A nonlinear control law evolution method based on large language model and control effect evaluation index

Abstract

This invention discloses a nonlinear control law evolution method based on a large language model and control effect evaluation index, including initializing the control law; converting the weights of the control law operators into sampling probabilities; sampling each control law operator according to the probability distribution of the control law operators in the large language model to generate a control law formula; inputting the set of control law formulas into an aircraft dynamics simulation model to obtain a tracking error sequence and determining the evaluation index matrix of the tracking error sequence; analyzing the relationship between the control law operators and the evaluation index and outputting the update gradient of each control law operator; updating the weights of each control law operator and generating multiple new control law operators, and initializing the weights of the new control law operators; ending the iteration when the number of iterations reaches the maximum limit and outputting the control structure and control parameters of the control law, otherwise resampling and iterating; this invention solves the problem that large language models cannot be embedded in the dynamics simulation environment and evaluate the effect of control laws.

Description

Technical Field

[0001] This invention relates to the field of large language model technology, specifically to a nonlinear control law evolution method based on large language models and control effect evaluation indicators. Background Technology

[0002] Flight control is the core of flight performance. Every aircraft needs a matching flight control law. The design of the control law needs to be based on the characteristics of the aircraft and the scope of the flight mission to meet the requirements of various operating conditions and the full flight envelope. The control law includes the structure of the controller and the parameters corresponding to the controller structure. For example, the PID controller is a three-dimensional linear structure of "position-integral-derivative", and each element has its own corresponding gain coefficient.

[0003] Current control law design patterns generally involve first determining the equilibrium state of the aircraft at a specific mission point (such as steady-state flight, steady-state turn, or climb), thereby determining the steady-state operating point of the aircraft. Then, the small disturbance assumption is introduced (i.e., assuming that the aircraft only undergoes small-amplitude motions near the steady-state operating point). Based on this assumption, the complex nonlinear differential equations are transformed into a linear state-space model with a clear structure using Taylor series. After zero-pole configuration, the control structure and corresponding gain coefficient design for a certain operating point are completed.

[0004] Because the dynamic characteristics of an aircraft vary greatly throughout its flight envelope (at different altitudes and Mach numbers), a single linear controller cannot adapt to all operating conditions. Therefore, it is necessary to use the "gain scheduling" technique to extend the design to the entire envelope and complete the engineering implementation from local linear design to global nonlinear control.

[0005] The lack of embedding dynamic simulation environments within machine learning models in existing technologies makes it difficult to evaluate the control effect of control law design schemes based on "control structure-control parameters" generated by machine learning models. As a result, control law design schemes based on "control structure-control parameters" generated by machine learning models may be ineffective. Summary of the Invention

[0006] The purpose of this invention is to provide a nonlinear control law evolution method based on a large language model and control effect evaluation index, in order to solve the technical problem in the prior art that the lack of embedding a dynamic simulation environment within the machine learning model makes it difficult to evaluate the control effect of the control law design scheme of "control structure-control parameters" generated by the machine learning model.

[0007] To solve the above-mentioned technical problems, the present invention specifically provides the following technical solution:

[0008] A nonlinear control law evolution method based on a large language model and control effect evaluation index includes the following steps:

[0009] Step 100: Initialize the set of control law operators, control law coefficients, and control law operator weights;

[0010] Step 200: Convert the weights of the control law operator into sampling probabilities;

[0011] Step 300: The large language model samples each control law operator according to the probability distribution of the control law operators and combines them to generate... One control law formula;

[0012] Step 400: The control law formula set is iteratively input into the aircraft dynamics simulation model in batches. The aircraft dynamics simulation model obtains the flight state sequence based on the control sequence of the control law formula set, calculates the difference between the flight state sequence and the commanded flight state sequence to obtain the tracking error sequence, and determines the evaluation index matrix of the tracking error sequence.

[0013] Step 500: Input the set of control law operators and the corresponding evaluation index matrix into the large language model, analyze the relationship between control law operators and evaluation indexes, and output the update gradient of each control law operator.

[0014] Step 600: Update the weights of each control law operator based on the analysis results of the large language model and generate multiple new control law operators, and initialize the weights of the new control law operators proposed by the large language model.

[0015] Step 700: Determine whether the number of iterations has reached the maximum limit. If yes, end the iteration and output the control structure and control parameters of the control law. If no, determine whether the control structure and control parameters are stably generated. If the control structure and control parameters are stably generated, output the control structure and control parameters of the control law. Otherwise, return to step 100 to iterate again.

[0016] As a preferred embodiment of the present invention, the initialized set of control law operators is: The control law operator includes operations on state variables. and tracking error Common elementary functions;

[0017] The initial control law coefficients are Initialize the weights of each control law operator as follows: ;

[0018] Among them, subscript The numbers representing the control law operators are totaled. Each number corresponds to a number of control law coefficients and control law operator weights;

[0019] Subscript The numbers representing the state variables are totaled. Each number corresponds to a number of tracking errors. ;

[0020] superscript This indicates the current iteration number.

[0021] In a preferred embodiment of the present invention, a temperature coefficient is introduced in step 200. To control the balance between exploration and exploitation, the probability distribution of each control law operator. for:

[0022] ;

[0023] Each control law operator is sampled according to the sampling probability distribution, forming... The set of control law formulas is as follows:

[0024] ,in, For the set of control law operators, The probability distribution corresponding to each control law operator;

[0025] The numbers representing the control laws are in total. indivual;

[0026] superscript This indicates the current iteration number.

[0027] As a preferred embodiment of the present invention, in step 300, the specific expressions of the control law operators, the coefficients of each operator, and the sampling probabilities of each operator are input into the large language model in text form, and the large language model replies with N control law formulas in text form.

[0028] In a preferred embodiment of the present invention, in step 400, after the set of control law formulas is iteratively input into the aircraft dynamics simulation model in batches, the following planning problem is defined:

[0029] ;

[0030] Subscript The numbers representing the control law operators are totaled. indivual;

[0031] Subscript The numbers representing the state variables are totaled. indivual;

[0032] superscript Indicates the current iteration number;

[0033] Subscript Indicates the number starting from 0. A timestamp;

[0034] Finding parameters using Bayesian optimization methods To minimize the error value formed by the accumulated evaluation index matrix of the tracking error sequence, the current control law is obtained. The optimal parameters are as follows.

[0035] As a preferred embodiment of the present invention, the method for calculating the tracking error sequence and the evaluation index matrix is ​​as follows:

[0036] Definition of the first Iterative generation The set of control law formulas is as follows: ;

[0037] The first The first iteration One control law Input into the aircraft dynamics simulation model, in discrete time series The above-mentioned aircraft dynamics simulation model is based on control sequences. Obtain the flight state sequence ;

[0038] Calculate the flight state sequence With command flight state sequence The difference between The tracking error sequence is obtained. For tracking error sequence Take the absolute value The tracking error sequence and the absolute value of the error band are compared. To make a comparison, when When the accuracy of the control structure and control parameters of the control law meets the requirements, the evaluation index matrix is ​​obtained based on the tracking error sequence. .

[0039] As a preferred embodiment of the present invention, the evaluation index matrix The indicators include mean absolute error, root mean square error, maximum error, integral of absolute error, time-weighted integral of absolute error, time percentage within the error band, time percentage of settling time, and control cost.

[0040] Among them, mean absolute error ;

[0041] Root mean square error ;

[0042] Maximum error ;

[0043] Integral of absolute error ;

[0044] Time-weighted absolute error integral ;

[0045] Percentage of time within the error band ;

[0046] Adjustment time percentage ;

[0047] Control cost consumption ;

[0048] For the The next iteration, matrix The horizontal parameters (row parameters) are the various evaluation indicators, and the vertical parameters (column parameters) are the various evaluation indicators arranged according to different control laws 1, 2, 3, ..., N.

[0049] As a preferred embodiment of the present invention, in step 500, each control law operator Update gradient :

[0050] ;

[0051] Updating the gradient means that the weights change from the first... The iteration to the... The direction of change in each iteration is described using the concept of gradient, since the weights are usually vectors.

[0052] Subscript Indicates the number of the control law operator;

[0053] superscript This indicates the current iteration number.

[0054] In a preferred embodiment of the present invention, in step 600, the weights are updated based on the analysis results of the large language model, specifically using an incremental update rule:

[0055] ;

[0056] in The learning rate is represented by the gradient update of the control law operator. Then the weight of the control law operator increases;

[0057] Subscript Indicates the number of the control law operator;

[0058] superscript This indicates the current iteration number.

[0059] As a preferred embodiment of the present invention, in step 600, the new set of control law operators is: The total number of control law operators is 1, initialize weights for the new operator:

[0060] ;

[0061] in,

[0062] .

[0063] In a preferred embodiment of the present invention, in step 700, the criterion for determining whether the control structure and parameters are stably generated is as follows:

[0064] ,in, For set value, and

[0065] All control effectiveness evaluation indicators met expectations;

[0066] Subscript here Indicates the number of the control law operator;

[0067] superscript Indicates the current iteration number;

[0068] A small, artificially set quantity indicates that if the change between the current iteration and the previous iteration is less than this quantity, the iteration is considered stable.

[0069] Compared with the prior art, the present invention has the following advantages:

[0070] This invention uses dynamic simulation data as input, without requiring the dynamics to be embedded in a large language model. The dynamic simulation model required by this invention can be arbitrary and can be applied to different models for different objects. By constructing a {control law-control effect evaluation index} data pair, the evolution of control law can be completed without embedding the dynamic simulation model, thus solving the problem that large language models cannot be embedded in the dynamic simulation environment and the effect of control law cannot be evaluated. Attached Figure Description

[0071] To more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are merely exemplary, and those skilled in the art can derive other embodiments based on the provided drawings without creative effort.

[0072] Figure 1 This is a schematic diagram of the overall structure of an embodiment of the present invention; Detailed Implementation

[0073] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0074] like Figure 1 As shown, this invention provides a nonlinear control law evolution method based on a large language model and control effect evaluation indicators. It quantifies the effect of the control law proposed by the large model in specific flight control through an evaluation indicator matrix, providing a large amount of textual {control law-control effect evaluation indicator} data pairs. This constructs a method for using the large language model as the evolution of nonlinear control laws for aircraft, specifically including the following steps:

[0075] Step 100: Initialize the set of control law operators, control law coefficients, and control law operator weights.

[0076] The initial set of control law operators is The control law operator includes operations on state variables. and tracking error Common elementary functions, such as the absolute value function Symbolic functions: Trigonometric functions: , and etc., mathematically represented as .

[0077] The initial control law coefficients are ;

[0078] Initialize the weights of each control law operator as follows: ;

[0079] Among them, subscript The numbers representing the control law operators are totaled. Each number corresponds to a number of control law coefficients and control law operator weights;

[0080] Subscript The numbers representing the state variables are totaled. Each number corresponds to a number of tracking errors. ;

[0081] superscript This indicates the current iteration number.

[0082] The purpose of step 100 is to prepare three types of data:

[0083] 1) Control Law Operator: , , , wait.

[0084] 2) Coefficients of the control law operator: The coefficients of the control law operators are variable constants, and the relationship between the control law operators is a multiplicative one.

[0085] 3) Weights between control law operators, such as The weight is 1. A weight of 2 indicates sampling probability ratio big.

[0086] Step 200: Convert the weights of the control law operator into sampling probabilities;

[0087] In step 200, a temperature coefficient is introduced. To control the balance between exploration and exploitation, the probability distribution of each control law operator. for:

[0088] ;

[0089] Each control law operator is sampled according to the sampling probability distribution, forming... The set of control law formulas is as follows:

[0090] ,in, For the set of control law operators, The probability distribution corresponding to each control law operator;

[0091] The numbers representing the control laws are in total. indivual;

[0092] superscript This indicates the current iteration number.

[0093] The purpose of this step is to convert the weights of each operator (relative quantities, which do not necessarily have to be between 0 and 1, but simply indicate which is more important) into sampling probabilities (0 to 1, and the sum of the probabilities is 1), to ensure that the subsequent sampling probabilities do not have logical errors and are mathematically valid. Among them, the sampling probability of the control law operator with the larger weight is higher, while the sampling probability of the control law operator with the smaller weight is lower.

[0094] Step 300: The large language model samples each control law operator according to the probability distribution of the control law operators and combines them to generate... A control law formula.

[0095] In step 300, the specific expressions of the control law operators, the coefficients of each operator, and the sampling probabilities of each operator are input into the large language model in text form. The large language model then responds with N control law formulas in text form.

[0096] Step 400: The set of control law formulas is iteratively input into the aircraft dynamics simulation model in batches. The aircraft dynamics simulation model obtains the flight state sequence based on the control sequence of the set of control law formulas, calculates the difference between the flight state sequence and the commanded flight state sequence to obtain the tracking error sequence, and determines the evaluation index matrix of the tracking error sequence.

[0097] After iteratively inputting the set of control law formulas into the aircraft dynamics simulation model in batches, the following planning problem is defined:

[0098] ;

[0099] Subscript The numbers representing the control law operators are totaled. indivual;

[0100] Subscript The numbers representing the state variables are totaled. indivual;

[0101] superscript Indicates the current iteration number;

[0102] Subscript Indicates the number starting from 0. A timestamp;

[0103] Finding parameters using Bayesian optimization methods To minimize the error value formed by the accumulated evaluation index matrix of the tracking error sequence, the current control law is obtained. The optimal parameters are as follows.

[0104] The method for calculating the tracking error sequence and evaluation index matrix is ​​as follows:

[0105] Definition of the first Iterative generation The set of control law formulas is as follows: ;

[0106] The first The first iteration One control law Input into the aircraft dynamics simulation model, in discrete time series The above-mentioned aircraft dynamics simulation model is based on control sequences. Obtain the flight state sequence ;

[0107] Calculate the flight state sequence With command flight state sequence The difference between The tracking error sequence is obtained. For tracking error sequence Take the absolute value The absolute value of the tracking error sequence and the absolute value of the error band are compared. To make a comparison, when When the accuracy of the control structure and control parameters of the control law meets the requirements, the evaluation index matrix is ​​obtained based on the tracking error sequence. .

[0108] Evaluation index matrix The indicators include mean absolute error, root mean square error, maximum error, integral of absolute error, time-weighted integral of absolute error, time percentage within the error band, time percentage of settling time, and control cost.

[0109] Among them, mean absolute error ;

[0110] Root mean square error ;

[0111] Maximum error ;

[0112] Integral of absolute error ;

[0113] Time-weighted absolute error integral ;

[0114] Percentage of time within the error band ;

[0115] Adjustment time percentage ;

[0116] Control cost consumption ;

[0117] For the The next iteration, matrix The horizontal parameters (row parameters) are the various evaluation indicators, and the vertical parameters (column parameters) are the various evaluation indicators arranged according to different control laws 1, 2, 3, ..., N.

[0118] Step 500: Input the set of control law operators and the corresponding evaluation index matrix into the large language model, analyze the relationship between control law operators and evaluation indexes, and output the update gradient of each control law operator.

[0119] In step 500, each control law operator Update gradient :

[0120] ;

[0121] Updating the gradient means that the weights change from the first... The iteration to the... The direction of change in each iteration is described using the concept of gradient, since the weights are usually vectors.

[0122] Subscript Indicates the number of the control law operator;

[0123] superscript This indicates the current iteration number.

[0124] Step 500 still involves calling the large language model. For the currently performing multimodal large language model, only the control law operator and evaluation metric need to be input in text form. The large language model can automatically handle the relationship between the data and obtain the updated gradient, ultimately providing feedback data in text form. In traditional methods, this step is performed by experienced human experts, but the efficiency of human experts is limited, so it is directly replaced by the large language model.

[0125] Step 600: Update the weights of each control law operator based on the analysis results of the large language model and generate multiple new control law operators, and initialize the weights of the new control law operators proposed by the large language model.

[0126] In step 600, the weights are updated based on the analysis results of the large language model, specifically using an incremental update rule:

[0127] ;

[0128] in The learning rate is represented by the gradient update of the control law operator. Then the weight of the control law operator increases;

[0129] Subscript Indicates the number of the control law operator;

[0130] superscript This indicates the current iteration number.

[0131] The new set of control law operators is: The total number of control law operators is 1, initialize weights for the new operator:

[0132] ;

[0133] in,

[0134] .

[0135] The large language model will automatically determine whether to generate new control law operators based on the current input data: control law operators and evaluation index matrix, because the large language model itself has a built-in analytical function. For example, it may input elementary functions such as sin, cos, and tan as operators, but during the iteration process, the large language model may automatically add sinh, cosh, and tanh functions as supplementary operators.

[0136] Step 700: Determine whether the number of iterations has reached the maximum limit. If yes, end the iteration and output the control structure and control parameters of the control law. If no, determine whether the control structure and control parameters are stably generated. If the control structure and control parameters are stably generated, output the control structure and control parameters of the control law. Otherwise, return to step 100 to iterate again.

[0137] In step 700, the criteria for determining whether the control structure and parameters are generated stably are as follows:

[0138] ,in, For set value, and

[0139] All control effectiveness evaluation indicators met expectations;

[0140] Subscript here Indicates the number of the control law operator;

[0141] superscript Indicates the current iteration number;

[0142] A small, manually set quantity indicates that if the change between the current iteration and the previous iteration is less than this quantity, the iteration is considered stable.

[0143] Typically, specific task evaluation metrics are provided by human experts, and these metrics vary from task to task. The desired outcome is achieved when the best evaluation metric in the evaluation metric matrix meets the requirements. Alternatively, the best metric can be considered to be superior to the metric calculated using the initial control law formula, thus satisfying the expectation.

[0144] This invention quantifies the effect of the control law proposed by the large model in specific flight control by evaluating the index matrix. It provides a large number of textual {control law-control effect evaluation index} data pairs and constructs a new method for using a large language model to evolve the nonlinear control law of an aircraft.

[0145] This invention uses dynamic simulation data as input, without requiring the dynamics to be embedded in a large language model. The dynamic simulation model required by this invention can be arbitrary and applicable to different models for different objects. Generally, training and fine-tuning large language models is difficult, and it is hard to train large language models specifically for control law evolution. However, this application achieves control law evolution without embedding a dynamic simulation model by constructing a {control law-control effect evaluation index} data pair, solving the problem that large language models cannot be embedded in dynamic simulation environments and evaluate control law effects. This allows for large-scale pre-evaluation and preprocessing of conjectures of potential control law structures and coefficients generated from a large number of sources, ultimately enabling the exploration of limiting control laws to be effectively advanced and converged.

[0146] The above embodiments are merely exemplary embodiments of this application and are not intended to limit this application. The scope of protection of this application is defined by the claims. Those skilled in the art can make various modifications or equivalent substitutions to this application within its substance and scope of protection, and such modifications or equivalent substitutions should also be considered to fall within the scope of protection of this application.

Claims

1. A nonlinear control law evolution method based on a large language model and control effect evaluation index, characterized in that, Includes the following steps: Step 100: Initialize the set of control law operators, control law coefficients, and control law operator weights; Step 200: Convert the weights of the control law operator into sampling probabilities; Step 300: The large language model samples each control law operator according to the probability distribution of the control law operators and combines them to generate... One control law formula; Step 400: The control law formula set is iteratively input into the aircraft dynamics simulation model in batches. The aircraft dynamics simulation model obtains the flight state sequence based on the control sequence of the control law formula set, calculates the difference between the flight state sequence and the commanded flight state sequence to obtain the tracking error sequence, and determines the evaluation index matrix of the tracking error sequence. Step 500: Input the set of control law operators and the corresponding evaluation index matrix into the large language model, analyze the relationship between control law operators and evaluation indexes, and output the update gradient of each control law operator. Step 600: Update the weights of each control law operator based on the analysis results of the large language model and generate multiple new control law operators, and initialize the weights of the new control law operators proposed by the large language model. Step 700: Determine whether the number of iterations has reached the maximum limit. If yes, end the iteration and output the control structure and control parameters of the control law. If no, determine whether the control structure and control parameters are stably generated. If the control structure and control parameters are stably generated, output the control structure and control parameters of the control law. Otherwise, return to step 100 to iterate again.

2. The nonlinear control law evolution method based on a large language model and control effect evaluation index as described in claim 1, characterized in that, The initial set of control law operators is The control law operator includes operations on state variables. and tracking error Common elementary functions; The initial control law coefficients are Initialize the weights of each control law operator as follows: ; Among them, subscript The numbers representing the control law operators are totaled. Each number corresponds to a number of control law coefficients and control law operator weights; Subscript The number represents the state variable; there are a total of Each number corresponds to a number of tracking errors. ; superscript This indicates the current iteration number.

3. The nonlinear control law evolution method based on a large language model and control effect evaluation index as described in claim 1, characterized in that, In step 200, a temperature coefficient is introduced. To control the balance between exploration and exploitation, the probability distribution of each control law operator. for: ； Each control law operator is sampled according to the sampling probability distribution, forming... The set of control law formulas is as follows: ,in, For the set of control law operators, The probability distribution corresponding to each control law operator; The numbers representing the control laws are in total. indivual; superscript This indicates the current iteration number.

4. The nonlinear control law evolution method based on a large language model and control effect evaluation index as described in claim 1, characterized in that, In step 300, the specific expressions of the control law operators, the coefficients of each operator, and the sampling probabilities of each operator are input into the large language model in text form. The large language model then responds with N control law formulas in text form.

5. The nonlinear control law evolution method based on a large language model and control effect evaluation index according to claim 1, characterized in that, In step 400, after iteratively inputting the set of control law formulas into the aircraft dynamics simulation model in batches, the following planning problem is defined: ； Subscript The numbers representing the control law operators are totaled. indivual; Subscript The number represents the state variable; there are a total of indivual; superscript Indicates the current iteration number; Subscript Indicates the number starting from 0. A timestamp; Finding parameters using Bayesian optimization methods To minimize the error value formed by the accumulated evaluation index matrix of the tracking error sequence, the current control law is obtained. The optimal parameters are as follows.

6. The nonlinear control law evolution method based on a large language model and control effect evaluation index as described in claim 5, characterized in that, The method for calculating the tracking error sequence and evaluation index matrix is ​​as follows: Definition of the first Iterative generation The set of control law formulas is as follows: ; The first The first iteration One control law Input into the aircraft dynamics simulation model, in discrete time series The above-mentioned aircraft dynamics simulation model is based on control sequences. Obtain the flight state sequence ; Calculate the flight state sequence With command flight state sequence The difference between The tracking error sequence is obtained. For tracking error sequence Take the absolute value The tracking error sequence and the absolute value of the error band are compared. To make a comparison, when When the accuracy of the control structure and control parameters of the control law meets the requirements, the evaluation index matrix is ​​obtained based on the tracking error sequence. .

7. The nonlinear control law evolution method based on a large language model and control effect evaluation index as described in claim 6, characterized in that, Evaluation index matrix The indicators include mean absolute error, root mean square error, maximum error, integral of absolute error, time-weighted integral of absolute error, time percentage within the error band, time percentage of settling time, and control cost. Among them, mean absolute error ; Root mean square error ; Maximum error ; Integral of absolute error ; Time-weighted absolute error integral ; Percentage of time within the error band ; Adjustment time percentage ; Control cost consumption ; For the The next iteration, matrix The horizontal parameters (row parameters) are the various evaluation indicators, and the vertical parameters (column parameters) are the various evaluation indicators arranged according to different control laws 1, 2, 3, ..., N.

8. The nonlinear control law evolution method based on a large language model and control effect evaluation index according to claim 1, characterized in that, In step 500, each control law operator Update gradient : ； Updating the gradient means that the weights change from the first... The iteration to the... The direction of change in each iteration is described using the concept of gradient, since the weights are usually vectors. Subscript Indicates the number of the control law operator; superscript This indicates the current iteration number.

9. The nonlinear control law evolution method based on a large language model and control effect evaluation index according to claim 1, characterized in that, In step 600, the weights are updated based on the analysis results of the large language model, specifically using an incremental update rule: ； in The learning rate is represented by the gradient update of the control law operator. Then the weight of the control law operator increases; Subscript Indicates the number of the control law operator; superscript This indicates the current iteration number.

10. The nonlinear control law evolution method based on a large language model and control effect evaluation index according to claim 1, characterized in that, In step 600, the new set of control law operators is: The total number of control law operators is 1, initialize weights for the new operator: ； in, 。 11. The nonlinear control law evolution method based on a large language model and control effect evaluation index according to claim 1, characterized in that, In step 700, the criteria for determining whether the control structure and parameters are generated stably are as follows: ,in, For set value, and All control effectiveness evaluation indicators met expectations; Subscript here Indicates the number of the control law operator; superscript Indicates the current iteration number; A small, artificially set quantity indicates that if the change between the current iteration and the previous iteration is less than this quantity, the iteration is considered stable.

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