CN-117010486-B - Parameter unknown chaotic system self-adaptive synchronous control method based on DNA strand displacement

CN117010486BCN 117010486 BCN117010486 BCN 117010486BCN-117010486-B

Abstract

The invention discloses a self-adaptive synchronous control method of a parameter unknown chaotic system based on DNA strand displacement, which comprises the steps of describing a emerging reaction, a triggering reaction and a degradation reaction process through a bimolecular chemical reaction to obtain a chemical reaction module of a nonlinear differential equation with a square term and a product term, constructing a Yang chaotic system through the DNA strand displacement reaction, and obtaining a self-adaptive controller capable of realizing synchronization and a self-adaptive law expression for estimating unknown parameters. The validity of the adaptive controller is verified according to the lyapunov stability principle. Through a DNA strand displacement mechanism, an internal synchronization mode which does not need external chaotic system participation is realized, namely, the synchronization among subsystems in one chaotic system is realized, and under random reaction or other disturbance, the estimation of the synchronization among the subsystems and the self-adaptive law on unknown parameters is verified. The method is robust to parameter bias and synchronizes different one-to-one and one-to-multiple combinations between subsystems by triggering a series of DNA reactions.

Inventors

LV HUI
LIU XIAOXIAO
ZHOU SHIHUA
WANG BIN
ZHANG QIANG

Assignees

大连大学

Dates

Publication Date: 20260512
Application Date: 20230808

Claims (7)

1. The method for adaptively and synchronously controlling the parameter unknown chaotic system based on DNA strand displacement is characterized by comprising the following steps of: Describing the processes of emerging reaction, triggering reaction and degradation reaction through bimolecular chemical reaction to obtain a chemical reaction module of a nonlinear differential equation with a square term and a product term; constructing a Yang chaotic system by utilizing a DNA strand displacement reaction; Acquiring an adaptive controller capable of realizing synchronization and an adaptive law expression for estimating unknown parameters; through a DNA strand displacement mechanism, an internal synchronization mode which does not need external chaotic system participation is realized, namely, the synchronization among subsystems in one chaotic system is realized; under random reaction or other disturbance, verifying the estimation of unknown parameters by the synchronization and self-adaptive law among subsystems; the process of the emergence reaction, the triggering reaction and the degradation reaction is described through a bimolecular chemical reaction, and specifically comprises the following steps: The reaction is: Wherein, the And Is the reaction rate of the DNA, , Represents a substrate, and is used to treat a substrate, And The expression "enzyme" is used to indicate an enzyme, , Represents an enzyme-substrate complex which is capable of binding to a substrate, And Representing an output substance; triggering a reaction: Wherein, the And The expression "enzyme" is used to indicate an enzyme, , Representing an enzyme-substrate complex; degradation reaction: Wherein, the And The expression "enzyme" is used to indicate an enzyme, , Represents an enzyme-substrate complex which is capable of binding to a substrate, Representing an output substance; combining mass action kinetics MAK, in emerging, triggering and degradation reactions The concentration changes of (a) are respectively abstracted as: , And The three nonlinear differential equations are used for constructing a chemical reaction module with square terms and product terms; The Yang chaotic system is constructed by utilizing DNA strand displacement reaction, and concretely comprises , And The state variables are the state variables respectively, , And Is a chaotic system parameter; the differential dynamic equation of the Yang chaotic system is as follows: The corresponding CRNs are: Wherein the first kind of reaction The corresponding DNA realizations are expressed as: reaction of the second kind The corresponding DNA realizations are expressed as: Reaction of the third kind The corresponding DNA is realized as a degradation reaction module; Wherein, the , And Is an intermediate product of the preparation method, , , And Is an auxiliary substance which participates in the reaction, Represents inert waste that does not interact with other materials, Indicating the reaction rate of the maximum strand displacement, The reaction rate is shown.
2. The method for adaptively controlling the synchronous control of the unknown-parameter chaotic system based on the DNA strand displacement of claim 1, further comprising verifying the validity of the adaptive controller according to the Lyapunov stability principle.
3. The method for adaptively synchronizing a chaotic system with unknown parameters based on DNA strand displacement of claim 1, wherein the expression of the adaptive controller capable of achieving synchronization is obtained by a response system And driving system Synchronization, error Zero error dynamic system Asymptotically stable, the results are as follows: Wherein, the Is a self-adaptive controller, which is used for controlling the power supply, Is an adaptive parameter greater than 0; 、 Representing unknown parameters And Is used for the estimation of the estimated value of (a).
4. The method for adaptively and synchronously controlling a parameter unknown chaotic system based on DNA strand displacement according to claim 3, wherein the method for adaptively and synchronously controlling the parameter unknown chaotic system based on DNA strand displacement is characterized by obtaining an adaptive law expression capable of estimating the unknown parameter, specifically comprising the following steps: Wherein, the Is a self-adaptive law of the design, And Is the difference between the unknown parameter and the estimated parameter.
5. The method for adaptively and synchronously controlling a parameter unknown chaotic system based on DNA strand displacement as defined in claim 1, wherein the validity of the adaptive controller is verified according to the principle of Lyapunov stability, specifically, a positive Lyapunov function PDLF is selected, Wherein, the method comprises the steps of, , , Along error dynamic system The track time derivative of (2) is as follows: Because of Is positive and the number of the electrodes is positive, Is semi-negative, so that the error is dynamic The global asymptotic stability, and the driving system and the response system realize synchronization.
6. The method for adaptively synchronizing and controlling a parameter-unknown chaotic system based on DNA strand displacement as set forth in claim 1, wherein an internal synchronizing manner is realized without participation of an external chaotic system by a DNA strand displacement mechanism, namely, an inter-subsystem synchronizing in the chaotic system is realized, specifically, an internal synchronizing based on DNA is realized by giving out an adaptive controller and CRNs corresponding to an adaptive law expression, the adaptive controller The CRNs of (c) are constructed as follows: self-adaptive law The CRNs of (c) are constructed as follows: type IV reaction The implementation of the DNA of (2) as a trigger reaction module, the internal synchronization is still valid in one-to-many situations.
7. The method for adaptively controlling a chaotic system with unknown parameters based on DNA strand displacement as set forth in claim 1, wherein the method comprises verifying the estimation of the unknown parameters by the synchronization and the adaptive law between the subsystems under the condition of random reaction or other disturbance, specifically, the unknown parameters are assumed to be Wherein As a result of the unknown parameters, Is a disturbance; Wherein the estimated value of the unknown parameter is continuously modified along with the product of the systematic error, the self-adaptive parameter and the parameter error, and the self-adaptive controller is adjusted Thereby completing the synchronization of the controlled chaotic system and the estimation of disturbance unknown parameters.

Description

Parameter unknown chaotic system self-adaptive synchronous control method based on DNA strand displacement Technical Field The invention relates to the technical field of chaotic synchronization of biological systems based on DNA strand displacement, in particular to a method for adaptively and synchronously controlling a chaotic system with unknown parameters based on DNA strand displacement. Background DNA molecules are widely recognized as ideal engineering materials for constructing molecular devices based on chemical reaction networks CRNs, particularly DNA strand displacement reactions DSD, and have become a means of formally programming and analyzing DNA devices. Meanwhile, the chemical reaction network CRNs is an effective programming language for designing complex network behavior, which means that any chemical reaction can be realized and approximated by DSD. Therefore, in designing applications such as chaotic systems, biochemical controllers, etc., it is a major goal to construct CRNs to represent the dynamics of the system. Combining with DNA strand displacement mechanism, further realizing digital circuit, signal processing calculation and simulation, etc. Chaos is an unpredictable, random-like phenomenon exhibited by nonlinear systems. The nonlinear functions of the chaotic system are different, and the dynamic characteristics are different. Chaotic synchronization is a precondition for realizing chaotic secret communication, and the synchronous result is that the action tracks of the response system and the driving system are gradually consistent. Along with the development of the chaos synchronization theory, scholars propose different kinds of synchronization modes. For example, shahzad M published in 2023 under International Journal of Robust and Nonlinear Control,33 (3), 2320-2335, article "Internal synchronization using ADAPTIVE SLIDING mode", gives the concept of internal synchronization, enables synchronization of a specific subsystem or the whole system, and eliminates the dependence on external systems. They are complementary improvements to full synchronization and find wide application in secure communications, physical and biological fields, etc. Therefore, the novel chaotic system synchronization mode is explored, and the control method of the novel synchronization mode is researched, so that the novel chaotic system synchronization method has important practical value. The DSD technology not only can realize compiling of the chaotic system, but also can enhance the synchronous safety of the chaotic system. Zou C, zhang Q, wei X. Published in 2021 under IEEE/ACM Transactions on Computational Biology and Bioinformatics,19 (3), article "Synchronization of hyper-Lorenz system based on DNA STRAND DISPLACEMENT" 1897-1908, constructed an ultra Lorenz system with ideal chemical networks, designed coupling terms by helper DNA strand and substitution reactions and achieved system synchronization. In addition, [31]Sun J,Shan Z,Liu P,Wang Y, published in IEEE Transactions on NanoBioscience in 2022, doi:10.1109/TNB.2022.3213946, "Backstepping Synchronization Control for Three-dimensional Chaotic Oscillatory System via DNA Strand Displacement",, based on inversion control theory and DNA reaction module, designed three synchronization controllers to ensure synchronization of two three-dimensional DNA chaotic systems. The inversion control of the chaotic system is realized for the first time in the DSD field, and the control speed is superior to PI control and coupling combination synchronization. The synchronous control result of the existing chaotic system based on DSD rarely discusses the condition that parameters of the chaotic system are unknown and structures are different. However, in practical applications, if these uncertainties are not taken into account, the synchronization performance of the system is affected and impaired. The self-adaptive control method can realize the synchronization of the chaotic system with uncertain parameters and has robustness, so that the research on the self-adaptive synchronization of the chaotic system based on DSD has practical significance. Disclosure of Invention The invention aims to provide a self-adaptive synchronous control method of a parameter unknown chaotic system based on DNA strand displacement, which has robustness to parameter deviation and can realize the synchronization of internal subsystems without the participation of an external chaotic system. In order to achieve the above purpose, the application provides a method for adaptively and synchronously controlling a parameter unknown chaotic system based on DNA strand displacement, which comprises the following steps: Describing the processes of emerging reaction, triggering reaction and degradation reaction through bimolecular chemical reaction to obtain a chemical reaction module of a nonlinear differential equation with a square term and a product term; constructing a Yang chaotic