Method and system for boundary estimation of a state-dependent switched system

Abstract

The application provides a boundary estimation method and system of a state-dependent switching system, comprising: establishing a state-dependent switching system of an object to be studied, defining an actual model and a nominal model, and an actual boundary and a nominal boundary; comparing the outputs of the nominal model and the actual model to obtain an actual switching point in the actual boundary neighborhood, and storing the actual switching point in a lookup table; based on the obtained actual switching point, using a genetic algorithm to optimize the nominal boundary parameters, fitting the actual boundary, and storing the parameter optimization result in the lookup table; and based on a K-nearest neighbor algorithm, filtering a plurality of parameter optimization results to obtain optimal nominal boundary parameters. The boundary estimation method provided by the patent can better avoid the mismatch between the controller and the subsystem near the boundary of the switching system, thereby causing the phenomenon of control failure or model instability.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of switching system control, in particular to a boundary estimation method and system of state-dependent switching system. BACKGROUND

[0002] In the nonlinear analysis and controller design of large complex systems, the theory and research results of switching systems have been widely applied. Bang-Bang control in the field of aerospace can effectively save fuel consumption, and variable structure control, sliding mode control and other algorithms inspired by the relay protection system in the field of power systems are also applied to systems such as robots, cars and missiles. The dynamic characteristics and stability of switching systems are determined by the structure and switching signal, and it is often difficult to obtain an accurate mathematical model for large complex systems, so switching systems still face many challenges:

[0003] 1. Uncertainty of internal parameters

[0004] There are many parameters in the subsystem, and some assumptions and simplifications inevitably discard some connections between parameters. For example, a motor is usually modeled as a relationship between current and output torque, but the gap between gears and the floating of working temperature have a certain influence on the output torque, and some parameters are time-varying, which causes modeling errors. By understanding the working rules of the model, the influence of parameter time-varying on the switching system can be suppressed by the method of feedforward control.

[0005] 2. External disturbance

[0006] For large complex switching systems, external disturbance sources come from many aspects, such as spacecraft operating in space, which will be impacted by electromagnetic radiation and high-energy charged particle flow generated by solar storms at irregular intervals. The effect of feedforward control method is not ideal under external random disturbance. The source and size of external disturbance have high randomness, which is difficult to compensate by prediction.

[0007] 3. Fuzziness of boundary

[0008] The above two points also exist in continuous systems. For switching systems, modeling inaccuracy exists not only in the subsystem but also in the boundary between each subsystem. The uncertainty of internal parameters and external disturbances can be suppressed to a certain extent by intelligent control algorithms with strong anti-interference ability, such as robust control and adaptive control. However, the fuzziness of the boundary will cause mismatch between the subsystem and the controller, that is, in the neighborhood interval of the boundary, the design of the controller does not match the current demand of the subsystem, which may cause system instability or control failure. Therefore, it is necessary to accurately fit the boundary between the subsystems by the boundary estimation algorithm in the control process. SUMMARY

[0009] To address the shortcomings of existing technologies, the purpose of this invention is to provide a boundary estimation method and system for state-dependent switching systems.

[0010] A boundary estimation method for a state-dependent switching system provided by the present invention includes:

[0011] Steps for establishing a state-dependent switching system: Establish the state-dependent switching system of the object under study, and define the actual model and nominal model, and the actual boundary and nominal boundary;

[0012] Single-step model prediction steps: Compare the outputs of the nominal model and the actual model, obtain the actual switching point in the actual boundary neighborhood, and store this actual switching point in a lookup table;

[0013] The steps for suboptimal boundary estimation based on genetic algorithm are as follows: Based on the obtained actual switching point, the nominal boundary parameters are optimized using a genetic algorithm to fit the actual boundary, and the parameter optimization results are stored in a lookup table.

[0014] The optimal boundary estimation steps based on the K-nearest neighbor algorithm are as follows: filter the optimization results of multiple sets of parameters based on the K-nearest neighbor algorithm to obtain the optimal nominal boundary parameters.

[0015] Preferably, the state-dependent switching system is:

[0016]

[0017] Where x = [x1, x2, ..., x N ] T Let N be the system state vector, and N be the number of system state vectors. and The first derivative of the system state vector with respect to time, f i (x1,…,x i ) and f N (x) represents the influence of system parameters on the dynamic model, ξ i With ξ N The external random disturbance is represented by sign(·), the sign function is represented by b(x), the state-dependent switching boundary is represented by g(x), the effect of the control input on the dynamic model is represented by u, and the control input is represented by u.

[0018] Actual model (f) i g) by the nominal model and the corresponding error (Δf) i The actual boundary b is composed of the nominal boundary (Δg) and the actual boundary b is composed of the nominal boundary. The error Δb is composed of the following formula:

[0019]

[0020] According to the prior information of the state-dependent switching system, the nominal boundary of the system is represented as:

[0021]

[0022] where B1 to B j are known explicit functions of the state vector j , c1 to c are parameters of the unknown actual boundary, B1 to B are parameters of the nominal boundary to be updated by the boundary estimation algorithm, and x is the state vector of the actual model.

[0023] Preferably, the single-step model prediction step comprises:

[0024] Based on the nominal system state - at the current time t and the actual system state x at the current time t + , the nominal system state at the adjacent time t

[0025] is predicted using the nominal model, the actual system state of the actual model is obtained through the sensor, the difference between the two at the current time t - and the difference at the adjacent time t + are considered, and the consideration of the nominal boundary of the system is introduced, when formula (4) or formula (5) is satisfied, it indicates that the actual model switches, and the nominal model does not switch, and the mismatch phenomenon between the controller and the subsystem occurs:

[0026]

[0027] where |·| represents the absolute value function, η is a constant, representing the tolerance of the error, and the actual switching point corresponding to formula (4) or formula (5) is stored in the lookup table.

[0028] Preferably, when the actual model switches, the motion flow of the system is located in the neighborhood of the actual boundary b in the state space, the actual system state corresponding to the actual switching point is used to replace the nominal system state, and is substituted into the nominal boundary , the nominal boundary parameters are optimized, and the optimization function is selected:

[0029]

[0030] where min(·) is the minimum function, |·| is the absolute value function, ∑ represents the sum of the absolute value operations on all actual switching points, B1 to B j are known explicit functions of the state vector to is the parameter of the nominal boundary to be updated by the boundary estimation algorithm, x is the state vector of the actual model;

[0031] The genetic algorithm (GA) toolbox is used to optimize the control parameters:

[0032] x = ga (fun, nvars, A, b, Aeq, beq, lb, ub, nonlcon, IntCon, options) (7)

[0033] wherein fun represents the optimization function, i.e., formula (6); nvars represents the number of elements of the x vector, the nominal boundary contains j internal parameters; IntCon represents the index of the positive integer of the x vector, herein from 1 to j; A, b, Aeq, beq represent linear constraints, i.e. nonlcon is a nonlinear function constraint; lb and ub represent the upper and lower bounds of the variable x, i.e., lb≤x≤ub, and options represent detailed settings.

[0034] Each time an actual switching point is generated, the genetic algorithm is activated to optimize all the past system switching points, to generate the optimized nominal boundary parameters, which are stored in the lookup table.

[0035] Preferably, the optimized nominal boundary parameters are presented in the form of a multi-dimensional vector, d = 1, 2,..., D, wherein D is the optimization number of the nominal boundary parameters, and when the obtained nominal boundary parameters reach a threshold value, the optimal nominal boundary parameters are obtained by the following formula:

[0036]

[0037] wherein ||·||2 represents the two-norm, K is a given constant of the nearest neighbor algorithm, is the centering processing of the nominal boundary parameters, i.e., the center point of the D nominal boundary parameters is obtained; after the minimum operation, the K nominal boundary parameters closest to the center point among the D nominal parameters are obtained, and the centering processing is performed on the K nominal boundary parameters to obtain the optimal nominal boundary parameters, and the optimal nominal boundary parameters are updated to the nominal boundary.

[0038] According to the boundary estimation system of the state-dependent switching system provided by the application, the boundary estimation system of the state-dependent switching system comprises:

[0039] The state-dependent switching system module: the state-dependent switching system to be studied is established, and the actual model and the nominal model, the actual boundary and the nominal boundary are defined;

[0040] Single-step model prediction module: Compare the output of the nominal model with the actual model, obtain the actual switching point in the actual boundary neighborhood, and store this actual switching point in a lookup table;

[0041] The suboptimal boundary estimation module based on genetic algorithm: Based on the obtained actual switching point, the nominal boundary parameters are optimized using a genetic algorithm to fit the actual boundary, and the parameter optimization results are stored in a lookup table;

[0042] The optimal boundary estimation module based on the K-nearest neighbor algorithm filters multiple sets of parameter optimization results based on the K-nearest neighbor algorithm to obtain the optimal nominal boundary parameters.

[0043] Preferably, the state-dependent switching system module is:

[0044]

[0045] Where x = [x1, x2, ..., x N ] T Let N be the system state vector, and N be the number of system state vectors. and The first derivative of the system state vector with respect to time, f i (x1,…,x i ) and f N (x) represents the influence of system parameters on the dynamic model, ξ i With ξ N The external random disturbance is represented by sign(·), the sign function is represented by b(x), the state-dependent switching boundary is represented by g(x), the effect of the control input on the dynamic model is represented by u, and the control input is represented by u.

[0046] Actual model (f) i g) by the nominal model and the corresponding error (Δf) i The actual boundary b is composed of the nominal boundary (Δg) and the actual boundary b is composed of the nominal boundary. The error Δb is composed of the following formula:

[0047]

[0048] Based on the prior information of the state-dependent switching system, the nominal boundary of the system is... The actual boundary b(x) is represented as:

[0049]

[0050] B1 to B j It is a known explicit function of the state vector, c1 to c j These are parameters of the unknown actual boundary. to is the parameter of the nominal boundary to be updated by the boundary estimation algorithm, x is the state vector of the actual model.

[0051] Preferably, the single-step model prediction module comprises:

[0052] Based on the nominal system state - and the actual system state x at the current time t , the nominal system state at the next time t + is predicted using the nominal model, the actual system state of the actual model is obtained through the sensor, the difference between the two at the current time t - and the difference at the next time t + are considered, and the consideration of the nominal boundary of the system is introduced at the same time. When formula (12) or formula (13) is satisfied, it indicates that the actual model switches, the nominal model does not switch, and the mismatch between the controller and the subsystem occurs:

[0053]

[0054]

[0055] where |·| represents the absolute value function, η is a constant, and represents the tolerance of the error. The actual switching point corresponding to formula (12) or formula (13) is stored in the lookup table.

[0056] Preferably, when the actual model switches, the motion flow of the system is located in the neighborhood of the actual boundary b in the state space. The actual system state corresponding to the actual switching point is used to replace the nominal system state, and is substituted into the nominal boundary . The nominal boundary parameters are optimized, and the optimization function is selected:

[0057]

[0058] where min(·) is the minimum value function, |·| is the absolute value function, ∑ represents the sum of the absolute value operations on all actual switching points, B1 to B j are known explicit functions about the state vector to is the parameter of the nominal boundary to be updated by the boundary estimation algorithm, x is the state vector of the actual model.

[0059] The genetic algorithm GA toolbox is used to optimize the control parameters:

[0060] x = ga (fun, nvars, A, b, Aeq, beq, lb, ub, nonlcon, IntCon, options) (15)

[0061] Wherein, fun represents an optimization function, that is, formula (14) ; nvars represents the number of elements of the x vector, the nominal boundary contains j internal parameters; IntCon represents the subscript of the x vector positive integer, here from 1 to j; A, b, Aeq, beq represent linear constraints, that is nonlcon is a nonlinear function constraint; lb and ub represent the upper and lower bounds of the variable x, that is, lb <= x <= ub, and options represent detailed settings.

[0062] Each time the actual switching point is generated, the genetic algorithm is activated to optimize all the system switching points in the past, and the optimized nominal boundary parameters are stored in the lookup table.

[0063] Preferably, the optimized nominal boundary parameters are presented in the form of a multi-dimensional vector, d=1,2,...,D, wherein D is the optimization number of nominal boundary parameters, when the obtained nominal boundary parameters reach a threshold, the optimal nominal boundary parameters obtained by the following formula:

[0064]

[0065] Wherein ||·||2 represents the two norm, K is a given constant of the nearest neighbor algorithm, is the centering processing of the nominal boundary parameters, that is, the center point of the D nominal boundary parameters is obtained; after the minimum operation, that is, the K nearest nominal boundary parameters in the D nominal parameters are obtained, and after centering processing, they are used as the optimal nominal boundary parameters.

[0066] Compared with the prior art, the present application has the following beneficial effects:

[0067] 1、The boundary estimation method of the state-dependent switching system provided by the present application comprises a single-step model prediction module, a boundary estimation module based on a genetic algorithm and a boundary estimation module based on a K nearest neighbor algorithm, the three modules are coupled and associated with each other, the single-step model prediction can identify the actual switching point, provide a learning sample for the boundary estimation based on the K nearest neighbor algorithm, further improve the accuracy of the nominal boundary, gradually reduce the difference between the nominal boundary and the actual boundary, and solve the problem of controller and subsystem mismatch.

[0068] 2、The single-step model prediction method provided by the patent can combine the outputs of the actual model and the nominal model to identify the actual switching point in real time. Due to the inaccuracy of modeling, the outputs of the actual model and the nominal model have differences, and the differences are caused by the uncertainty of the internal parameters of the system, external interference and the fuzziness of the boundary. The identification function in the single-step model prediction module can identify the actual switching point caused by the boundary fuzziness, and provide data samples for subsequent optimization.

[0069] 3、The patent adopts the genetic algorithm and the K nearest neighbor algorithm to optimize the nominal boundary parameters, and can gradually improve the fitting accuracy of the nominal boundary. The genetic algorithm has strong global optimization ability and can give a better suboptimal solution. However, considering the difference in sample quality, further optimization of the suboptimal solution of the genetic algorithm can weaken the influence of the sample quality problem on the fitting effect of the nominal boundary, and improve the effectiveness of the boundary estimation algorithm. BRIEF DESCRIPTION OF DRAWINGS

[0070] Other features, objects and advantages of the present application will become more apparent from the following detailed description of non-limiting embodiments, made with reference to the following drawings:

[0071] Figure 1 The flow chart of the boundary estimation method of the state-dependent switching system of the present application. DETAILED DESCRIPTION

[0072] The present application will be described in detail below with reference to specific embodiments. The following embodiments will help those skilled in the art to further understand the present application, but do not limit the present application in any form. It should be pointed out that, for those skilled in the art, without departing from the concept of the present application, a number of changes and improvements can be made. These all belong to the protection scope of the present application.

[0073] Example 1

[0074] The present application discloses a boundary estimation method of a state-dependent switching system. The research object of the present application is a state-dependent switching system. The boundary between each subsystem is determined by a function containing the system state. When the system motion flow moves from one side of the boundary to the other side in the state space, the system is said to have completed switching, and the corresponding controller also needs to be selected to meet the needs of the system for stability and controllability.

[0075] The boundary estimation method of the state-dependent switching system disclosed by the present application comprises four steps, which are described with reference to Figure 1As shown, the process includes: Step 1: Establishing a state-dependent switching system for the object under study. This involves defining the actual and nominal models, as well as the actual and nominal boundaries, and briefly describing the harm caused by boundary ambiguity. Step 2: Single-step model prediction. This describes the working principle of single-step model prediction, comparing the outputs of the nominal and actual models, obtaining the actual switching point within the neighborhood of the actual boundary, and storing this actual switching point in a lookup table. Step 3: Suboptimal boundary estimation based on a genetic algorithm. Based on the obtained actual switching point, a genetic algorithm is used to optimize the nominal boundary parameters, fitting the actual boundary, and storing the parameter optimization results in a lookup table. Step 4: Optimal boundary estimation based on the K-nearest neighbor algorithm. This involves filtering multiple sets of parameter optimization results using the K-nearest neighbor algorithm to obtain the optimal nominal boundary parameters. Each step is described in detail below.

[0076] Steps for establishing a state dependency switching system:

[0077] The state dependency switching system is as follows:

[0078]

[0079] Where x = [x1, x2, ..., x N ] T Let N be the system state vector, and N be the number of system state vectors. and The first derivative of the system state vector with respect to time, f i (x1,…,x i ) and f N (x) represents the influence of system parameters on the dynamic model, ξ i With ξ N Let represent external random disturbance, sign(·) represent the sign function, b(x) represent the state-dependent switching boundary, g(x) represent the influence of the control input on the dynamic model, and u represent the control input.

[0080] Due to the common existence of errors in the modeling process, the actual model (f) in formula (1) i g) is usually derived from the nominal model and the corresponding error (Δf) i The actual boundary b is composed of the nominal boundary (Δg) and the actual boundary b is composed of the nominal boundary. The error Δb is composed of the following formula:

[0081]

[0082] Uncertainties in the model's internal parameters and external disturbances can be suppressed through feedforward and feedback control, combined with adaptive control, robust control, and fuzzy control. However, when the system's motion flow is at the nominal boundary... The switching between the subsystem and the controller is not synchronized with the actual boundary b, causing the mismatch between the controller and the subsystem, and having unknown negative effects on the stability of the switching system, which may cause control failure or model instability. From the prior information of the system, the nominal boundary The actual boundary b(x) is represented as:

[0083]

[0084] where B1 to B j are known explicit functions of the state vector, c1 to c j are unknown parameters of the actual boundary, to are parameters of the nominal boundary to be updated by the boundary estimation algorithm, and x is the state vector of the actual model, which can be directly obtained by a state observer or a sensor.

[0085] Single-step model prediction step:

[0086] Based on the nominal system state - and the actual system state x at the current time t , the nominal system state at the adjacent time t + is predicted using the nominal model, the actual system state of the actual model is obtained by a sensor, and the difference between the two at the current time t - and the difference at the adjacent time t + are considered, and the consideration of the nominal boundary of the system is introduced. When formula (4) or formula (5) is satisfied, it indicates that the actual model switches, and the nominal model does not switch, and the mismatch between the controller and the subsystem occurs:

[0087]

[0088]

[0089] where |·| represents the absolute value function, η is a constant, and represents the tolerance of the error. The actual switching points corresponding to formula (4) or formula (5) are stored in the lookup table. These actual switching points are in the neighborhood of the actual boundary in the state space, and through the single-step model prediction method, the system switching points in the neighborhood of the actual boundary can be identified, providing data support for the optimization of the nominal boundary in the suboptimal boundary estimation step based on the genetic algorithm.

[0090] Suboptimal boundary estimation step based on genetic algorithm:

[0091] According to formula (3), when the actual model switches, the motion flow of the system is located in the neighborhood of the actual boundary b in the state space, the actual system state corresponding to the actual switching point is used to replace the nominal system state, and is substituted into the nominal boundary In the middle, the nominal boundary parameters are optimized to make the nominal boundary approach the actual boundary. The optimization function is selected as:

[0092]

[0093] where min(·) is the minimum value function, |·| is the absolute value function, ∑ represents the summation of the absolute value operation on all actual switching points, B1 to B j is an explicit function of the state vector known is the parameter of the nominal boundary to be updated by the boundary estimation algorithm, and x is the state vector of the actual model.

[0094] Genetic algorithm is used to optimize the above formula. Genetic algorithm simulates the natural selection and genetic mechanism of evolutionary theory, and searches for the optimal solution by simulating the natural evolution process, including chromosome gene initialization, selection, crossover, mutation and other processes. In the face of complex combinatorial optimization problems, it can usually quickly obtain better optimization results. Based on the Matlab 2021a platform, the genetic algorithm GA toolbox is used to optimize the control parameters, so that the optimization function reaches the optimal value. The genetic algorithm GA toolbox is called:

[0095] x = ga (fun, nvars, A, b, Aeq, beq, lb, ub, nonlcon, IntCon, options) (7)

[0096] where fun represents the optimization function, i.e. formula (6); nvars represents the number of elements of the x vector, and the nominal boundary contains j internal parameters; IntCon represents the index of the positive integer of the x vector, which is from 1 to j here; A, b, Aeq, beq represent linear constraints, i.e. nonlcon is the non-linear function constraint, the boundary estimation method does not contain no constraint, so it is all empty matrix; lb and ub represent the upper and lower bounds of the variable x, i.e. lb≤x≤ub, which can be empty without special requirements; options represents detailed settings, which uses the default value without special requirements.

[0097] Each time an actual switching point is generated, the genetic algorithm is activated to optimize all past system switching points, generate optimized nominal boundary parameters, and output updated nominal boundary parameters to the optimal boundary estimation step based on the K-nearest neighbor algorithm, while storing them in the lookup table.

[0098] Optimal boundary estimation step based on K-nearest neighbor algorithm:

[0099] ​With the growth of system running time, the samples generated by the single-step model prediction module are sufficient, but the quality of the data is uneven, and the nominal boundary parameters after genetic algorithm optimization are also different. In the actual boundary neighborhood range, the samples with closer spatial distance are expected to be trained to generate results that can better describe the actual boundary. To weaken the influence of poor samples on the genetic algorithm optimization results, the K-nearest neighbor classification algorithm is introduced, which is one of the relatively mature machine learning algorithms. This method believes that in the feature space, if the K nearest neighbors of a sample belong to a certain category, then this sample also belongs to this category.

[0100] The optimized nominal boundary parameters are presented in the form of a multi-dimensional vector, d = 1, 2, …, D, wherein D is the optimization number of nominal boundary parameters, and when the obtained nominal boundary parameters reach a threshold value, the optimal nominal boundary parameters are obtained by the following formula:

[0101]

[0102] wherein ||·||2 represents the two-norm, K is a given constant of the nearest neighbor algorithm, is the centering processing of the nominal boundary parameters, that is, the center point of the D nominal boundary parameters is obtained. After the minimum operation, the K nearest nominal boundary parameters to the center point are obtained from the D nominal parameters, and the centering processing is performed on the K nearest nominal boundary parameters to obtain the optimal nominal boundary parameters.

[0103] Through this step, the nominal system parameters generated in the suboptimal boundary estimation step based on the genetic algorithm can be filtered, and the optimal nominal boundary parameters better than those obtained by directly optimizing the genetic algorithm are obtained, and the optimal nominal boundary parameters are updated to the nominal boundary.

[0104] Example 2

[0105] Embodiment 2 is a preferred example of Embodiment 1, which more specifically illustrates the present application.

[0106] The application discloses a boundary estimation method of a state-dependent switching system, and relates to the technical field of switching system control.

[0107] With single degree of freedom dead zone model as the preferred example, the state-dependent dynamics actual model is given as:

[0108]

[0109] where x1 is the system state vector, is the first order derivative of the system state vector with respect to time, sign(·) represents the sign function, (d0x1-d1) represents the switching boundary of the dead zone model, d1 represents the influence of the control input on the dynamics model, u is the control input, (d3x1) 2 represents the influence of the system parameters on the dynamics model, d4sin(x1) represents the external random disturbance, d0, d1, d2, d3 and d4 are the constant parameters of the actual system;

[0110] Considering the modeling error, the nominal model of the state-dependent dynamics is:

[0111]

[0112] where, is the state parameter of the nominal model, and are the nominal model parameters, which have errors with the actual system parameters in equation (1) due to the modeling error, thus introducing boundary error, internal error and external disturbance, where and can be updated by the boundary estimation algorithm.

[0113] The model internal parameter uncertainty caused by the parameters and and the external disturbance caused by can be suppressed by feedforward and feedback control, which is relatively mature. However, when the system motion flow is in the area between the nominal boundary of the dead zone model and the actual boundary (d0x1-d1), the switching of the subsystem and the controller does not proceed synchronously, resulting in mismatch between the controller and the subsystem, which may cause control failure or model instability. Therefore and the boundary estimation method proposed in this patent needs to be updated to reduce the ambiguous area.

[0114] The single-step model prediction module can capture the actual switching point in the neighborhood of the actual switching boundary. The nominal system state at the adjacent time is predicted using the nominal model, the actual system state of the actual model is obtained through the sensor, the difference between the two is considered, and the consideration of the nominal boundary of the system is introduced. When equation (3) or equation (4) is satisfied, it indicates that the actual model switches, and the nominal model does not switch, the mismatch between the controller and the subsystem occurs, and the corresponding state quantity is the state of the actual switching point:

[0115]

[0116]

[0117] where |·| represents the absolute value function, η is a constant, representing the tolerance of error, and the actual switching points corresponding to formula (3) or formula (4) are stored in the lookup table. These actual switching points are in the neighborhood of the actual boundary in the state space, and through the single-step model prediction module, the system switching points in the neighborhood of the actual boundary can be identified, providing data support for the optimization of the nominal boundary in the suboptimal boundary estimation step based on the genetic algorithm.

[0118] The suboptimal boundary is estimated based on the genetic algorithm, and the optimization function is selected as:

[0119]

[0120] where min(·) is the minimum value function, |·| is the absolute value function, and ∑ represents the summation of the absolute values of all actual switching points. When the optimization function of formula (5) is optimal, it indicates that the optimized and can minimize the boundary fuzzy area.

[0121] The genetic algorithm is used to optimize the above formula. Genetic algorithm simulates the natural selection and genetic mechanism of evolutionary theory, and searches for the optimal solution by simulating the natural evolution process, including the initialization of chromosome genes, selection, crossover, mutation and other processes. In the face of complex combinatorial optimization problems, it can usually quickly obtain good optimization results. Based on the Matlab 2021a platform, the genetic algorithm GA toolbox is used to optimize the control parameters, so that the optimization function is optimal. The genetic algorithm GA toolbox is called as:

[0122] x = ga (fun, nvars, A, b, Aeq, beq, lb, ub, nonlcon, IntCon, options) (6)

[0123] where fun represents the optimization function, i.e. formula (6); nvars represents the number of elements in the x vector, and the nominal boundary contains j internal parameters; IntCon represents the index of the positive integer in the x vector, which is from 1 to j here; A, b, Aeq, beq represent linear constraints, i.e. nonlcon is the nonlinear function constraint, and the boundary estimation method does not contain unconstrained, so it is all empty matrices; lb and ub represent the upper and lower bounds of the variable x, i.e. lb≤x≤ub, which can be empty without special requirements; options represents the detailed settings, which uses the default value without special requirements.

[0124] With the growth of system running time, the samples generated by the single-step model prediction module are sufficient, but the quality of the data is uneven, and the nominal boundary parameters after genetic algorithm optimization are also different. In the actual boundary neighborhood range, the samples with closer spatial distance are expected to be trained to generate results that can better describe the actual boundary. To weaken the influence of poor samples on the genetic algorithm optimization results, the K-nearest neighbor classification algorithm is introduced, which is one of the relatively mature machine learning algorithms. This method believes that in the feature space, if the K nearest neighbors of a sample belong to a certain category, then this sample also belongs to this category.

[0125] Optimal boundary estimation is performed using the K-nearest neighbor algorithm, and the optimized nominal boundary parameters are presented in the form of a multi-dimensional vector, d = 1, 2, …, D, where D is the optimization number of nominal boundary parameters, and when the obtained nominal boundary parameters reach a threshold, the optimal nominal boundary parameters are obtained by the following formula:

[0126]

[0127] where ||·||2 represents the two-norm, K is a given constant of the nearest neighbor algorithm, is the centering processing of the nominal boundary parameters, that is, the center point of the D nominal boundary parameters is obtained. After the minimum operation, the K nearest nominal boundary parameters to the center point are obtained from the D nominal parameters, and after centering processing, they are used as the optimal nominal boundary parameters. Through this step, the nominal system parameters generated in the suboptimal boundary estimation step based on the genetic algorithm can be filtered to obtain more optimal optimal nominal boundary parameters than the direct genetic algorithm optimization, and the optimal nominal boundary parameters are updated to the nominal boundary.

[0128] Those skilled in the art can understand this embodiment as a more specific description of embodiment 1 and embodiment 2.

[0129] Those skilled in the art know that in addition to implementing the system and each device, module and unit thereof provided by the present application in the form of pure computer readable program code, the same function can also be achieved by logically programming the method steps to make the system and each device, module and unit thereof provided by the present application in the form of logic gates, switches, application specific integrated circuits, programmable logic controllers and embedded microcontrollers. Therefore, the system and each device, module and unit thereof provided by the present application can be considered as a hardware component, and the devices, modules and units included therein for achieving various functions can also be considered as structures within the hardware component. The devices, modules and units for achieving various functions can also be considered as both software modules for implementing methods and structures within hardware components.

[0130] The specific embodiments of the present application have been described. It is to be understood that the application is not limited to particular details described herein and that various modifications can be made therein without departing from the scope of the claimed application. Embodiments and features disclosed in this document, including in the examples, can be combined with each other, unless specifically contradicted by or inconsistent with each other.

Claims

1. A method of estimating a boundary of a state-dependent switched system, characterized by, Comprise: State-dependent switching system establishment step: establishing a state-dependent switching system of the object to be studied, defining the actual model and the nominal model, the actual boundary and the nominal boundary; Single-step model prediction step: comparing the outputs of the nominal model and the actual model, obtaining the actual switching point in the neighborhood of the actual boundary, and storing the actual switching point in the lookup table; Sub-optimal boundary estimation step based on genetic algorithm: based on the obtained actual switching point, using genetic algorithm to optimize the nominal boundary parameters, fitting the actual boundary, and storing the parameter optimization result in the lookup table; Optimal boundary estimation step based on K-nearest neighbor algorithm: filtering multiple sets of parameter optimization results based on K-nearest neighbor algorithm to obtain optimal nominal boundary parameters; The state-dependent switching system is: Where x = [x1, x2, ..., x N ] T Let N be the system state vector, and N be the number of system state vectors. and The first derivative of the system state vector with respect to time, f i (x1,…,x i ) and f N (x) represents the influence of system parameters on the dynamic model, ξ i With ξ N The external random disturbance is represented by sign(·), the sign function is represented by b(x), the state-dependent switching boundary is represented by g(x), the effect of the control input on the dynamic model is represented by u, and the control input is represented by u. the actual model (f i g) is composed of the nominal model (f and the corresponding error (Δf i , Δg), the actual boundary b is composed of the nominal boundary and the error Δb, as follows: According to the a priori information of the state-dependent switched system, the nominal boundary is represented as the actual boundary b(x). where B1to B j are known explicit functions of the state vector, c1to c j are parameters of the unknown actual boundary, to are parameters of the nominal boundary to be updated by the boundary estimation algorithm, x is the state vector of the actual model; The single-step model prediction step comprises: Based on the nominal system state - at the current time t and the actual system state x, the nominal system state at the adjacent time t + is predicted using the nominal model, the actual system state of the actual model is obtained through the sensor, and the difference at the current time t - and the difference at the adjacent time t + are considered, and the consideration of the nominal boundary of the system is introduced at the same time, and when formula (4) or formula (5) is satisfied, it indicates that the actual model switches, and the nominal model does not switch, and the mismatch phenomenon of the controller and the subsystem occurs: Where |·| represents the absolute value function, η is a constant, and represents the tolerance of the error. The actual switching point satisfying formula (4) or formula (5) is stored in the lookup table.

2. The boundary estimation method of the state-dependent switching system according to claim 1, wherein: When the actual model switches, the system's motion flow is in the neighborhood of the actual boundary b in the state space, the nominal system state is replaced by the actual system state corresponding to the actual switching point, and substituted into the nominal boundary In the actual model switching, the system's motion flow is in the neighborhood of the actual boundary b in the state space, the nominal system state is replaced by the actual system state corresponding to the actual switching point, and substituted into the nominal boundary In the actual model switching, the system's motion flow is in the neighborhood of the actual boundary b in the state space, the nominal system state is replaced by the actual system state corresponding to where min( ) is the minimum function, | | is the absolute value function, ∑ denotes the summation of the absolute values of all actual switching points, B1 to B j is an explicit function of the state vector to is the parameter of the nominal boundary to be updated by the boundary estimation algorithm, x is the state vector of the actual model; The genetic algorithm GA toolbox is used to optimize the control parameters: x=ga(fun,nvars,A,b,Aeq,beq,lb,ub,nonlcon,IntCon,options) (7) wherein fun denotes the optimization function, i.e. equation (6); nvars denotes the number of elements of the x vector, nominal bounds contain j internal parameters; IntCon denotes the index of the x vector positive integer, herein from 1 to j; A, b, Aeq, beq denote linear constraints, i.e. nonlcon is a non-linear function constraint; lb and ub denote the upper and lower bounds of the variable x, i.e. lb≤x≤ub, options denotes detailed settings; Each time an actual switching point is generated, the genetic algorithm is activated to optimize all past system switching points, and the optimized nominal boundary parameters are generated and stored in the lookup table.

3. The boundary estimation method of a state-dependent switching system according to claim 1, characterized by: The optimized nominal boundary parameters are presented in the form of a multi-dimensional vector, d = 1, 2, …, D, wherein D is the number of optimization of the nominal boundary parameters, and the optimal nominal boundary parameters are obtained by the following formula: where ||·||2 denotes the two-norm, K is a given constant for the nearest neighbor algorithm, is the centering process of nominal boundary parameters, that is, the center point of D nominal boundary parameters is obtained; the minimum value After the operation, the K nominal boundary parameters closest to the center point among the D nominal parameters are obtained, and after the centering process, they are used as the optimal nominal boundary parameters. The optimal nominal boundary parameters are updated to the nominal boundary.

4. A boundary estimation system for a state-dependent switching system, characterized by Comprise: State-dependent switching system module: establishing a state-dependent switching system of the object to be studied, defining the actual model and the nominal model, the actual boundary and the nominal boundary; Single-step model prediction module: comparing the outputs of the nominal model and the actual model, obtaining the actual switching point in the neighborhood of the actual boundary, and storing the actual switching point in the lookup table; Sub-optimal boundary estimation module based on genetic algorithm: based on the obtained actual switching point, using genetic algorithm to optimize the nominal boundary parameters, fitting the actual boundary, and storing the parameter optimization result in the lookup table; Optimal boundary estimation module based on K-nearest neighbor algorithm: filtering multiple sets of parameter optimization results based on K-nearest neighbor algorithm to obtain optimal nominal boundary parameters; The state-dependent switching system module is: Where x = [x1, x2, ..., x N ] T Let N be the system state vector, and N be the number of system state vectors. and The first derivative of the system state vector with respect to time, f i (x1,…,x i ) and f N (x) represents the influence of system parameters on the dynamic model, ξ i With ξ N The external random disturbance is represented by sign(·), the sign function is represented by b(x), the state-dependent switching boundary is represented by g(x), the effect of the control input on the dynamic model is represented by u, and the control input is represented by u. a real model (f i g) consisting of a nominal model (f and corresponding errors (Δf i , Δg), a real boundary b consisting of a nominal boundary and an error Δb, as follows: According to the a priori information of the state-dependent switched system, the nominal boundary is represented as the actual boundary b(x). B1 to B j is a known explicit function of the state vector, c1 to c j is a parameter of the unknown actual boundary, to is a parameter of the nominal boundary to be updated by the boundary estimation algorithm, x is the state vector of the actual model; The single-step model prediction module comprises: Based on the nominal system state - at the current time t and the actual system state x, the nominal system state at the adjacent time t + is predicted using the nominal model, the actual system state of the actual model is obtained through the sensor, and the difference at the current time t - and the difference at the adjacent time t + are considered, and the consideration of the nominal boundary of the system is introduced, when formula (12) or formula (13) is satisfied, it indicates that the actual model switches, and the nominal model does not switch, and the mismatch phenomenon of the controller and the subsystem occurs: Where |·| represents the absolute value function, η is a constant, and represents the tolerance of the error. The actual switching point satisfying formula (12) or formula (13) is stored in the lookup table.

5. The boundary estimation system of the state-dependent switching system according to claim 4, wherein: When the actual model switches, the system's motion flow is in the neighborhood of the actual boundary b in the state space, the nominal system state is replaced by the actual system state corresponding to the actual switching point, and substituted into the nominal boundary In the actual model switching, the system's motion flow is in the neighborhood of the actual boundary b in the state space, the nominal system state is replaced by the actual system state corresponding to the actual switching point, and substituted into the nominal boundary In the actual model switching, the system's motion flow is in the neighborhood of the actual boundary b in the state space, the nominal system state is replaced by the actual system state corresponding to where min( ) is the minimum function, | | is the absolute value function, ∑ denotes the summation of the absolute values of all actual switching points, B1 to B j is a known explicit function of the state vector to is a parameter of the nominal boundary to be updated by the boundary estimation algorithm, x is the state vector of the actual model; The genetic algorithm GA toolbox is used to optimize the control parameters: x=ga(fun,nvars,A,b,Aeq,beq,lb,ub,nonlcon,IntCon,options) (15) where fun denotes the optimization function, i.e., equation (14); nvars denotes the number of elements of the x vector, nominal bounds contain j interior parameters; IntCon denotes the index of the x vector positive integer, here from 1 to j; A, b, Aeq, beq denote linear constraints, i.e. nonlcon is a nonlinear function constraint; lb and ub denote the upper and lower bounds of the variable x, i.e., lb≤x≤ub, options denotes detailed settings; Each time an actual switching point is generated, the genetic algorithm is activated to optimize all past system switching points, and the optimized nominal boundary parameters are generated and stored in the lookup table.

6. The boundary estimation system of a state-dependent switching system according to claim 4, characterized by: The optimized nominal boundary parameters are presented in the form of a multi-dimensional vector, d = 1, 2, …, D, wherein D is the number of optimization of the nominal boundary parameters, and the optimal nominal boundary parameters are obtained by the following formula: where ||·||2 denotes the two-norm, K is a given constant for the nearest neighbor algorithm, is a centering process of the nominal boundary parameters, i.e., obtaining a center point of the D nominal boundary parameters; passing through the minimum After the operation, the K nominal boundary parameters closest to the center point among the D nominal parameters are obtained, and after centering processing, they are used as the optimal nominal boundary parameters.

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