded model predictive control method, medium and equipment

Abstract

The invention discloses a confidence embedded model predictive control method, a medium and equipment, and belongs to the technical field of suspension control. According to the method, a kinetic equation of a suspension system is established, a data-mechanism dual-drive uncertainty quantification method is adopted, original operation data of a maglev train and suspension state information measured on line are utilized, and dynamic characteristic learning modeling is conducted on the suspension system under the constraint of the kinetic equation; state quantity distribution of suspension air gaps, vertical speed, electromagnet current and the like at future moments is predicted, and prediction mean values and prediction standard deviations of corresponding states are obtained. In model prediction control optimization, a nominal trajectory of the suspension system is constructed by a predicted state mean value, and a penalty term proportional to prediction uncertainty is added into a cost function; meanwhile, confidence coefficient constraint is constructed based on the predicted standard deviation, and dynamic constraint tightening of key physical quantities such as suspension air gaps, vertical speed and coil current is achieved. According to the invention, real-time sensing and self-adaptive closed-loop control of the operation risk of the suspension system are realized.

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: (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; (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

[0004] 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 time domain, 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. Therefore, 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 realize quantitative characterization of uncertainties in the levitation system, adaptive risk constraint contraction, and high-precision real-time control.

[0005] According to a first aspect of the present application, a confidence embedded model predictive control method is provided, comprising the following steps: (1) establishing a dynamic equation of the levitation system of a maglev train to describe the nonlinear coupling relationship between a levitation air gap, a vertical velocity, a coil current of an electromagnet, and an electromagnetic force; (2) based on the dynamic equation and multiple sets of state observation data, using a data-mechanism dual-driven uncertainty quantification method, obtaining a predicted mean value and a predicted standard deviation of the state of the levitation system in a future prediction time domain; (3) constructing a confidence embedded model predictive control optimization problem, wherein: a nominal trajectory of the levitation system is generated based on the predicted mean value of the state, and is used for optimization calculation; an uncertainty penalty term is constructed based on the predicted standard deviation of the state, and is used to form a dynamic constraint contraction based on confidence; (4) solving the optimization problem to obtain an optimal levitation control input of the levitation system of the maglev train in the prediction time domain, and applying the first control input to a levitation actuator to realize real-time closed-loop control.

[0006] 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.

[0007] 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.

[0008] 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 on a disturbance set and too many modeling assumptions of a traditional RMPC, and uses the predicted mean value to construct a nominal trajectory, 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 constraints, the geometric conservativeness problem of the 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 train 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.

[0009] 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

[0010] 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.

[0011] Figure 1 is a flow chart of a confidence embedded model predictive control method according to an embodiment of the application; Figure 2 is a schematic diagram of a maglev train suspension system structure according to an embodiment of the application; Figure 3 is a schematic diagram of a Bayesian physical information neural network modeling framework according to an embodiment of the application. DETAILED DESCRIPTION

[0012] Various exemplary embodiments of the present application will now be described in detail with reference to the accompanying drawings. Note that the relative arrangement, numerical expressions, and numerical values of components and steps set forth in these embodiments are not limiting to the scope of the present application unless otherwise specifically stated.

[0013] 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.

[0014] Techniques, methods, and apparatus known to those of ordinary skill in the relevant art(s) can not be discussed in detail herein, but should be considered as part of the specification.

[0015] 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.

[0016] It should be noted that like reference numerals and letters in the various figures indicate like elements, and thus, discussions of certain items in one figure can also apply to like items in another figure.

[0017] At present, a data-mechanism dual-driven uncertainty quantification method (such as a Bayesian Physics-Informed Neural Network (B-PINN)) can drive network training together with historical data and real-time operation data by taking system dynamics equations as constraint conditions, thereby realizing learning of system dynamics laws 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 a traditional MPC optimization framework. The method uses state mean and standard deviation predicted by the uncertainty quantification method to construct dynamic risk constraints and penalty terms, and realizes risk adaptive control driven by data and mechanism.

[0018] In the application, state prediction mean and prediction standard deviation obtained by the uncertainty quantification method are used to construct dynamic nominal trajectory, probability constraints and uncertainty penalty terms respectively, thereby realizing a risk adaptive control strategy driven by data and mechanism. Compared with a nominal trajectory obtained by a deterministic nominal model in a traditional robust MPC, the application uses prediction mean as an optimization benchmark, so that the optimization result is more consistent with the real running characteristics of the maglev train suspension system, and control deviation caused by model mismatch can be significantly reduced. At the same time, the prediction standard deviation is used to construct probability constraints and dynamic penalty terms, so that the controller can adaptively adjust the risk level according to the confidence requirement, and realize the balance between performance and safety.

[0019] Compared with the traditional RMPC, the application has the following advantages: no need to fix the disturbance set and construct the robust tube, avoiding conservative geometric constraint assumptions; using prediction mean instead of nominal trajectory, improving prediction accuracy and control flexibility; introducing a dynamic risk trade-off mechanism to realize performance optimization on the premise of guaranteeing confidence safety; having stronger adaptability and data self-learning ability for nonlinear and time-varying systems.

[0020] 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 by the application is given. Referring to Figure 1 The confidence embedded model predictive control method of the application mainly includes the following steps.

[0021] 1. System modeling Taking the magnetic levitation train suspension system structure of Figure 2 , a nonlinear dynamic model of the magnetic levitation train suspension system is established, considering the nonlinear relationship between the suspension force and the suspension gap, the number of turns of the electromagnet, the current and other parameters, and introducing the load mass, the number of turns of the electromagnet, the effective cross-sectional area and other parameters as the uncertainty parameters into the model. 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.

[0022] For example, the discrete dynamic model of a single-point suspension system is constructed as follows: (1) 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.

[0023] 2. Uncertainty modeling The uncertainty modeling is based on the data-mechanism dual-driven uncertainty quantification method, which predicts the future state of the magnetic levitation train suspension system and obtains the prediction mean and prediction standard deviation 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.

[0024] 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 by combining the prior distribution and the likelihood function constructed based on data and physical residual in the Bayesian framework. 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.

[0025] 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 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.

[0026] 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.

[0027] 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.

[0028] 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 maglev electromagnet, and then the optimization is re-implemented according to the new state measurement in the next sampling period to realize real-time closed-loop control.

[0029] 3. Designing a confidence embedded robust controller The data-mechanism dual-driven uncertainty quantification method outputs the mean and standard deviation of the state variables 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 taken 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.

[0030] Specifically, applying the prediction results output by the data-mechanism dual-driven uncertainty quantification method to the confidence embedded model predictive control method includes: 3.1. Taking the state prediction mean obtained by the data-mechanism dual-driven uncertainty quantification method as the nominal trajectory, the stage cost in the cost function of the confidence embedded model predictive control method obtained therefrom is: (2) 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, which has been corrected by data, thereby making up for the model deviation. The state mean is used to replace the nominal trajectory in the traditional robust MPC; 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: (3) Wherein is the matrix trace, indicating the total variance (the sum of all state variances), and the coefficient​ controlling the degree of punishment, the state covariance at time When the variance is large, it indicates that the uncertainty of the state is large, the prediction confidence is low, and the punishment term is large, so the control is more conservative, and vice versa. Thus, the "terminal state penalty" in traditional robust MPC is extended to "penalty for uncertainty in the entire prediction horizon", which is used to weight the state prediction variance in the prediction horizon; 3.3、The data-mechanism dual-driven uncertainty quantification method can directly give the distribution characteristics of the future state, including the prediction mean and standard deviation, under the condition of integrating historical data, online measurement data and system dynamics equations, thereby describing the range in which the future state may fall. Therefore, in the confidence embedded model predictive control framework of the present application, there is no need to artificially assume a set of deterministic disturbances, but the prediction standard deviation can be used to construct constraint conditions, which can include deterministic and probabilistic forms, for dynamically adjusting the state safety margin and realizing risk adaptive control. The deterministic form is: (4) wherein is a constraint direction matrix, is a constraint upper limit. When the system state is 1-dimensional, the deterministic form is: (5) wherein is a confidence coefficient, which can be adjusted according to engineering practice. is the state standard deviation predicted by the uncertainty quantification method when the system state is 1-dimensional.

[0031] The probabilistic form is: (6) that is, the constraint is satisfied with a probability of at least .

[0032] When the system state is 1-dimensional, the probabilistic form is: (7) wherein is the allowed violation probability, which is used to affect the constraint tightening range.

[0033] The state distribution-based constraint adopts a probabilistic form, allowing the constraint to be defined within a set violation probability range.

[0034] In summary, the final form of the cost function of the proposed confidence embedded model predictive control method is: (8) 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 permissible probability of default; To control the input feasible region, s.t Indicates constraints.

[0035] 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.

[0036] 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.

[0037] 4. Adaptive control based on real-time measurement updates During the operation of a maglev train levitation system, the system dynamics are affected by multiple factors such as changes in ambient temperature, vehicle load fluctuations, electromagnetic parameter drift, and track irregularities, resulting in significant time-varying characteristics and uncertainties. To continuously maintain the controller's accurate characterization of the system state and uncertainties, this invention introduces an adaptive control mechanism based on real-time measurement updates during the control execution phase, enabling the control model and control law to automatically adjust as the system's operating state changes.

[0038] Specifically, the following steps are included: (1) Real-time measurement data acquisition At the end of each sampling period, the system collects the key state variables of the levitation module in real time, including the levitation 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 to correct the model prediction bias.

[0039] (2) Model posterior update (Bayesian physics-informed neural network online learning) After obtaining new observation data, the data-mechanism dual-driven uncertainty quantification model (such as the Bayesian physics-informed neural network implementation form) used in the present application 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 through 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, making the mean of the state prediction closer to the actual evolution process of the system, and making the prediction standard deviation more accurately reflect the uncertainty level of the system under the current working condition. Through this online learning mechanism, the present application can ensure that the uncertainty model remains effective in the long-term operation, thereby avoiding the gradual decline in performance of traditional fixed model MPC under system parameter drift or external condition changes.

[0040] (3) Dynamic prediction and control law correction After the model posterior update is completed, the present 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 is used to dynamically adjust the tightening amplitude of the state constraint and the action strength of the uncertainty penalty term. When the prediction standard deviation increases, the controller will automatically enhance the safety margin, making the constraint condition more conservative to ensure safety; on the contrary, when the prediction standard deviation decreases, the constraint will be appropriately relaxed, allowing the controller to adopt a more aggressive optimal control strategy to improve performance. Through this dynamic risk adjustment mechanism based on confidence, the present application realizes the real-time balance between performance and safety.

[0041] (4) Rolling optimization execution 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 obtain the optimal control sequence in the time domain. Among 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 complex working condition changes.

[0042] 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, this mechanism significantly improves the long-term adaptability, dynamic robustness and prediction reliability of the control. In summary, the application proposes a confidence embedded model predictive control method based on the uncertainty quantification method driven by data and mechanism. 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 operation 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 of state prediction and system uncertainty, thereby realizing probabilistic modeling and dynamic adaptive adjustment of 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 fixed disturbance sets 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.

[0043] 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 precision, 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.

[0044] Computer readable storage media can be tangible storage media which can retain and store instructions for use by an instruction execution device. Computer readable storage media 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. More specific examples (a non-exhaustive list) of computer readable storage media include 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.

[0045] 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.

[0046] 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.

[0047] According to an embodiment of the present application, the flowcharts and block diagrams illustrated in the specification show the architecture, functionality, or operation of methods, apparatuses and computer program products. Each block in the flowcharts or block diagrams can be implemented by computer readable program instructions. The single block or a combination of blocks can be executed by a processor in a general purpose computer, a special purpose computer, or other programmable data processing apparatus to produce a computing device that implements the specified functions after the execution of the instructions.

[0048] The computer readable program instructions can be provided to a processor of a general purpose computer, a 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.

[0049] 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 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.

[0050] 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 data carrier, such as a ROM, a programmable logic unit, a flash memory etc. and can be implemented on the hard disk of a data carrier, or can be stored and / or distributed via a network, such as the Internet or a mobile telephone network. The computer program can be implemented in the object-oriented, modular programming technique, and can comprise the program code of the application and / or the program code of the application in combination with the program codes of other computer programs, such as an operating system.

[0051] The embodiments of the application described above have been described in an illustrative manner. The terminology used is intended to be in the nature of words of description rather than of limitation. Many modifications and variations of the present embodiments are possible in light of the above teachings. The particular features of the application are set forth with specific details to provide a thorough and enabling disclosure for purposes of patentability. It will be appreciated by those skilled in the art that the scope of the application encompasses embodiments that do not require one or more of the specific features or one or more of the specific integers employed. It is therefore contemplated to cover any and all modifications, variations or equivalents that fall within the scope of the present application. It is intended that the scope of the application shall be limited only to the extent required by the patenting authorities issuing this patent.

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.

2. The method of claim 1, 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 predicted state covariance at step .

3. The method of claim 2, wherein, Constraint conditions of the cost function include confidence tightening constraints constructed based on the state prediction mean values and state prediction covariances, and the constructed constraint conditions include a deterministic form and a probabilistic form, for dynamically adjusting state safety margins and realizing 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.

4. The method of claim 1, wherein, The state observation data include a raw operation data set of the levitation system of the maglev train and online measured levitation state data.

5. The method of claim 4, wherein, The raw operation 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 operation 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 loads, or track irregularity excitations.

6. 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 raw operation 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.

7. 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 6.

8. 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 6.

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