A fractional order chaotic system parameter identification method, system, device and medium

Abstract

The present application relates to a kind of sensitivity-based fractional chaotic system parameter identification method, system, equipment and readable storage medium.The measurement response data of fractional chaotic system time domain signal is collected, the calculation response data of system is calculated using step-by-step strategy, the least square objective function of measurement response data and calculation response data is established, the least square objective function is linearized, sensitivity matrix is constructed, Tikhonov regularization and confidence limit are introduced to solve the ill-posed problem that may occur in identification, the optimal solution that satisfies the minimum value of least square objective function is solved by step-by-step response sensitivity algorithm, and the fractional order and system parameters of the system are determined according to the optimal solution.The fractional chaotic system can be accurately parameter identified, it is suitable for non-commensurate fractional chaotic system with different fractional orders, and the parameter identification efficiency of fractional chaotic system is improved.

Description

Technical Field

[0001] This invention relates to the field of fractional chaotic systems, and more particularly to a sensitivity-based method, system, computer device, and readable storage medium for identifying parameters of fractional chaotic systems. Background Technology

[0002] Fractional calculus is widely used in various engineering research fields, extending integer calculus to any order. Fractional models differ from integer models in several ways: the fractional derivative is a non-ideal operator, which can be divided into non-integer and integer values; it is a nonlocal operator with unlimited storage capacity for the entire dynamic evolution process; and it is merely an additional parameter to improve the flexibility of system modeling. Compared to integer models, fractional models can more accurately describe the dynamic behavior of a system.

[0003] With the development of numerical methods for fractional-order calculus, chaos can be modeled more accurately. Chaos is an interesting nonlinear phenomenon, highly sensitive to even small perturbations. Fractional-order chaotic systems are particularly sensitive to initial values ​​and exhibit long-term unpredictability. Currently, the dynamic behavior of fractional-order chaotic systems, including bifurcation, chaotic control, and chaotic synchronization, is a hot research topic. When the fractional order and system parameters are known, there are many methods to control and synchronize fractional-order chaotic systems. However, for asymmetric fractional-order chaotic systems with unknown fractional order and system parameters, control and synchronization present a very challenging problem. To achieve control and synchronization of such systems, we typically need to obtain precise values ​​for the system parameters and the fractional order. Summary of the Invention

[0004] This invention provides a sensitivity-based method, system, computer device, and readable storage medium for identifying parameters of fractional-order chaotic systems. This addresses the technical problem of controlling and synchronizing asymmetric fractional-order chaotic systems with unknown fractional-order order and parameters. It obtains accurate values ​​of the fractional-order order and system parameters of the fractional-order chaotic system, thereby enabling control and synchronization of the system.

[0005] To address the aforementioned technical problems, in a first aspect, embodiments of the present invention provide a method for identifying parameters of a fractional-order chaotic system based on sensitivity, the method comprising:

[0006] The numerical discretization scheme of the fractional-order chaotic system is derived based on the Grünwald-Letnikov definition and the short memory principle.

[0007] The measurement response data of the time-domain signal of the fractional-order chaotic system is collected, the calculation step size is set, and the calculation response data is obtained step by step according to the numerical discretization format and the measurement response data.

[0008] A least-squares objective function is established based on the calculated response data and the measured response data;

[0009] The least squares objective function is linearized to construct a sensitivity matrix. The optimal solution that satisfies the minimum value of the least squares objective function is obtained by using a stepwise response sensitivity algorithm. The fractional order and system parameters of the fractional chaotic system are determined based on the optimal solution.

[0010] In a further embodiment, the derivation of the numerical discretization scheme for the fractional-order chaotic system based on the Grünwald-Letnikov definition and the short memory principle includes:

[0011] The specific equations of the fractional-order chaotic system are expressed using a fractional-order Lorenz-Chen-Lü system:

[0012]

[0013] Where α1, α2, and α3 are the fractional orders of the fractional chaotic system, a is the parameter of the fractional chaotic system, and x(t), y(t), and z(t) are the responses of the fractional chaotic system with respect to time t, respectively.

[0014] By combining the Grünwald-Letnikov definition and the short memory principle, the specific equations of the fractional-order chaotic system are discretized to obtain the numerical discretization scheme:

[0015]

[0016] Where x(t) k ), y(t) k ), z(t) k Let be the response of the fractional-order chaotic system at time k. is the binomial coefficient, and h is the calculation step size.

[0017] In a further embodiment, the step of progressively calculating the computational response data based on the numerical discrete format and the measurement response data includes:

[0018] The measured response data is sequentially substituted into the numerical discrete format to calculate the next step response data corresponding to the measured response data step by step, and the calculated response data is composed of the response data obtained in each step of the calculation.

[0019] In a further embodiment, establishing the least squares objective function based on the calculated response data and the measured response data specifically involves:

[0020]

[0021] in, Let x represent the measurement response data at time k (k = 1, 2, ..., N). st (t k ) represents the computational response data at time k (k = 1, 2, ..., N), a = [a, α1, α2, α3] represents the set of fractional orders to be identified and system parameters, and R st (a) represents a nonlinear implicit function with respect to a. This represents a 2-norm matrix.

[0022] In a further embodiment, the linearization of the least squares objective function, the construction of a sensitivity matrix, and the solving of the optimal solution that satisfies the minimum value of the least squares objective function through a stepwise response sensitivity algorithm include:

[0023] The least squares objective function exist Linearization is performed at this point, retaining the first-order terms, specifically:

[0024]

[0025] in, In response to residuals, Update the parameter value. For stepwise response sensitivity matrix;

[0026] The stepwise response sensitivity matrix is ​​solved using a hybrid strategy.

[0027] In a further embodiment, the linearization of the least squares objective function, the construction of the sensitivity matrix, and the solving for the optimal solution that satisfies the minimum value of the least squares objective function using a stepwise response sensitivity algorithm further include:

[0028] Introducing Tikhonov regularization, the linearized least squares objective function is:

[0029]

[0030] Where λ is the regularization parameter, δa λ Specifically, it is expressed as follows:

[0031]

[0032] Where I is the identity matrix;

[0033] Introduce confidence region constraints and set the following consistency metrics:

[0034]

[0035] Under the condition of satisfying the confidence region constraint, the optimal solution of the objective function is found by selecting an appropriate regularization parameter.

[0036] In a further embodiment, the stepwise response sensitivity matrix is ​​solved using a hybrid strategy, specifically as follows:

[0037] The fractional-order chaotic system is rewritten by replacing the fractional-order sensitivity with a difference scheme.

[0038] Solve the rewritten fractional-order chaotic system to obtain the sensitivity response of the fractional-order chaotic system with respect to each fractional order;

[0039] The sensitivity response of the parameters of the fractional-order chaotic system is solved using the direct differentiation method;

[0040] The stepwise response sensitivity matrix is ​​obtained based on the sensitivity responses of each fractional order of the fractional chaotic system and the sensitivity responses of the system parameters.

[0041] Secondly, embodiments of the present invention provide a sensitivity-based fractional-order chaotic system parameter identification system, the system comprising:

[0042] Preprocessing module: used to derive the numerical discretization scheme of the fractional-order chaotic system according to the Grünwald-Letnikov definition and the short memory principle;

[0043] The module for obtaining computational response data is used to collect the measurement response data of the time-domain signal of the fractional-order chaotic system, set the calculation step size, and calculate the computational response data step by step according to the numerical discretization format and the measurement response data.

[0044] Objective function establishment module: used to establish a least squares objective function based on the calculated response data and the measured response data;

[0045] The computation module is used to linearize the least squares objective function, construct the sensitivity matrix, solve for the optimal solution that satisfies the minimum value of the least squares objective function through a stepwise response sensitivity algorithm, and determine the fractional order and system parameters of the fractional chaotic system based on the optimal solution.

[0046] Thirdly, embodiments of the present invention provide a computer device, including a memory, a processor, and a transceiver, which are connected to each other via a bus; the memory is used to store a set of computer program instructions and data, and can transmit the stored data to the processor, and the processor can execute the program instructions stored in the memory to perform the above-described method steps.

[0047] Fourthly, embodiments of the present invention provide a computer-readable storage medium storing a computer program that, when executed, implements the above-described method steps.

[0048] This invention provides a sensitivity-based method, system, computer device, and readable storage medium for identifying parameters of fractional-order chaotic systems. The method involves acquiring measurement response data of the time-domain signal of the fractional-order chaotic system, calculating the computational response data of the system using a stepwise strategy, establishing a least-squares objective function for the measurement and computational response data, linearizing the least-squares objective function, and introducing Tikhonov regularization and confidence region constraints to address potential ill-posed problems during identification. The optimal solution satisfying the minimum value of the least-squares objective function is found using a stepwise response sensitivity algorithm. Based on the optimal solution, the fractional-order order and system parameters of the fractional-order chaotic system are determined. This invention requires only short-time time-domain response data to identify parameters of fractional-order chaotic systems, is insensitive to noise, and has very high accuracy. It can achieve control and synchronization of asymmetric fractional-order chaotic systems with unknown fractional-order order and system parameters. Attached Figure Description

[0049] Figure 1 This is a schematic diagram of the steps of a sensitivity-based fractional-order chaotic system parameter identification method in an embodiment of the present invention;

[0050] Figure 2 This is the fractional-order Lorenz, Lü, and Chen system attractor in the embodiments of the present invention;

[0051] Figure 3 This is a schematic diagram of the stepwise objective function of the fractional Lorenz system in an embodiment of the present invention;

[0052] Figure 4 This is a schematic diagram of the sensitivity matrix solution steps in an embodiment of the present invention;

[0053] Figure 5 This is a diagram showing the parameter identification results of a fractional-order chaotic system under different noise levels in an embodiment of the present invention.

[0054] Figure 6 This is a schematic diagram of a sensitivity-based fractional-order chaotic system parameter identification system in an embodiment of the present invention;

[0055] Figure 7 This is a schematic diagram of a computer device according to an embodiment of the present invention. Detailed Implementation

[0056] The embodiments of the present invention are described in detail below with reference to the accompanying drawings. The embodiments are provided for illustrative purposes only and should not be construed as limiting the scope of the invention. The accompanying drawings are for reference and illustration only and do not constitute a limitation on the scope of protection of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of this invention.

[0057] Please refer to Figure 1 In an embodiment of the present invention, a sensitivity-based method for identifying parameters of a fractional-order chaotic system is provided. In a fractional-order chaotic system, this method is applied to determine the fractional order of the system and the precise values ​​of the system parameters, including the following steps:

[0058] S1. Based on the Grünwald-Letnikov definition and the short memory principle, derive the numerical discretization scheme for fractional-order chaotic systems.

[0059] Taking the general form of the fractional unified system as an example, also known as the fractional Lorenz-Chen-Lü system, its specific expression is as follows:

[0060]

[0061] Where α1, α2, and α3 are the fractional orders of the fractional chaotic system, a is the parameter of the fractional chaotic system, and x(t), y(t), and z(t) are the system responses with respect to time t.

[0062] In the above equation, when the fractional order α1 = α2 = α3 = 0.9 and the system parameters a = 0.4, a = 0.8, or a = 1, the system exhibits characteristics equivalent to the fractional Lorenz, Lü, and Chen systems, with specific attractors as follows: Figure 2 .

[0063] By combining the Grünwald-Letnikov definition and the short memory principle, the specific equations of the above fractional chaotic system are discretized to obtain the numerical discretization scheme:

[0064]

[0065] Where x(t) k ), y(t) k ), z(t) k Let be the system response at time k. is the binomial coefficient, and h is the calculation step size.

[0066] The solution obtained recursively is as follows:

[0067] S2. Collect the measurement response data of the time-domain signal of the fractional-order chaotic system, set the calculation step size, and calculate the calculation response data step by step according to the numerical discretization format and the measurement response data.

[0068] Take a segment of time-domain measurement response signal in, x(t N-1 ), y(t) N-1), z(t) N-1 ) represents the system's time t N-1 The response. And based on the numerical discrete equation, it can be calculated step by step. The next step is to calculate the response x. st (t1),x st (t2),…,x st (t N ), where the calculation step size is specifically h. st .by Taking y(t0), z(t0) as an example, the next computational response data x of the fractional-order chaotic system is obtained using a numerical discretization scheme. st (t1)=(x st (t1),y st (t1),z st (t1)), the specific calculation method is as follows:

[0069]

[0070] Using the same method based on the measured response data The measurement response data were obtained by sequential calculation. The computational response data x of the corresponding fractional-order chaotic system st (t2),x st (t3),…,x st (t N ).

[0071] S3. Establish a least squares objective function based on the calculated response data and the measured response data. The least squares objective function is established based on the calculated response data and the measured response data as follows:

[0072]

[0073] in, Let x represent the measurement response data at time k (k = 1, 2, ..., N). st (t k ) represents the computational response data at time k (k = 1, 2, ..., N), a = [a, α1, α2, α3] represents the set of fractional orders to be identified and system parameters, and R st (a) represents a nonlinear implicit function with respect to a. This represents a 2-norm matrix.

[0074] like Figure 3 The figure shows a schematic diagram of the stepwise objective function of a fractional Lorenz system. It can be seen that the established stepwise objective function has a minimum value within a certain parameter region.

[0075] S4. Linearize the least squares objective function, construct the sensitivity matrix, and solve for the optimal solution that satisfies the minimum value of the least squares objective function through the stepwise response sensitivity algorithm. Determine the fractional order and system parameters of the fractional chaotic system based on the optimal solution.

[0076] Given a set of initial parameter values, the nonlinear least squares objective function described above can be solved using an iterative method. The key issue then lies in determining a suitable iterative update from the known parameters. In this embodiment of the invention, the objective function... exist Linearization is performed at the point where first-order terms are retained, specifically including:

[0077]

[0078] in, In response to residuals, Update the parameter value. This is the stepwise response sensitivity matrix. Its specific form at time k is as follows:

[0079]

[0080] in The system calculates the response x at time k. st Regarding parameters The set of progressive sensitivities, specifically, taking a fractional-order unified system as an example:

[0081]

[0082] The sensitivity matrix in the above equation can be obtained by solving a hybrid strategy, such as... Figure 4 As shown, the specific steps are as follows:

[0083] S10. The fractional-order chaotic system is rewritten by replacing the fractional-order sensitivity with a difference scheme.

[0084] The sensitivity is replaced by a difference scheme instead of fractional order, and α is set. i To obtain the parameters after a small perturbation e, the perturbed system is rewritten, with α1 as:

[0085]

[0086] S20. Solve the rewritten fractional-order chaotic system to obtain the sensitivity response of the fractional-order chaotic system with respect to each fractional order.

[0087] Solving the rewritten fractional-order chaotic system yields the numerical solution to the above equation. The difference response at time k is then:

[0088]

[0089] The above shows the sensitivity response of the fractional chaotic system with respect to α1. The same method is used to obtain the sensitivity responses of the fractional chaotic system with respect to α2 and α3.

[0090] S30. Use the direct differential method to solve the sensitivity response of the fractional chaotic system to the system parameters.

[0091] The sensitivity response of the fractional-order chaotic system to system parameters is solved using the direct differentiation method. Taking a fractional-order unified system as an example, the sensitivity response of the fractional-order chaotic system to system parameter a at time k is obtained as follows:

[0092]

[0093] S40. Obtain the stepwise response sensitivity matrix based on the sensitivity response of the fractional-order chaotic system to each fractional order and the sensitivity response of the system parameters.

[0094] Substitute the sensitivity responses of each fractional order of the obtained fractional chaotic system and the sensitivity responses of the system parameters into the following values: Obtain the stepwise response sensitivity matrix.

[0095] The stepwise response sensitivity matrix of the fractional-order chaotic system with respect to each fractional order and system parameters is obtained using the above hybrid strategy. Since the linearized objective function may be ill-posed, Tikhonov regularization and confidence region constraints can be introduced, and the iterative update amount can be calculated in combination with the system response parameters.

[0096] Introducing Tikhonov regularization, the linearization objective function is transformed as follows:

[0097]

[0098] Where λ is the regularization parameter, then δa λ The specific form is as follows:

[0099]

[0100] Where I is the identity matrix, and δa is determined by the regularization parameter λ. The L-curve method is a commonly used method for finding appropriate regularization parameters. The essence of the L-curve method is to calculate ‖δa‖ using different regularization parameters λ. 2 and The L-curve method only considers the linearized approximate objective function, without taking into account the nonlinearity of the original objective function. Obtaining an exact solution requires, for a chosen λ or δa, that the approximate objective function closely approximates the original objective function.

[0101] For fractional-order chaotic systems, considering the nonlinearity of the least-squares objective function, the norm ‖δa‖ is updated. 2 It should be small enough to ensure that the approximate objective function matches the original objective function well. Therefore, it is necessary to introduce a confidence region constraint and set the following consistency index:

[0102]

[0103] The confidence region constraint ensures that the linearized approximate objective function is sufficiently close to the nonlinear original objective function. Generally, good consistency requires the agreement index ρ... cr It should be greater than a positive value. Based on experience, the agreement index should satisfy condition ρ. cr ∈[0.25, 0.75]. Under the condition of satisfying the confidence region constraint, choosing an appropriate regularization parameter can find the optimal solution of the objective function. Therefore, under the condition of satisfying... Under the conditions, there are

[0104] and

[0105] As shown in the above equation, if the regularization parameter λ is chosen to be sufficiently large, the update norm ‖δa‖ will be updated. 2 It is small enough to easily satisfy the confidence region constraint. In other words, the final regularization parameter λ can be obtained through an iterative process to ensure the confidence region constraint is met.

[0106] The above method can be used to obtain suitable regularization parameters λ and update norm ‖δa‖. 2 When the iteration termination condition is met, the optimal solution is obtained. Based on the optimal solution, the fractional order of the fractional chaotic system and the precise values ​​of the system parameters are determined.

[0107] Figure 5 The graph shows the parameter identification results of a fractional-order chaotic system under different noise levels. Figure 5 It can be concluded that, under noise-free conditions and with ∈ = 0.05, the relative error of the identification results for the three systems is below 0.2%, indicating accurate parameter identification. Even when the noise increases to ∈ = 0.3, the maximum relative error of parameter identification for the three systems does not exceed 7.2%, which is acceptable. This demonstrates that the parameter identification technology is insensitive to noise and has good noise resistance.

[0108] In summary, this invention primarily relies on the memory properties of fractional-order operators and the sensitivity of fractional-order chaotic systems to long-term data. It collects measurement response data of the time-domain signal of the fractional-order chaotic system, calculates the computational response data using a step-by-step strategy, establishes a least-squares objective function between the measurement and computational response data, linearizes the least-squares objective function, introduces Tikhonov regularization and confidence region constraints to address ill-posed problems that may arise during identification, and uses a step-by-step response sensitivity algorithm to find the optimal solution that satisfies the minimum value of the least-squares objective function. Based on the optimal solution, the fractional-order order and system parameters of the fractional-order chaotic system are determined. This method can accurately identify the parameters of fractional-order chaotic systems, is applicable to asymmetric fractional-order chaotic systems with different fractional orders, and improves the efficiency of parameter identification for fractional-order chaotic systems.

[0109] In this embodiment of the invention, a sensitivity-based fractional-order chaotic system parameter identification system is also provided, such as... Figure 6 As shown, the system includes:

[0110] Preprocessing module 1: used to derive the numerical discretization scheme of the fractional-order chaotic system based on the Grünwald-Letnikov definition and the short memory principle.

[0111] Module 2 for obtaining computational response data: It is used to collect the measurement response data of the time-domain signal of the fractional-order chaotic system, set the calculation step size, and calculate the computational response data step by step according to the numerical discretization format and the measurement response data.

[0112] Objective function establishment module 3: used to establish a least squares objective function based on the calculated response data and the measured response data.

[0113] Calculation module 4: used to linearize the least squares objective function, construct the sensitivity matrix, solve for the optimal solution that satisfies the minimum value of the least squares objective function through the stepwise response sensitivity algorithm, and determine the fractional order and system parameters of the fractional chaotic system based on the optimal solution.

[0114] Specific limitations regarding the sensitivity-based fractional-order chaotic system parameter identification system can be found in the aforementioned limitations regarding the sensitivity-based fractional-order chaotic system parameter identification method, and will not be repeated here. Those skilled in the art will recognize that the various modules and steps described in conjunction with the embodiments disclosed in this application can be implemented in hardware, software, or a combination of both. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0115] like Figure 7 As shown in the figure, an embodiment of the present invention provides a computer device including a memory, a processor, and a transceiver, which are connected to each other via a bus; the memory is used to store a set of computer program instructions and data, and can transmit the stored data to the processor; the processor can execute the program instructions stored in the memory to perform the steps of the above-described sensitivity-based fractional-order chaotic system parameter identification method.

[0116] The memory may include volatile memory or non-volatile memory, or both; the processor may be a central processing unit, a microprocessor, an application-specific integrated circuit, a programmable logic device, or a combination thereof. By way of example, but not limitation, the programmable logic device described above may be a complex programmable logic device, a field-programmable gate array, a general-purpose array logic, or any combination thereof.

[0117] In addition, memory can be a physically independent unit or integrated with the processor.

[0118] Those skilled in the art will understand that Figure 7 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have the same component arrangement.

[0119] This invention also provides a readable storage medium storing a processor-executable computer program, which, when executed by a processor, is used to perform the sensitivity-based fractional-order chaotic system parameter identification method.

[0120] The processor can be composed of any or more processor chips, including microcontrollers, FPGAs, CPLDs, DSPs, and ARMs, along with their peripheral circuits and programs. In this embodiment, the storage medium used for the memory can be, but is not limited to, electrical, magnetic, optical, infrared, or semiconductor systems, devices, or combinations thereof. Specifically, it can include, but is not limited to, electrical connections with one or more wires, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fibers, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any combination thereof. The storage medium can be any tangible medium containing or storing a program, which can be executed by an instruction execution system. The program contained in the memory can be transmitted using any suitable medium, including but not limited to: wireless, wires, optical fibers, RF, etc., or any suitable combination thereof. The program's code can be written in one or more programming languages ​​or a combination thereof, including object-oriented programming languages ​​such as Java, Smalltalk, and C++, as well as conventional procedural programming languages ​​such as C or similar languages. The program can be executed entirely on the user side, partially on the user side, as a standalone software package, partially on the user side and partially remotely, or entirely remotely or on a server.

[0121] Similarly, the content of the above method embodiments is applicable to this storage medium embodiment. The specific functions implemented in this storage medium embodiment are the same as those in the above method embodiments, and the beneficial effects achieved are also the same as those achieved in the above method embodiments.

[0122] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when the computer program is executed, it can include the processes of the embodiments of the above methods.

[0123] This embodiment provides a sensitivity-based parameter identification method, system, computer device, and readable storage medium for fractional-order chaotic systems. It primarily relies on the memory properties of fractional-order operators and the sensitivity of fractional-order chaotic systems to long-term data. The method involves collecting measurement response data of the time-domain signal of the fractional-order chaotic system, calculating the computational response data of the system using a stepwise strategy, establishing a least-squares objective function for both the measurement and computational response data, linearizing the least-squares objective function, and introducing Tikhonov regularization and confidence region constraints to address potential ill-posed problems during identification. The optimal solution satisfying the minimum value of the least-squares objective function is found using a stepwise response sensitivity algorithm. Based on the optimal solution, the fractional-order order and system parameters of the fractional-order chaotic system are determined. This method can accurately identify the parameters of fractional-order chaotic systems and is applicable to asymmetric fractional-order chaotic systems with different fractional orders, thus improving the efficiency of parameter identification for fractional-order chaotic systems.

[0124] The embodiments described above are merely preferred embodiments of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various improvements and substitutions without departing from the technical principles of this invention, and these improvements and substitutions should also be considered within the scope of protection of this application. Therefore, the scope of protection of this patent application should be determined by the scope of the claims.

Claims

1. A sensitivity-based fractional-order chaotic system parameter identification method, characterized in that, The method includes: The numerical discretization scheme of the fractional-order chaotic system is derived based on the Grünwald-Letnikov definition and the short memory principle. The measurement response data of the time-domain signal of the fractional-order chaotic system is collected, the calculation step size is set, and the calculation response data is obtained step by step according to the numerical discretization format and the measurement response data. A least-squares objective function is established based on the calculated response data and the measured response data; Linearize the least squares objective function, construct a sensitivity matrix, and solve for the optimal solution that satisfies the minimum value of the least squares objective function through a stepwise response sensitivity algorithm. Determine the fractional order and system parameters of the fractional order chaotic system based on the optimal solution. The least squares objective function is specifically as follows: wherein, denotes the measured response data at time k, k = 1, 2,... N, denotes the calculated response data at time k, k = 1, 2,... N, denotes the set of fractional order and system parameters to be identified, denotes the nonlinear implicit function for denotes the 2-norm matrix.​ 2. The sensitivity-based fractional-order chaotic system parameter identification method as described in claim 1, characterized in that, The derivation of the numerical discretization scheme for the fractional-order chaotic system based on the Grünwald-Letnikov definition and the short memory principle includes: Using fractional Lorenz-Chen-L The system represents the specific equations of the fractional-order chaotic system: , in, , , For a fractional-order chaotic system, the fractional order is... For parameters of a fractional-order chaotic system, , , These are fractional-order chaotic systems with respect to time. The response; By combining the Grünwald-Letnikov definition and the short memory principle, the specific equations of the fractional-order chaotic system are discretized to obtain the numerical discretization scheme: ， in, , , For the first The response of a fractional-order chaotic system at time step The coefficients are binomial coefficients. , To calculate the step size.

3. The sensitivity-based fractional-order chaotic system parameter identification method as described in claim 1, characterized in that, The step-by-step calculation of the computational response data based on the numerical discretization format and the measurement response data includes: The measured response data is sequentially substituted into the numerical discrete format to calculate the next step response data corresponding to the measured response data step by step, and the calculated response data is composed of the response data obtained in each step of the calculation.

4. The sensitivity-based fractional-order chaotic system parameter identification method as described in claim 1, characterized in that, The process of linearizing the least squares objective function, constructing a sensitivity matrix, and solving for the optimal solution that satisfies the minimum value of the least squares objective function using a stepwise response sensitivity algorithm includes: The least squares objective function exist Linearization is performed at this point, retaining the first-order terms, specifically: in, In response to residuals, Update the parameter value. For stepwise response sensitivity matrix; The stepwise response sensitivity matrix is ​​solved using a hybrid strategy.

5. The sensitivity-based fractional-order chaotic system parameter identification method as described in claim 4, characterized in that, The process of linearizing the least squares objective function, constructing a sensitivity matrix, and solving for the optimal solution that satisfies the minimum value of the least squares objective function using a stepwise response sensitivity algorithm further includes: Introducing Tikhonov regularization, the linearized least squares objective function is: in, For regularization parameters, Specifically, it is expressed as follows: ， Where I is the identity matrix; Introduce confidence region constraints and set the following consistency metrics: ； Under the condition of satisfying the confidence region restriction, select appropriate regularization parameters to find the objective function. The optimal solution.

6. The sensitivity-based fractional-order chaotic system parameter identification method as described in claim 4, characterized in that, The method of solving the stepwise response sensitivity matrix using a hybrid strategy is as follows: The fractional-order chaotic system is rewritten by replacing the fractional-order sensitivity with a difference scheme; Solve the rewritten fractional-order chaotic system to obtain the sensitivity response of the fractional-order chaotic system with respect to each fractional order; The sensitivity response of the fractional-order chaotic system to system parameters is solved using the direct differentiation method; The stepwise response sensitivity matrix is ​​obtained based on the sensitivity responses of the fractional-order chaotic system to each fractional order and the sensitivity responses of the system parameters.

7. A sensitivity-based fractional-order chaotic system parameter identification system, characterized in that, The system includes: Preprocessing module: used to derive the numerical discretization scheme of the fractional-order chaotic system according to the Grünwald-Letnikov definition and the short memory principle; The module for obtaining computational response data is used to collect the measurement response data of the time-domain signal of the fractional-order chaotic system, set the calculation step size, and calculate the computational response data step by step according to the numerical discretization format and the measurement response data. Objective function establishment module: used to establish a least squares objective function based on the calculated response data and the measured response data; The calculation module is used to linearize the least squares objective function, construct the sensitivity matrix, solve for the optimal solution that satisfies the minimum value of the least squares objective function through the stepwise response sensitivity algorithm, and determine the fractional order and system parameters of the fractional chaotic system based on the optimal solution. The least squares objective function is specifically as follows: in, express Measurement response data at time points, k=1,2,...N. express The calculated response data at time points k=1,2,...N. This represents the set of fractional orders to be identified and system parameters. Indicates about nonlinear implicit functions, This represents a 2-norm matrix.

8. A computer device, characterized in that: It includes a memory, a processor, and a transceiver, which are connected to each other via a bus; the memory is used to store a set of computer program instructions and data, and can transfer the stored data to the processor, which can execute the program instructions stored in the memory to perform the method as described in any one of claims 1 to 6.

9. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program that, when executed, implements the method as described in any one of claims 1 to 6.

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