A method and system for controlling the concentration of activated substances in a finite time adaptive manner for a Brusselator system

Abstract

The present invention relates to the technical field of Brusselator system control, and in particular to a method and system for controlling the concentration of a finite-time adaptive activated substance in a Brusselator system, the method comprising: S1: constructing a mechanism model of a Brusselator system; S2: converting the mechanism model into a controlled random non-strict feedback nonlinear system model; S3: using a neural network to approximate the unmodeled dynamic and coupling terms in the controlled random non-strict feedback nonlinear system model, and combining an adaptive adjustment algorithm to construct a finite-time virtual controller; based on the finite-time virtual controller, constructing an actual neural network finite-time adaptive controller; S4: based on the actual neural network finite-time adaptive controller, obtaining a control signal; S5: applying the control signal to the Brusselator system, tracking the concentration of the activated substance through the output of the Brusselator system, and achieving the desired control target. The present invention can ensure good performance during the operation of the Brusselator system and enhance the stability of the system.

Description

Technical Field

[0001] The present invention relates to the technical field of Brusselator system control, and in particular to a method and system for controlling the concentration of activated substances in a finite time adaptive manner in a Brusselator system. Background Art

[0002] In chemical engineering, the Brusselator system is a typical reaction-diffusion system, which is often used to simulate and study the self-organization phenomenon and spatiotemporal pattern formation in chemical reactions. The Brusselator system usually involves nonlinear reactions between two or more chemical substances, in which the concentration change of the activated substance has an important influence on the overall behavior of the system. Therefore, precise control of the concentration of the activated substance in the Brusselator system is crucial to achieve the expected function and performance of the system.

[0003] However, due to the complexity of the Brusselator system, its mechanism model often contains multiple mutually coupled nonlinear terms and unmodeled dynamics, which makes it difficult to directly apply traditional linear control methods. In addition, the Brusselator system may also be affected by various random factors, such as ambient temperature and pressure fluctuations, which further increase the difficulty of system control.

[0004] In recent years, with the development of control theory, nonlinear control methods such as adaptive control and neural network control have gradually been applied to the control of complex systems. These control methods can effectively deal with nonlinearity, coupling and random interference in the system, thereby achieving precise control of system behavior. However, the existing Brusselator system still has the problem of low tracking accuracy of process parameters due to the inability to adaptively adjust when subjected to concentration constraints, random concentration unmodeled dynamics and accompanied by random disturbances. Therefore, it is difficult to achieve the desired control target. Summary of the invention

[0005] In order to solve the above technical problems, the present invention provides a finite-time adaptive activation material concentration control method and system for a Brusselator system, which solves the problem of concentration constraints in the Brusselator system by introducing nonlinear mapping technology, and designs an adaptive algorithm. Combined with the designed neural network adaptive controller, it solves the problem that the Brusselator system is subject to concentration constraints, random concentration unmodeled dynamics, and accompanied by random disturbances. It can self-regulate, thereby improving control accuracy and work efficiency.

[0006] The Brusselator system finite time adaptive activation material concentration control method comprises the following steps:

[0007] S1: Construct the mechanism model of the Brusselator system;

[0008] S2: converting the mechanism model into a controlled random non-strict feedback nonlinear system model;

[0009] S3: using a neural network to approximate the unmodeled dynamic and coupling terms in the controlled random non-strict feedback nonlinear system model, and combining it with an adaptive adjustment algorithm to construct a finite-time virtual controller; based on the finite-time virtual controller, constructing an actual neural network finite-time adaptive controller;

[0010] S4: obtaining a control signal based on the inter-neural network finite time adaptive controller;

[0011] S5: Applying the control signal to the Brusselator system, tracking the concentration of the activated substance through the output of the Brusselator system, and achieving the desired control target.

[0012] In one embodiment of the present invention, the mechanism model is:

[0013]

[0014] Where Q and H both represent the concentration of the intermediate reactant, Q represents the concentration of the activating substance, and H represents the concentration of the inhibiting substance. represents the derivative of Q in the time direction, represents the derivative of H in the time direction; A0>0 and B0>0 are parameters describing the supply of reservoir chemicals; k1, k2, k3 and k4 are all reaction rate constants; A and B are reactants of the overall reaction of the Brusselator system, X and Y are intermediate reactants of the overall reaction of the Brusselator system; Q 2 H represents the autocatalytic reaction of the Brusselator system; -Q 2 H represents the inhibitory response of the Brusselator system.

[0015] In one embodiment of the present invention, the controlled random non-strict feedback nonlinear system model is:

[0016]

[0017] Wherein, χ1=Q represents the concentration of the activating substance, χ2=H represents the concentration of the inhibiting substance, dχ1 represents the Ito differential of χ1, and dχ2 represents the Ito differential of χ2; represents the autocatalytic reaction of the Brusselator system; represents the inhibition reaction of the Brusselator system; A0 = 0.5, B0 = 1.5 are parameters describing the supply of reservoir chemicals, which control the generation and consumption rates of the reaction substances; u represents the control input, ξ∈R represents the random concentration unmodeled dynamics, dξ represents the Ito derivative of ξ, ζ = [ζ1,ζ2] T ∈R 2 represents the input unmodeled dynamics, ν∈R is the output of the input unmodeled dynamic subsystem and the input of the controlled random non-strict feedback nonlinear system; w is the r-dimensional standard Brownian motion defined on the complete probability space (Ω, F, P), Ω is the sample space, F is the σ algebra, and P is the probability measure.

[0018] In one embodiment of the present invention, the construction method of the finite-time virtual controller and the actual neural network finite-time adaptive controller is:

[0019] S31: Select the concentration of the activation substance of the desired controlled Brusselator system as the reference concentration y of the activation substance d , define s1 as the concentration of the activated substance obtained by nonlinear transformation in the controlled Brusselator system, and s2 as the concentration of the inhibited substance obtained by nonlinear transformation in the controlled Brusselator system, which can be expressed as:

[0020]

[0021]

[0022] Among them, χ i represents the concentration of the intermediate substance before the nonlinear transformation, i = 1, 2, χ1 represents the concentration of the activating substance before the nonlinear transformation, χ2 represents the concentration of the inhibiting substance before the nonlinear transformation; k i1 (t) and k i2 (t) is a positive function, 0<K i1 <k i1 (t), 0<K i2 <k i2 (t), k i1 (t),k i2 (t) represents a known positive function, K i1 , K i2 , is a known positive constant, It is k i1 (t) is the derivative in the time direction, It is k i2 (t) derivative in the time direction;

[0023] S32: Using nonlinear mapping technology to convert the reference concentration y of the activated substance d Convert and obtain the converted reference concentration The converted reference concentration The difference between the concentration s1 of the activated substance at this time and the concentration of the controlled random non-strict feedback nonlinear system model is obtained to obtain the error z1 between the two, and the kinetic equation is differentially solved;

[0024] S33: Approximating the unmodeled dynamic nonlinear terms and coupling terms in the Brusselator system mechanism model using a neural network system, converting the activated substance concentration s1 of the Brusselator system model and the converted reference concentration and its first-order derivative As the input of the neural network system corresponding to the dynamic subsystem of the activated substance concentration, the output is And contains the corresponding accuracy level error ε1(S1);

[0025] S34: Using two signals output by the neural network system and Establishing the weights of the neural network system Adaptive adjustment algorithm in is the estimated value of λ1, yes Derivative in the time direction;

[0026] S35: Based on the adaptive adjustment algorithm Combined with the given corresponding positive parameters κ1, a1, Υ1, σ1, the finite-time virtual controller α1 is designed;

[0027] S36: For the dynamic subsystem of the inhibitory substance concentration, based on the finite time virtual controller α1 and the adaptive adjustment algorithm The concentration s2 of the inhibitory substance is processed to obtain the error signal z2 corresponding to the virtual controller of the dynamic subsystem of the activating substance concentration, which is input into the neural network system corresponding to the dynamic subsystem of the inhibitory substance concentration, and the weight of the neural network system is established. Adaptive adjustment algorithm for regularized signal m and And combined with the corresponding given positive parameters κ2, a2, Γ, Υ2, σ2, Υ3, σ3, design practical neural network finite time adaptive controller u;

[0028] in, is the estimated value of λ2, is an estimate of M, yes The derivative in the time direction, yes Derivative in the time direction;

[0029] S37: Compare the concentration of the activated substance of the Brusselator system at the next moment with the reference concentration of the operation target. If the desired accuracy is not achieved, return to S31 and continue to loop through steps S31-S36 until the desired control target is achieved.

[0030] In one embodiment of the present invention, in S33, the method for constructing the neural network system is:

[0031] For any continuous function P1(S1):R 5 →R, any given compact set and any positive constant There exists an ideal constant weight vector and a radial basis function vector Make

[0032]

[0033] holds, where the approximation error ε1(S1) satisfies l>1 is the number of nodes in the neural network, is defined as a Gaussian function of the form:

[0034]

[0035] Where exp(a) represents e a , μ 1j and σ 1j Gaussian basis functions The width and center of ||S1-μ 1j || represents S1-μ 1j The Euclidean norm of; the optimal weight vector is defined as follows:

[0036] In one embodiment of the present invention, for the activation substance concentration dynamic subsystem, the adaptive adjustment algorithm for:

[0037]

[0038] The finite time virtual controller α1 is:

[0039]

[0040] Where z1 represents the concentration of activated substance s1 and the reference concentration of activated substance The error, X1=[s1,ω1] T , And a1, Υ1, σ1 and κ1 all represent design positive constants, Design constants for finite time.

[0041] In one embodiment of the present invention, for the dynamic subsystem of the inhibitory substance concentration, the adaptive adjustment algorithm and for:

[0042]

[0043] The actual neural network finite time adaptive controller u is:

[0044]

[0045] Where z2 represents the error between the inhibitor concentration and the output of the first-order filter of the inhibitor concentration dynamic subsystem. X2=[s1,s2,ω2] T , tanh(·) represents the hyperbolic tangent function, α2 is the transition parameter, and a2, Γ, Υ2, σ2 and κ2 represent design positive constants, Design constants for finite time.

[0046] In one embodiment of the present invention, the converted reference concentration for:

[0047]

[0048] Based on the same inventive concept, the present invention provides a Brusselator system finite time adaptive activation material concentration control system, the system is used to implement the Brusselator system finite time adaptive activation material concentration control method, specifically including:

[0049] A mechanism model building module, wherein the mechanism model building module is used to build a mechanism model of the Brusselator system;

[0050] A model conversion module, wherein the model conversion module is used to convert the mechanism model into a controlled random non-strict feedback nonlinear system model;

[0051] A virtual controller and an adaptive controller building module, wherein the virtual controller and the adaptive controller building module are used to use a neural network to approximate the unmodeled dynamic and coupling terms in the controlled random non-strict feedback nonlinear system model, and to construct a finite-time virtual controller in combination with an adaptive adjustment algorithm; based on the finite-time virtual controller, an actual neural network finite-time adaptive controller is constructed;

[0052] A control signal calculation module, wherein the control signal calculation module is used to obtain a control signal based on the inter-neural network finite time adaptive controller;

[0053] The concentration tracking and regulating module is used to apply the control signal to the Brusselator system, and track the concentration of the activated substance through the output of the Brusselator system to achieve the desired control target.

[0054] The present invention also provides a computer storage medium, which stores a computer software product. The computer software product includes several instructions for enabling a computer device to execute the instructions of the Brusselator system finite time adaptive activation material concentration control method.

[0055] The above technical solution of the present invention has the following advantages compared with the prior art:

[0056] The present invention enables the Brusselator system to overcome random disturbances while having asymmetric time-varying concentration constraints and random concentration unmodeled dynamics, and thus still be able to operate the control target and achieve adaptive regulation, thereby improving system performance and work efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] In order to make the content of the present invention more clearly understood, the present invention is further described in detail below according to specific embodiments of the present invention in conjunction with the accompanying drawings, wherein

[0058] Figure 1 It is a flow chart of the method for implementing the finite time adaptive activation material concentration control method of the Brusselator system provided by the embodiment of the present invention;

[0059] Figure 2 is a tracking effect diagram between the output concentration of the Brusselator system of the present invention and the reference concentration of the activated substance, wherein y represents the concentration of the activated substance, y d Indicates the reference concentration of the activated substance, -k 11 ,k 12 Respectively represent y d The time-varying upper and lower bounds of constraints;

[0060] Figure 3 is the inhibitory substance concentration effect diagram of the inhibitory substance concentration dynamic subsystem of the Brusselator system of the present invention, wherein χ2 represents the inhibitory substance concentration, -k 21 ,k 22 are the time-varying upper and lower bounds of χ2;

[0061] Figure 4 It is the effect diagram of the control signal u of the Brusselator system of the present invention;

[0062] Figure 5 is the adjustment parameter of the Brusselator system of the present invention and Adaptive change curve graph;

[0063] Figure 6 is the adjustment parameter of the Brusselator system of the present invention Adaptive change curve graph;

[0064] Figure 7 It is a graph of the dynamic ξ change of random concentration of the Brusselator system of the present invention without modeling;

[0065] Figure 8 It is the unmodeled dynamic ζ1,ζ2 change curve diagram of the Brusselator system input of the present invention;

[0066] Fig. 9 It is a schematic diagram of the structure of a finite-time adaptive activation material concentration control system of a Brusselator system provided by an embodiment of the present invention;

[0067] Explanation of the reference numerals in the specification: 100, mechanism model building module; 200, model conversion module; 300, virtual controller and adaptive controller building module; 400, control signal calculation module; 500, concentration tracking and regulation module. DETAILED DESCRIPTION

[0068] The present invention is further described below in conjunction with the accompanying drawings and specific embodiments so that those skilled in the art can better understand the present invention and implement it, but the embodiments are not intended to limit the present invention.

[0069] Embodiment 1

[0070] Reference Figure 1 As shown, the present invention provides a finite time adaptive activation material concentration control method for a Brusselator system, comprising the following steps:

[0071] S1: Construct the mechanism model of the Brusselator system;

[0072] S2: converting the mechanism model into a controlled random non-strict feedback nonlinear system model;

[0073] S3: using a neural network to approximate the unmodeled dynamic and coupling terms in the controlled random non-strict feedback nonlinear system model, and combining it with an adaptive adjustment algorithm to construct a finite-time virtual controller; based on the finite-time virtual controller, constructing an actual neural network finite-time adaptive controller;

[0074] S4: obtaining a control signal based on the inter-neural network finite time adaptive controller;

[0075] S5: Applying the control signal to the Brusselator system, tracking the concentration of the activated substance through the output of the Brusselator system, and achieving the desired control target.

[0076] The overall reaction of the Brusselator system describes the process of converting reactants A and B into products D and E, that is, A+B→D+E. The concentrations of A, B, D and E in the system are kept constant by controlling the inflow rate of A and B and the outflow rate of D and E. At this time, the irreversible Brusselator reaction consists of the following four steps:

[0077]

[0078] The most critical part of the equations is to use the trimolecular reaction 2X+Y→3X to connect the intermediate products X and Y to ensure the existence of the oscillating system. Without loss of generality, all rate constants k1, k2, k3 and k4 are set as unified constants.

[0079] By scaling the variables in the above equations, the Brusselator system is dimensionless and the kinetic equations about X and Y are constructed, that is, the mechanism model is:

[0080]

[0081] in, Q and H both represent the concentration of the intermediate reactant, Q represents the concentration of the activating substance, and H represents the concentration of the inhibiting substance. represents the derivative of Q in the time direction, represents the derivative of H in the time direction; A0>0 and B0>0 are parameters describing the supply of reservoir chemicals; Q 2 H represents the autocatalytic reaction of the Brusselator system; -Q 2 H represents the inhibitory response of the Brusselator system.

[0082] The finite-time neural network control algorithm is based on the controlled Brusselator system after the above-mentioned Brusselator system is transformed, that is, the controlled random non-strict feedback nonlinear system model is:

[0083]

[0084] Among them, χ1=Q represents the concentration of the activating substance, χ2=H represents the concentration of the inhibiting substance, dχ1 represents the Ito differential of χ1, dχ2 represents the Ito differential of χ2, χ1 and χ2 are the key components in the Brusselator system; represents the autocatalytic reaction of the Brusselator system; represents the inhibition reaction of the Brusselator system; A0 = 0.5, B0 = 1.5 are parameters describing the supply of reservoir chemicals. These two parameters control the generation and consumption rates of the reaction substances and affect the dynamic behavior of the system. Different parameter values ​​may cause the system to exhibit different stability, oscillation and chaotic behaviors; u represents the control input, ξ∈R represents the random concentration unmodeled dynamics, dξ represents the Ito differential of ξ, ζ = [ζ1,ζ2] T ∈R 2 represents the input unmodeled dynamics, ν∈R is the output of the input unmodeled dynamic subsystem and the input of the controlled random non-strict feedback nonlinear system; w is the r-dimensional standard Brownian motion defined on the complete probability space (Ω, F, P), Ω is the sample space, F is the σ algebra, and P is the probability measure.

[0085] The concentrations of activating and inhibiting substances in the original Brusselator system are x i , i = 1, 2, is constrained to be in the interval (-k i1 (t),k i2 (t)) on, k i1 (t) and k i2 (t) is a positive function, 0<K i1 <k i1 (t), 0<K i2 <k i2 (t), k i1 (t),k i2 (t) represents a known positive function, K i1 , K i2 , is a known positive constant, It is k i1 (t) is the derivative in the time direction, It is k i2(t) The derivative in the time direction. The nonlinear mapping transformation method based on a specific function proposed by the present invention is processed as follows to obtain the transformed concentrations of the activating substance s1 and the inhibiting substance s2:

[0086]

[0087] The reference concentration of the activated substance after transformation is for:

[0088]

[0089] In this embodiment, the construction method of the finite time virtual controller and the actual neural network finite time adaptive controller is:

[0090] S31: Select the concentration of the activation substance of the desired controlled Brusselator system as the reference concentration y of the activation substance d ;

[0091] S32: Using nonlinear mapping technology to convert the reference concentration y of the activated substance d Convert and obtain the converted reference concentration The converted reference concentration The difference between the concentration s1 of the activated substance at this time and the concentration of the controlled random non-strict feedback nonlinear system model is obtained to obtain the error z1 between the two, and the kinetic equation is differentially solved;

[0092] S33: Approximating the unmodeled dynamic nonlinear terms and coupling terms in the Brusselator system mechanism model using a neural network system, converting the activated substance concentration s1 of the Brusselator system model and the converted reference concentration and its first-order derivative As the input of the neural network system corresponding to the dynamic subsystem of the activated substance concentration, the output is And contains the corresponding accuracy level error ε1(S1);

[0093] Due to the particularity of non-strict feedback systems, the unmodeled dynamic nonlinear terms and coupling terms are related to the concentrations of both the activating and inhibiting substances. Here X1=[s1,ω1] T , ω1 represents the reference concentration of the activated substance after nonlinear mapping conversion, represents the derivative of ω1 in the time direction, ω2 represents the output of the first-order filter in the dynamic subsystem of the activated substance concentration, and S 1j represents the jth element in S1, X 1j represents the jth element in X1. Based on the inequality relationship, the properties of the Gaussian function can be applied as follows:

[0094]

[0095] Among them, μ 1j and σ 1j Gaussian basis functions width and center.

[0096] S34: Using two signals output by the neural network system and Establishing the weights of the neural network system Adaptive adjustment algorithm in is the estimated value of λ1, yes Derivative in the time direction;

[0097] S35: Based on the adaptive adjustment algorithm Combined with the given corresponding positive parameters κ1, a1, Υ1, σ1 and the finite time design constant Design a finite-time virtual controller α1 for the dynamic subsystem of the concentration of activated substances;

[0098] S36: For the dynamic subsystem of the inhibitory substance concentration, based on the finite time virtual controller α1 and the adaptive adjustment algorithm The concentration s2 of the inhibitory substance is processed to obtain an error signal z2 corresponding to the virtual controller of the activating substance concentration dynamic subsystem, which is input into the neural network system corresponding to the inhibitory substance concentration dynamic subsystem and output as the neural network system of the inhibitory substance concentration dynamic subsystem. And contains the corresponding accuracy level error ε2(S2);

[0099] Because of the particularity of non-strict feedback systems, strong nonlinear terms and coupling terms are related to the concentrations of both activating and inhibiting substances. Here X2=[s1,s2,ω2] T , ω2 represents the output of the first-order filter in the dynamic subsystem of the activated species concentration, represents the derivative of ω2 in the time direction, S 2j represents the jth element in S2, X 2j represents the jth element in X2. Based on the inequality relationship, the properties of the Gaussian function can be applied as follows:

[0100]

[0101] Among them, μ 2j and σ 2j Gaussian basis functions width and center.

[0102] Using the signal output by the neural network system And the regularization signal m(t), respectively establish the weight of the neural network system Adaptive adjustment algorithm for regularized signal m and And combined with the corresponding given positive parameters κ2, a2, Γ, Υ2, σ2, Υ3, σ3, design practical neural network finite time adaptive controller u;

[0103] in, is the estimated value of λ2, is an estimate of M, yes The derivative in the time direction, yes Derivative in the time direction;

[0104] S37: Compare the concentration of the activated substance of the Brusselator system at the next moment with the reference concentration of the operation target. If the desired accuracy is not achieved, return to S31 and continue to loop through steps S31-S36 until the desired control target is achieved.

[0105] In one embodiment of the present invention, in S33, the method for constructing the neural network system is:

[0106] For any continuous function P1(S1):R 5 →R, any given compact set and any positive constant There exists an ideal constant weight vector and a radial basis function vector Make

[0107]

[0108] holds, where the approximation error ε1(S1) satisfies l>1 is the number of nodes in the neural network, is defined as a Gaussian function of the form:

[0109]

[0110] Where exp(a) represents e a , μ 1j and σ 1j Gaussian basis functions The width and center of ||S1-μ 1j || represents S1-μ 1j The Euclidean norm of; the optimal weight vector is defined as follows:

[0111] In one embodiment of the present invention, for the activation substance concentration dynamic subsystem, the adaptive adjustment algorithm for:

[0112]

[0113] The finite time virtual controller α1 is:

[0114]

[0115] Where z1 represents the concentration of activated substance s1 and the reference concentration of activated substance The error, X1=[s1,ω1] T , And a1, Υ1, σ1 and κ1 all represent design positive constants, Design constants for finite time.

[0116] In this embodiment, for the dynamic subsystem of the inhibitory substance concentration, the adaptive adjustment algorithm and for:

[0117]

[0118] The actual neural network finite time adaptive controller u is:

[0119]

[0120] Where z2 represents the error between the inhibitor concentration and the output of the first-order filter of the inhibitor concentration dynamic subsystem. X2=[s1,s2,ω2] T , tanh(·) represents the hyperbolic tangent function, α2 is the transition parameter, and a2, Γ, Υ2, σ2 and κ2 represent design positive constants, Design constants for finite time.

[0121] In one embodiment of the present invention, the converted reference concentration for:

[0122]

[0123] In order to verify the effectiveness of the method proposed in the present invention, a simulation experiment is carried out on this embodiment, and the simulation results are as follows: Figures 2 to 8 As shown. Figure 2It can be obtained that the concentration of the activated substance satisfies the asymmetric time-varying constraint condition in the probabilistic sense and can achieve the control target well. The solid line y represents the output trajectory of the Brusselator system, that is, the trajectory of the concentration of the activated substance, and the dotted line y d Represents the tracking trajectory, the trajectory diagram of the reference concentration of the activated substance; Figure 3 The simulation results show that the concentration of the inhibitory substance in the dynamic subsystem of the Brusselator system also satisfies the asymmetric time-varying constraints in the probabilistic sense. In addition, Figure 4 It shows that the control signal u is bounded; Figure 5 and Figure 6 The adaptive change curve of the adjustment parameters λ1, λ2, and M is shown; Figure 7 and Figure 8 It is shown that the random concentration unmodeled dynamics ξ and the input unmodeled dynamics ζ1,ζ2 are probabilistically bounded in the closed-loop system.

[0124] From the above simulation results, it can be concluded that the finite-time adaptive control scheme proposed in the present invention has been effectively simulated on the most common chemical kinetics nonlinear oscillation model - the Brusselator system mechanism model, and can achieve the expected goal very well, which means that this method is also very practical in specific practical applications.

[0125] Embodiment 2

[0126] Based on the same inventive concept as that of the first embodiment, the present invention provides a Brusselator system finite time adaptive activation material concentration control system, the system is used to implement the Brusselator system finite time adaptive activation material concentration control method described in the first embodiment, such as Fig. 9 As shown, the system specifically includes the following modules:

[0127] A mechanism model building module 100, wherein the mechanism model building module is used to build a mechanism model of the Brusselator system;

[0128] A model conversion module 200, the model conversion module is used to convert the mechanism model into a controlled random non-strict feedback nonlinear system model;

[0129] A virtual controller and adaptive controller building module 300, the virtual controller and adaptive controller building module is used to use a neural network to approximate the unmodeled dynamic and coupling terms in the controlled random non-strict feedback nonlinear system model, and combine with an adaptive adjustment algorithm to build a finite-time virtual controller; based on the finite-time virtual controller, build an actual neural network finite-time adaptive controller;

[0130] A control signal calculation module 400, the control signal calculation module is used to obtain a control signal based on the inter-neural network finite time adaptive controller;

[0131] The concentration tracking and regulating module 500 is used to apply the control signal to the Brusselator system, and to track the concentration of the activated substance through the output of the Brusselator system to achieve the desired control target.

[0132] The present embodiment proposes a Brusselator system finite time adaptive activation material concentration control system, which is used to implement the aforementioned Brusselator system finite time adaptive activation material concentration control method. Therefore, the specific implementation method of the Brusselator system finite time adaptive activation material concentration control system can be seen in the embodiment part of the aforementioned Brusselator system finite time adaptive activation material concentration control method. For example, the mechanism model construction module 100, the model conversion module 200, the virtual controller and adaptive controller construction module 300, the control signal calculation module 400 and the concentration tracking and regulation module 500 are respectively used to implement the steps S1, S2, S3, S4 and S5 of the Brusselator system finite time adaptive activation material concentration control method in the first embodiment. Therefore, its specific implementation method can refer to the description of the corresponding embodiments of each part. In order to avoid redundancy, it will not be repeated here.

[0133] Embodiment 3

[0134] The present invention also provides a computer storage medium, which stores a computer software product. The computer software product includes several instructions for enabling a computer device to execute the instructions of the Brusselator system finite time adaptive activation material concentration control method described in Example 1.

[0135] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application may adopt the form of a computer program product implemented in one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that include computer-usable program code.

[0136] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0137] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0138] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0139] Obviously, the above embodiments are merely examples for clear explanation and are not intended to limit the implementation methods. For those skilled in the art, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to list all the implementation methods here. The obvious changes or modifications derived from these are still within the protection scope of the invention.

Claims

1. A method for controlling the concentration of activated substances in a finite time adaptive manner in a Brusselator system, characterized in that: The following steps are involved: S1: Construct a mechanism model of the Brusselator system, the mechanism model is: Where Q and H both represent the concentration of the intermediate reactant, Q represents the concentration of the activating substance, and H represents the concentration of the inhibiting substance. represents the derivative of Q in the time direction, represents the derivative of H in the time direction; A0>0 and B0>0 are parameters describing the supply of reservoir chemicals; k1, k2, k3 and k4 are all reaction rate constants; A and B are reactants of the overall reaction of the Brusselator system, X and Y are intermediate reactants of the overall reaction of the Brusselator system; Q 2 H represents the autocatalytic reaction of the Brusselator system; -Q 2 H represents the inhibitory response of the Brusselator system; S2: Convert the mechanism model into a controlled random non-strict feedback nonlinear system model, wherein the controlled random non-strict feedback nonlinear system model is: Wherein, χ1=Q represents the concentration of the activating substance, χ2=H represents the concentration of the inhibiting substance, dχ1 represents the Ito differential of χ1, and dχ2 represents the Ito differential of χ2; represents the autocatalytic reaction of the Brusselator system; represents the inhibition reaction of the Brusselator system; A0 = 0.5, B0 = 1.5 are parameters describing the supply of reservoir chemicals, which control the generation and consumption rates of the reaction substances; u represents the control input, ξ∈R represents the random concentration unmodeled dynamics, dξ represents the Ito derivative of ξ, ζ = [ζ1,ζ2] T ∈R 2 represents the input unmodeled dynamics, ν∈R is the output of the input unmodeled dynamic subsystem and the input of the controlled random non-strict feedback nonlinear system; w is the r-dimensional standard Brownian motion defined on the complete probability space (Ω, F, P), Ω is the sample space, F is the σ-algebra, and P is the probability measure; S3: using a neural network to approximate the unmodeled dynamic and coupling terms in the controlled random non-strict feedback nonlinear system model, and combining it with an adaptive adjustment algorithm to construct a finite-time virtual controller; based on the finite-time virtual controller, constructing an actual neural network finite-time adaptive controller; S4: obtaining a control signal based on the inter-neural network finite time adaptive controller; S5: Applying the control signal to the Brusselator system, tracking the concentration of the activated substance through the output of the Brusselator system, and achieving the desired control target.

2. The method for controlling the concentration of activated substances in a finite time adaptive manner for a Brusselator system according to claim 1, characterized in that: The construction method of the finite time virtual controller and the actual neural network finite time adaptive controller is: S31: Select the concentration of the activation substance of the desired controlled Brusselator system as the reference concentration y of the activation substance d , define s1 as the concentration of the activated substance obtained by nonlinear transformation in the controlled Brusselator system, and s2 as the concentration of the inhibited substance obtained by nonlinear transformation in the controlled Brusselator system, which can be expressed as: Among them, χ i represents the concentration of the intermediate substance before the nonlinear transformation, i = 1, 2, χ1 represents the concentration of the activating substance before the nonlinear transformation, χ2 represents the concentration of the inhibiting substance before the nonlinear transformation; k i1 (t) and k i2 (t) is a positive function, 0<K i1 <k i1 (t), 0<K i2 <k i2 (t), k i1 (t),k i2 (t) represents a known positive function, K i1 , K i2 , is a known positive constant, It is k i1 (t) is the derivative in the time direction, It is k i2 (t) derivative in the time direction; S32: Using nonlinear mapping technology to convert the reference concentration y of the activated substance d Convert and obtain the converted reference concentration The converted reference concentration The difference between the concentration s1 of the activated substance at this time and the concentration of the controlled random non-strict feedback nonlinear system model is obtained to obtain the error z1 between the two, and the kinetic equation is differentially solved; S33: Approximating the unmodeled dynamic nonlinear terms and coupling terms in the Brusselator system mechanism model using a neural network system, converting the activated substance concentration s1 of the Brusselator system model and the converted reference concentration and its first-order derivative As the input of the neural network system corresponding to the dynamic subsystem of the activated substance concentration, the output is And contains the corresponding accuracy level error ε1(S1); S34: Using two signals output by the neural network system and Establishing the weights of the neural network system Adaptive adjustment algorithm in is the estimated value of λ1, yes Derivative in the time direction; S35: Based on the adaptive adjustment algorithm Combined with the given corresponding positive parameters κ1, a1, Υ1, σ1, the finite-time virtual controller α1 is designed; S36: For the dynamic subsystem of the inhibitory substance concentration, based on the finite time virtual controller α1 and the adaptive adjustment algorithm The concentration s2 of the inhibitory substance is processed to obtain the error signal z2 corresponding to the virtual controller of the dynamic subsystem of the activating substance concentration, which is input into the neural network system corresponding to the dynamic subsystem of the inhibitory substance concentration, and the weight of the neural network system is established. Adaptive adjustment algorithm for regularized signal m and And combined with the corresponding given positive parameters κ2, a2, Γ, Υ2, σ2, Υ3, σ3, design practical neural network finite time adaptive controller u; in, is the estimated value of λ2, is an estimate of M, yes The derivative in the time direction, yes Derivative in the time direction; S37: Compare the concentration of the activated substance of the Brusselator system at the next moment with the reference concentration of the operation target. If the desired accuracy is not achieved, return to S31 and continue to loop through steps S31-S36 until the desired control target is achieved.

3. The method for controlling the concentration of activated substances in a finite time adaptive manner for a Brusselator system according to claim 2, characterized in that: In S33, the method for constructing the neural network system is: For any continuous function P1(S1):R 5 →R, any given compact set and any positive constant There exists an ideal constant weight vector and a radial basis function vector Make holds, where the approximation error ε1(S1) satisfies l>1 is the number of nodes in the neural network, is defined as a Gaussian function of the form: Where exp(a) represents e a , μ 1j and σ 1j Gaussian basis functions The width and center of ||S1-μ 1j || represents S1-μ 1j The Euclidean norm of; the optimal weight vector is defined as follows:

4. The method for controlling the concentration of activated substances in a finite time adaptive manner for a Brusselator system according to claim 2, characterized in that: For the active substance concentration dynamic subsystem, the adaptive adjustment algorithm for: The finite time virtual controller α1 is: Where z1 represents the concentration of activated substance s1 and the reference concentration of activated substance The error, X1=[s1,ω1] T , And a1, Υ1, σ1 and κ1 all represent design positive constants, Design constants for finite time.

5. The method for controlling the concentration of activated substances in a finite time adaptive manner in a Brusselator system according to claim 2, characterized in that: For the dynamic subsystem of inhibitory substance concentration, the adaptive adjustment algorithm and for: The actual neural network finite time adaptive controller u is: Where z2 represents the error between the inhibitor concentration and the output of the first-order filter of the inhibitor concentration dynamic subsystem. X2=[s1,s2,ω2] T , tanh(·) represents the hyperbolic tangent function, α2 is the transition parameter, and a2, Γ, Υ2, σ2 and κ2 represent design positive constants, Design constants for finite time.

6. The method for controlling the concentration of activated substances in a finite time adaptive manner for a Brusselator system according to claim 2, characterized in that: The converted reference concentration for:

7. A Brusselator system finite time adaptive activation material concentration control system, characterized in that: The system is used to implement the Brusselator system finite time adaptive activation material concentration control method according to any one of claims 1 to 6, specifically comprising: A mechanism model building module, wherein the mechanism model building module is used to build a mechanism model of the Brusselator system; A model conversion module, wherein the model conversion module is used to convert the mechanism model into a controlled random non-strict feedback nonlinear system model; A virtual controller and an adaptive controller building module, wherein the virtual controller and the adaptive controller building module are used to use a neural network to approximate the unmodeled dynamic and coupling terms in the controlled random non-strict feedback nonlinear system model, and to construct a finite-time virtual controller in combination with an adaptive adjustment algorithm; based on the finite-time virtual controller, an actual neural network finite-time adaptive controller is constructed; A control signal calculation module, wherein the control signal calculation module is used to obtain a control signal based on the inter-neural network finite time adaptive controller; The concentration tracking and regulating module is used to apply the control signal to the Brusselator system, and track the concentration of the activated substance through the output of the Brusselator system to achieve the desired control target.

8. A computer storage medium, characterized in that The computer storage medium stores a computer software product, and the computer software product includes several instructions for enabling a computer device to execute the instructions of the Brusselator system finite time adaptive activation material concentration control method according to any one of claims 1 to 6.

Images