A simulation method and system for dynamic surface regulation of tumor immune processes

Abstract

The application discloses a tumor immune process regulation simulation method and system, which belongs to the cross field of nonlinear system control and biomedical engineering. The method comprises the following steps: constructing a tumor immune nonlinear dynamic model and performing coordinate transformation; setting a continuous bounded desired reference trajectory; defining a tracking error surface and introducing a first-order filter to replace the derivative of a virtual control quantity to simplify the controller structure; adopting a radial basis neural network to online approximate unknown nonlinear functions; aiming at the problem that the control gain function in the model is unknown, constructing an integral type Lyapunov function and designing a control law and an adaptive law to ensure that the closed-loop system is semi-global uniformly ultimately bounded; and performing simulation to obtain an intervention regulation reference signal. The application effectively avoids the parameter explosion problem of traditional backstepping control, can process system uncertainty and unknown control gain without an accurate mathematical model, has a simple controller structure and small calculation amount, and provides a reliable theory and simulation tool for tumor immune intervention effect prediction.

Description

Technical Field

[0001] This invention belongs to the field of dynamic surface control technology, and in particular relates to a simulation method and system for dynamic surface regulation of tumor immune processes. Background Technology

[0002] In the field of tumor immune process modeling, mathematical models have been widely used to describe the complex nonlinear dynamic relationships between tumor cells, immune cells, and cytokines such as interleukin-2. To achieve accurate prediction of intervention effects, researchers have gradually introduced nonlinear control theory into tumor immune simulation systems. Among these, pushback control, due to its ability to handle the structured nature of nonlinear systems, has become a hot topic in early research.

[0003] Pushback control recursively constructs Lyapunov functions, progressively designs virtual control laws, and ultimately obtains the actual control input. This method has been preliminarily applied to tumor immune models. For example, researchers transformed a tumor-immunity-drug model into a strict feedback form and used pushback control to design regulatory strategies for immune intervention and chemotherapy. Simulation results show that this method can simulate and predict the inhibitory effect on tumor cell growth to a certain extent.

[0004] However, in practical applications, pushback control faces the following key issues.

[0005] (1) Parameter explosion: When the system order increases, the derivative terms of the virtual control law increase exponentially, the controller structure becomes complex, and it is difficult to implement in actual simulation or auxiliary decision-making equipment; (2) Strong model dependence: Traditional push-back control requires the system model to be completely known, while there are a large number of unknown nonlinear functions and parameters in the tumor immune model, making it difficult to model accurately.

[0006] To overcome the parameter explosion problem in push-back control, researchers have proposed dynamic surface control, which simplifies the controller structure by introducing a first-order filter to replace the direct calculation of the virtual control derivative. However, existing control methods still have the following shortcomings in the simulation application of tumor immune processes.

[0007] (1) The research assumes that the dynamics of the system are known, while the tumor immune system has strong nonlinearity and uncertainty; (2) Use fuzzy logic system or neural network to estimate unknowns, but processing each unknown separately leads to too many adaptive parameters.

[0008] (3) The model is based on fractional differential equations, which are difficult to differentiate and the controller structure is complex.

[0009] Based on the above reasons, this invention designs a dynamic surface regulation simulation method and system for tumor immune processes. Summary of the Invention

[0010] The purpose of this invention is to solve the problems in the prior art, and to propose a dynamic surface regulation simulation method and system for tumor immune processes.

[0011] This invention first discloses a dynamic surface regulation simulation method for tumor immune processes, characterized by comprising: S1: Construct a nonlinear dynamic model describing the biological process to be regulated. The model includes multiple state variables and control input variables, and contains unknown nonlinear functions, unknown gain functions, and unknown bounded perturbations. The unknown gain function is a signed function, and its sign is known in advance. S2: Set the reference trajectory that the simulation process is expected to track. The reference trajectory is continuous and available in advance, and the reference trajectory and its time derivative are both within a predefined bounded compact set. S3: Transform the nonlinear dynamic model into a strict feedback form that facilitates controller design through coordinate transformation; S4: Based on the transformed model, a controller is designed using dynamic surface control technology, including: Based on the reference trajectory, a set of error surfaces is defined, including the tracking error between the actual system output and the reference trajectory, and the deviation between the current system state and the virtual control signal after filtering and smoothing. A first-order filter is introduced to replace the direct differentiation of the virtual control law in order to avoid computational complexity explosion; The unknown nonlinear functions that arise during the design process are approximated online using neural networks; S5: For the unknown gain function in the nonlinear dynamic model, construct an integral Lyapunov function, design control law and adaptive law based on the neural network approximation and the integral Lyapunov function, and prove that all signals in the closed-loop system are semi-globally consistent and eventually bounded through Lyapunov stability theory. S6: The biological process is simulated using the designed controller to generate a simulation reference signal for intervention and regulation, so as to predict the effect of the intervention on the biological process.

[0012] In the above method, the nonlinear dynamic model adopts a nonlinear dynamic model that includes three variables: tumor, immunity, and interleukin-2, and is described by the following formula:

[0013] in Indicates the concentration of effector immune cells. This represents an unknown bounded perturbation in the proliferation, activation, migration, and survival of effector immune cells. This represents the tumor cell concentration, expressed in cells per mL. This indicates the concentration of interleukin-2. This indicates the rate at which tumor cells induce the production of effector immune cells. This indicates the natural mortality rate / decay of effector immune cells. Rate, This indicates the maximum rate of interleukin-2 induced effector immune cell proliferation. This represents the half-saturation constant of interleukin-2 activity. This indicates the inherent growth rate of tumor cells. This represents the correlation coefficient between the environmental carrying capacity of tumor cells and their actual carrying capacity. This represents the maximum rate at which effector immune cells kill tumor cells. This represents the half-saturation constant of the tumor cell killing process. This represents the maximum rate at which effector immune cells secrete interleukin-2 in response to tumor antigen stimulation. This represents the half-saturation constant of the interleukin-2 secretion process. This indicates the natural degradation / clearance rate of interleukin-2. This indicates the rate of infusion of exogenous effector immune cells. This indicates the rate of exogenous interleukin-2 input.

[0014] In the above method, transforming the nonlinear dynamic model into a strict feedback form that facilitates controller design through coordinate transformation includes: transforming the nonlinear dynamic model in the following manner: , , ; At this point, the nonlinear dynamic model is transformed into the following equation:

[0015] in:

[0016]

[0017]

[0018]

[0019] in, , , It is an unknown nonlinear function that is smooth. It is an unknown gain function.

[0020] In the above method, the reference trajectory is a vector. and express, and It is a known compact set; The defined set of error surfaces includes defined errors z1, z2, and z3:

[0021]

[0022]

[0023] in, This represents the difference between the number of tumor cells output by the model simulation and the expected number of tumor cells. This represents the difference between the number of effector cells and the filter output. This represents the difference between interleukin levels and their expected values. It is the system status. It is tracking trajectory. This is the filter output.

[0024] In the above method, the form of the neural network approximating the unknown nonlinear function that appears during the online design process is as follows:

[0025] in, It is an intermediate unknown smooth function. For ideal weights, As basis functions, To approximate the error; At the same time, in this process, define This avoids directly manipulating the weight vector. The online estimation simplifies controller design by estimating only the square of its magnitude.

[0026] In the above method, the virtual control law takes the form of: (The first-order filter is introduced to replace the direct differentiation of the virtual control quantity.)

[0027] in, These are positive design parameters. For adaptive parameters, These are the basis functions of a radial basis function neural network; The digital form of the first-order filter is:

[0028] in It is a time constant. It is the output of a first-order linear filter. The virtual control is used as the input to the first-order filter.

[0029] In the above method, the design of control and adaptive laws based on the neural network approximation and the integral Lyapunov function is as follows: The actual control law includes the infusion rate of exogenous effector immune cells. and the rate of infusion of exogenous interleukin-2 Both serve as regulatory reference signals, used to ensure that the simulated values ​​of tumor cell number and interleukin-2 follow the expected trajectory, while maintaining a stable level of effector immune cells. The design formula for the actual control law is as follows:

[0030]

[0031] Adaptive laws include:

[0032] in, These are positive design parameters. For adaptive parameters, These are the basis functions of a radial basis function neural network, which can be chosen as Gaussian functions. For the input vector, It is a positive design constant.

[0033] In the above method, proving that all signals in the closed-loop system are semi-globally consistent and eventually bounded using Lyapunov stability theory specifically includes: Define compact sets:

[0034] in It is a positive constant used for stability analysis. , , ; The integral Lyapunov function includes:

[0035] in: , , , For design parameters; right Regarding time Differentiation yields:

[0036] in It is obtained from the approximation error of the neural network. It deals with first-order filter errors. The resulting This is the upper bound of the disturbance; Using Young's inequality, we can obtain...

[0037] if Then there is and ; make Substituting the above formula into the equation, we get:

[0038] Select the following design parameters: ,and ; if For a given set You can choose a sufficiently large one. To obtain a sufficiently large And because and It is irrelevant, therefore we can obtain This leads to This means if So for all They all ; In summary, the variables of a closed-loop system , It is bounded. And, and It also has boundaries.

[0039] Secondly, the present invention provides a dynamic surface regulation simulation system for tumor immune processes, used to implement the above-mentioned method, including: The model building module is used to build a three-variable nonlinear dynamic model; The controller generation module is used to generate virtual control laws, actual control laws, and adaptive laws based on the model and the set desired trajectory, and output external input signals. The simulation module is used to drive the model according to the exogenous input signal, perform dynamic simulation of the tumor immune process, and output simulation results.

[0040] In the above system, the controller generation module specifically includes: Error definition unit, used to define the tracking error surface; The virtual control unit is used to generate virtual control laws for each step and input the virtual control laws into a first-order filter. The filtering unit is used to generate a filtered output signal based on the first-order filter, replacing the derivative of the virtual control law; The actual control unit is used to generate the actual control law based on the final error surface. An adaptive unit is used to run the adaptive law and update the single adaptive parameter online. The parameter determination unit is used to perform stability analysis based on the integral Lyapunov function and determine the design parameters.

[0041] The beneficial effects of this invention are as follows: (1) The present invention completes the controller design based on the ordinary differential model of tumor immune dynamics. The control structure is simple and easy to simulate. It can accurately simulate the tumor cell inhibition trend and the dynamic changes of immune cells. It can be used for clinical immunotherapy effect reference prediction and auxiliary decision-making, and has strong practicality.

[0042] (2) Relying on the radial basis neural network adaptive approximation technology, it does not require the system model to be completely and accurately known. It can effectively adapt to the unknowns and physiological perturbation uncertainties of the tumor immune model and has strong robustness.

[0043] (3) By constructing an integral Lyapunov function, the design problem of unknown control gain function is solved, and the semi-global consistency and eventual boundedness of the closed-loop system state are strictly guaranteed, and the control process is stable and reliable.

[0044] (4) The present invention forms a complete simulation verification process for tumor immune regulation, with high experimental repeatability, which can provide effective technical reference and engineering support for intelligent regulation simulation research of tumor immunotherapy. Attached Figure Description

[0045] Figure 1 This is a flowchart of a dynamic surface regulation simulation method for tumor immune processes disclosed in this invention.

[0046] Figure 2 This is a simulation curve of tumor changes in this invention.

[0047] Figure 3 This is a simulation curve of the effector cells in this invention.

[0048] Figure 4 This is a simulation curve of interleukin-2 in this invention.

[0049] Figure 5 For the control input in this invention The simulation curve.

[0050] Figure 6 For the control input in this invention The simulation curve.

[0051] Figure 7 The adaptive parameters in this invention Simulation curves Detailed Implementation To facilitate understanding of this application and to make the aforementioned objectives, features, and advantages of this application more apparent, a detailed description of specific embodiments of this application is provided below in conjunction with the accompanying drawings. Numerous specific details are set forth in the following description to provide a thorough understanding of this application, and preferred embodiments are shown in the accompanying drawings. However, this application can be implemented in many different forms and is not limited to the embodiments described herein. Rather, these embodiments are provided to provide a more thorough and complete understanding of the disclosure of this application. This application can be implemented in many other ways different from those described herein, and those skilled in the art can make similar modifications without departing from the spirit of this application; therefore, this application is not limited to the specific embodiments disclosed below. Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this application, "a plurality of" means at least two, such as two, three, etc., unless otherwise explicitly specified. In the description of this application, "several" means at least one, such as one, two, etc., unless otherwise explicitly specified. It should be noted that when an element is referred to as being "fixed to" another element, it can be directly attached to the other element or there may be an intervening element. When an element is referred to as being "connected to" another element, it can be directly connected to the other element or there may be an intervening element. The terms "vertical," "horizontal," "left," "right," and similar expressions used herein are for illustrative purposes only and do not represent the only possible implementations. Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used herein is only for describing particular implementations and is not intended to limit the scope of this application. The term "and / or" as used herein includes any and all combinations of one or more of the associated listed items.

[0052] Reference Figures 1-7 A dynamic surface regulation simulation method for tumor immune processes. This method includes the following steps: S1: Construct a nonlinear dynamic model describing the biological process to be regulated. The model includes multiple state variables and control input variables, and contains unknown nonlinear functions, unknown gain functions, and unknown bounded perturbations. The unknown gain function is a signed function, and its sign is known in advance. S2: Set the reference trajectory that the simulation process is expected to track. The reference trajectory is continuous and available in advance, and the reference trajectory and its time derivative are both within a predefined bounded compact set. S3: Transform the nonlinear dynamic model into a strict feedback form that facilitates controller design through coordinate transformation; S4: Based on the transformed model, a controller is designed using dynamic surface control technology, including: Based on the reference trajectory, a set of error surfaces is defined, including the tracking error between the actual system output and the reference trajectory, and the deviation between the current system state and the virtual control signal after filtering and smoothing. A first-order filter is introduced to replace the direct differentiation of the virtual control law in order to avoid computational complexity explosion; The unknown nonlinear functions that arise during the design process are approximated online using neural networks; S5: For the unknown gain function in the nonlinear dynamic model, construct an integral Lyapunov function, design control law and adaptive law based on the neural network approximation and the integral Lyapunov function, and prove that all signals in the closed-loop system are semi-globally consistent and eventually bounded through Lyapunov stability theory. S6: The biological process is simulated using the designed controller to generate a simulation reference signal for intervention and regulation, so as to predict the effect of the intervention on the biological process.

[0053] In practical implementation, the nonlinear dynamic model used in this scheme for the tumor regulation process is the following tumor-immunity-interleukin-2 dynamic model. (1) in This indicates the concentration of effector immune cells, such as CTLs and NK cells (cells / mL). It describes the unknown bounded perturbations in the proliferation, activation, migration, and survival of effector immune cells. This represents the concentration of tumor cells (cells / mL). Indicates the concentration of interleukin-2 ( or Other system parameters are as follows: This indicates the rate at which tumor cells induce the production of effector immune cells ( ), Natural mortality rate / decay rate of effector immune cells ( ), The maximum rate of interleukin-2 induced effector immune cell proliferation ( ), The half-saturation constant of interleukin-2 action ( ), This is the inherent growth rate of tumor cells (1 / day). The correlation coefficient for the environmental carrying capacity of tumor cells (mL / cell number). This indicates the maximum rate at which effector immune cells kill tumor cells (mL / (cell number)). sky)), It is the half-saturation constant (cells / mL) of the tumor cell killing process. The maximum rate at which effector immune cells secrete IL-2 upon stimulation by tumor antigens (pg / (cell number)) sky)), It represents the half-saturation constant (cells / mL) for the interleukin-2 secretion process. The natural degradation / clearance rate of interleukin-2 ( ), It is the rate of infusion of exogenous effector immune cells (cell count / (mL)). sky)), Indicates the rate of exogenous interleukin-2 infusion (pg / (mL)). sky)).

[0054] The control objective of this scheme is to design a dynamic surface controller. and As a regulatory reference signal, the simulated values ​​of tumor cell number and interleukin-2 are tracked to the expected trajectory, and the effector immune cells maintain a stable level. All signals are semi-globally terminated and uniformly stable. To achieve the above objectives, the nonlinear dynamic model is transformed into a rigorous feedback form that facilitates controller design through coordinate transformation, as follows: make , , The original system is transformed into the following formula: (2)

[0055]

[0056]

[0057]

[0058] in, , , It is an unknown nonlinear function that is smooth. It is an unknown gain function.

[0059] Assume function 1 Given the sign of , there exists a known positive constant. , making Without loss of generality, we assume .

[0060] Assumption 2: Desired trajectory vector and It is continuous and available, among which, and It is a known compact set.

[0061] Assumption 3: For uncertain external disturbances There exists an unknown constant. , making Established.

[0062] In the design of tumor immune process controllers based on dynamic surface methodology, this method considers the system , , In the case of unknown and smooth conditions, a controller is designed using a radial basis function neural network to approximate the unknown function, as shown in equation (3) below: (3) in, It is an unknown smooth function in the design process. For ideal weights, As basis functions, To approximate the error. For ease of controller design, define... .

[0063] To avoid the need for differentiation of virtual control in the traditional push-back process, this invention introduces a first-order linear filter to replace the differentiation, the structure of which is shown in equation (4) below: (4) in It is a time constant. It is the output of a first-order linear filter. The virtual control is used as the filter input, and its specific form will be given later.

[0064] The controller design is completed in three steps across three subsystems. First, the following error surface is introduced:

[0065]

[0066]

[0067]

[0068] in, It is the system status. It is tracking trajectory. This is the filter output.

[0069] The control law and adaptive rate are designed using dynamic surface control technology as follows: (1) Define the Lyapunov function as: (5) in, Let be the variable of integration, and obtain from the second mean value theorem for integration. .

[0070] Differentiating equation (5) yields: (6) in, For an unknown smooth function, .

[0071] By applying radial basis function approximation, we can obtain: (7) Applying Young's inequality again, we get: (8) (9) Substituting equations (7), (8), and (9) into equation (6) yields: (10) The virtual control and adaptive law are designed as follows: (11) (12) Therefore: (13) Wherein, the unknown smooth function satisfy Using Young's inequality, we can obtain Therefore: (14) And from We can obtain: (15) Rearranging the terms, we get: (16) Therefore: (17) (2) Define the Lyapunov function as: (18) Similar to Step 1, the following control law and adaptive law of equation (6) (i=2) are designed: (19) Therefore, we get: (20) (3) Define the Lyapunov function as: (twenty one) Similar to step (2), the following control law is designed: (twenty two) Therefore, we get: (twenty three) Here These are positive design parameters. For adaptive parameters, These are the basis functions of a radial basis function neural network, typically chosen as Gaussian functions. For the input vector, It is a positive design constant.

[0072] (3) Stability analysis Theorem: For the tumor-immune-interleukin-2 dynamic model system described by equations (1) and (2), under virtual control (11), actual control laws (19) and (22), and adaptive law (12), all signals in the closed-loop system are uniformly bounded at the semi-global termination, and the design constant is... and Satisfying equation (24): (twenty four) Proof: Define compact sets: (25) in It is a positive constant and is only used for stability analysis. , , .

[0073] Choose the following Lyapunov functions: (26) in, , , , These are design parameters.

[0074] right Regarding time Differentiating and substituting into equations (14), (17), (20), and (23), we obtain: (27) in It is obtained from the approximation error of the neural network, and It is about handling filter errors. The resulting This is the upper bound of the perturbation; other variables are as described above.

[0075] Using Young's inequality, we can obtain: (28) if Then there is and ,make:

[0076] Substituting equation (13) into equation (12), we get: (29) Select the following design parameters: (30) and .

[0077] if For a given set You can choose a sufficiently large one. To obtain a sufficiently large And because and It is irrelevant, therefore we can obtain This leads to This means that if So for all They all .

[0078] In summary, the variables of a closed-loop system , It is bounded. And, and It also has boundaries.

[0079] (5) Simulation study To demonstrate the effectiveness of the adaptive dynamic surface control method proposed in this implementation case, the following system parameters were selected for simulation. The system parameters are shown in the table below: Table 1 System Parameter Table

[0080] The basis functions of the radial basis neural network are chosen as shown in equation (31).

[0081] (31) in, Choose the Gaussian function, as shown in equation (32): (32) Here, the center of the neural network is ,and , The center vector of each layer is given by equation (33): (33) in, .

[0082] Tumor concentration expected tracking trajectory is defined as Interleukin-2 expected tracking trajectory is defined as Effector immune cell perturbation is The design parameters are: , , , , , , , , The initial value is , , , , Virtual controller for application design and actual controller , Conduct simulation experiments on the system.

[0083] The system was simulated using both the virtual and actual controllers designed in the application. The various states of the system and the desired trajectory curves are shown below. Figures 2-4 As shown, the controller output simulation curve is as follows: Figure 5 , 6 As shown, the adaptive law curve is as follows: Figure 7 As shown.

[0084] Simulation results: Under the influence of the control signal, the simulated values ​​of tumor cells rapidly decreased along the desired trajectory and remained at a low level; the simulated values ​​of immune cells tended to stabilize after a certain period of time; and the simulated value of interleukin-2 showed good trajectory tracking. This design method achieved a relatively ideal simulation effect of tumor immune process regulation, with all signals being bounded, verifying the effectiveness of the control method. This method can also be extended to the simulation of other nonlinear biological systems, such as artificial pancreas blood glucose regulation and dynamic intervention simulation of human metabolic systems.

[0085] As is known from common technical knowledge, this invention can be implemented through other embodiments that do not depart from its spirit or essential characteristics. Therefore, the disclosed embodiments described above are merely illustrative and not exhaustive. All modifications within the scope of this invention or its equivalents are included in this invention.

Claims

1. A simulation method for dynamic surface regulation of tumor immune processes, characterized in that, include: S1: Construct a nonlinear dynamic model describing the biological process to be regulated. The model includes multiple state variables and control input variables, and contains unknown nonlinear functions, unknown gain functions, and unknown bounded perturbations. The unknown gain function is a signed function, and its sign is known in advance. S2: Set the reference trajectory that the simulation process is expected to track. The reference trajectory is continuous and available in advance, and the reference trajectory and its time derivative are both within a predefined bounded compact set. S3: Transform the nonlinear dynamic model into a strict feedback form that facilitates controller design through coordinate transformation; S4: Based on the transformed model, a controller is designed using dynamic surface control technology, including: Based on the reference trajectory, a set of error surfaces is defined, including the tracking error between the actual system output and the reference trajectory, and the deviation between the current system state and the virtual control signal after filtering and smoothing. A first-order filter is introduced to replace the direct differentiation of the virtual control law in order to avoid computational complexity explosion; The unknown nonlinear functions that arise during the design process are approximated online using neural networks; S5: For the unknown gain function in the nonlinear dynamic model, construct an integral Lyapunov function, design control law and adaptive law based on the neural network approximation and the integral Lyapunov function, and prove that all signals in the closed-loop system are semi-globally consistent and eventually bounded through Lyapunov stability theory. S6: The biological process is simulated using the designed controller to generate a simulation reference signal for intervention and regulation, so as to predict the effect of the intervention on the biological process.

2. The method according to claim 1, characterized in that, The nonlinear dynamic model employs a three-variable approach, including tumor, immunity, and interleukin-2, and is described by the following formula: in Indicates the concentration of effector immune cells. This represents an unknown bounded perturbation in the proliferation, activation, migration, and survival of effector immune cells. This represents the tumor cell concentration, expressed in cells per mL. This indicates the concentration of interleukin-2. This indicates the rate at which tumor cells induce the production of effector immune cells. This represents the natural mortality rate / decay rate of effector immune cells. This indicates the maximum rate of interleukin-2 induced effector immune cell proliferation. This represents the half-saturation constant of interleukin-2 activity. This indicates the inherent growth rate of tumor cells. This represents the correlation coefficient between the environmental carrying capacity of tumor cells and their actual carrying capacity. This indicates the maximum rate at which effector immune cells kill tumor cells. This represents the half-saturation constant of the tumor cell killing process. This represents the maximum rate at which effector immune cells secrete interleukin-2 in response to tumor antigen stimulation. This represents the half-saturation constant of the interleukin-2 secretion process. This indicates the natural degradation / clearance rate of interleukin-2. This indicates the rate of infusion of exogenous effector immune cells. This indicates the rate of exogenous interleukin-2 input.

3. The method according to claim 2, characterized in that, The process of transforming the nonlinear dynamic model into a rigorous feedback form that facilitates controller design via coordinate transformation includes: transforming the nonlinear dynamic model in the following manner: ， ， ； At this point, the nonlinear dynamic model is transformed into the following equation: in: in, , , For an unknown nonlinear smooth function, It is an unknown gain function.

4. The method according to claim 2, characterized in that, The reference trajectory uses a vector. and express, and It is a known compact set; The defined set of error surfaces includes defined errors z1, z2, and z3: in, This represents the difference between the number of tumor cells output by the model simulation and the expected number of tumor cells. This represents the difference between the number of effector cells and the filter output. This represents the difference between interleukin-2 and its expected value. It is the system status. It is tracking trajectory. This is the filter output.

5. The method according to claim 2, characterized in that, In the process of using a neural network to approximate the unknown nonlinear function during the design, the approximation form of the unknown nonlinear function by the neural network is as follows: in, It is an intermediate unknown smooth function. For ideal weights, As basis functions, To approximate the error; At the same time, in this process, define Used to simplify controller design.

6. The method according to claim 4, characterized in that, In the direct differentiation of the virtual control quantity by introducing a first-order filter to replace the virtual control quantity, the form of the virtual control law is: in, These are positive design parameters. For adaptive parameters, These are the basis functions of a radial basis function neural network; The digital form of the first-order filter is: in It is a time constant. It is the output of a first-order linear filter. The virtual control is used as the input of a first-order filter.

7. The method according to claim 1, characterized in that, In the design of control and adaptive laws based on the neural network approximation and the integral Lyapunov function: The actual control law includes the infusion rate of exogenous effector immune cells. and the rate of infusion of exogenous interleukin-2 Both serve as regulatory reference signals, used to ensure that the simulated values ​​of tumor cell number and interleukin-2 follow the expected trajectory, while maintaining a stable level of effector immune cells. The design formula for the actual control law is as follows: Adaptive laws include: in, These are positive design parameters. For adaptive parameters, These are the basis functions of a radial basis function neural network, which can be chosen as Gaussian functions. For the input vector, It is a positive design constant.

8. The method according to claim 1, characterized in that, In step S5, proving that all signals in the closed-loop system are semi-globally consistent and eventually bounded using Lyapunov stability theory specifically includes: Define compact sets: in It is a positive constant used for stability analysis. , , ; The integral Lyapunov function includes: in: , , , For design parameters; right Regarding time Differentiation yields: in It is obtained from the approximation error of the neural network. It deals with first-order filter errors. The resulting This is the upper bound of the disturbance; Using Young's inequality, we can obtain... if Then there is and ; make Substituting the above formula into the equation, we get: Select the following design parameters: ,and ; if For a given set You can choose a sufficiently large one. To obtain a sufficiently large And because and It is irrelevant, therefore we can obtain This leads to This means if So for all They all ; In summary, the variables of a closed-loop system , It is bounded. And, and It also has boundaries.

9. A dynamic surface regulation simulation system for tumor immune processes, used to implement any one of the methods described in claims 1 to 8, characterized in that, include: The model building module is used to build a three-variable nonlinear dynamic model; The controller generation module is used to generate virtual control laws, actual control laws, and adaptive laws based on the model and the set desired trajectory, and output external input signals. The simulation module is used to drive the model according to the exogenous input signal, perform dynamic simulation of the tumor immune process, and output simulation results.

10. The simulation system according to claim 7, characterized in that, The controller generation module specifically includes: Error definition unit, used to define the tracking error surface; The virtual control unit is used to generate virtual control laws for each step and input the virtual control laws into a first-order filter. The filtering unit is used to generate a filtered output signal based on the first-order filter, replacing the derivative of the virtual control law; The actual control unit is used to generate the actual control law based on the final error surface. An adaptive unit is used to run the adaptive law and update the single adaptive parameter online. The parameter determination unit is used to perform stability analysis based on the integral Lyapunov function and determine the design parameters.

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