CN111624881A - Synchronous control method and system based on gene network - Google Patents
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Abstract
The invention discloses a synchronous control method and a synchronous control system based on a gene network, and provides stability and synchronous control for the system aiming at a quorum sensing system in cellular immunity. The invention researches the projection synchronization control under the synchronization condition, namely, the driving system and the response system are in proportional relation, and the proportionality coefficient is random. The synchronization can better observe the stability and other performances of the quorum sensing system in the quorum sensing background, and amplify various information exchange processes in the quorum sensing process. The synchronous introduction of the gene into a quorum sensing system is another progress of human beings on biotechnology, and after further research, the gene can control the vital activities of cells, thereby having great significance to life science.
Description
Technical Field
The invention belongs to the field of gene network synchronous control, and particularly relates to a synchronous control method and system based on a gene network.
Background
In recent years, the quorum sensing has received extensive attention, and since 1996, the quorum sensing was first discovered in bacteria to date, and breakthroughs and advances have been made in the aspects of environmental protection, disease prevention and treatment and the like. Research shows that in agriculture, quorum sensing is also gradually valued by biologists and agriculturists. Particularly, in the case of food shortage accompanied by population growth facing the world, the quorum sensing inhibitor can achieve the effect of controlling the density of pathogenic bacteria by influencing the expression of pathogenic bacteria genes under the condition of limited cultivated land area, the reduction of the density can effectively reduce the capability of damaging crops, reduce the damage degree of the pathogenic bacteria to plants, and produce high-yield and high-quality food crops.
Quorum sensing is present in bacteria and fungi. Quorum sensing also affects the luminescence of organisms, the colony behavior of natural world such as plant symbiosis and the like, affects the formation of biological membranes, some block communication by inhibiting quorum sensing to cause bacterial infection pathogens, and also affect the transcription and expression of sRNA (single stranded ribonucleic acid), and quorum sensing phenomena are closely related to biological swarm phenomena. The above phenomena indicate that the study of quorum sensing is very necessary, and therefore the tracking of cell life activities based on quorum sensing studies is one of the hot spots and focuses of microbiological research.
At present, a quorum sensing system is mainly analyzed and controlled in a mathematical modeling mode, wherein firstly, a mathematical model for simulating the biological function of the system is established; in order to further research the action principle of quorum sensing, people summarize different models aiming at different types of quorum sensing systems, abstract a mathematical model and further better analyze and research quorum sensing. Wherein, the abstract mathematical model comprises:
the nonlinear system dynamics model roughly comprises researches on several dynamic behaviors such as chaos, bifurcation and synchronization. Unlike the linear system model, the nonlinear system cannot apply the superposition principle, and the stability of the nonlinear system is complicated. Because, the nonlinear system has a plurality of equilibrium states, and the different equilibrium states are stable and have the possibility of being branched. The stability or bifurcation is related to the initial conditions of the system and has an inseparable relationship with the parameters and structure of the system. The starting point is different, the time lag is different, and the state of the system can be different if the system is stable or unstable. Non-linear systems are more focused on specific problem analysis than linear systems. Due to the complexity of mathematical computation, the nonlinear system has no specific complete model to describe the outline so far, and under the premise that an accurate mathematical model is suggested to track the cell life activity, the method is very important.
Disclosure of Invention
The invention aims to solve the technical problem that a non-linear system does not have a specific complete model to describe defects so far due to the complexity of mathematical computation in the prior art, and provides a synchronous control method and system based on a gene network.
The technical scheme adopted by the invention for solving the technical problems is as follows: a synchronous control method based on a gene network is constructed, and comprises the following steps:
s1, based on a quorum sensing system, the quorum sensing system comprises a driving model and a response model, and infection models of the driving model and the response model under a quorum sensing background are respectively constructed;
s2, based on the infection model constructed in the step S1, stability analysis is carried out on the quorum sensing system to obtain a plurality of free balance points, and when the system is judged to be stable through the free balance points, the next step is executed;
s3, adding a synovial membrane controller u (t) into the response model, and adjusting the control parameters of the quorum sensing system according to the parameter self-adaptation law; the projection synchronous control method is used, the output signal of the driving model is used for driving the response model, and when the error function of the response system and the driving system reaches a stable state and the synchronous errors of the response system and the driving system approach to 0, namely the response system and the driving system are synchronously controlled by the projection synchronous control method
Realizing the synchronous control of the gene network, and controlling the life activities of the cells based on the gene network after the synchronous control; wherein:
e＝[e1e2e3]T；
in the above first formula, e1＝V'-m1V,e2＝R'-m2R,e3＝N'-m3N, wherein mi∈R，i＝1,2,3,miNot equal to 0 is a scalar scale factor, e1、e2、e3Are all predefined error values, V, V' respectively representing driving and response modesThe number of susceptible host cells under type; r, R' represents the number of infected cells under the driving and response models, respectively; n, N' represents the number of immune cells under the driving and response model;
in the second formula, t is the input signal of the driving model, τ is the delay parameter, b, β, c are constants taking positive values, c1,c2R is a design parameter greater than 0, s is a synovial surface in a synovial controller, and s ═ e3+c1e1+c2e2；
Which is an estimate of the error control parameter α, sign () is a sign function.
The invention discloses a synchronous control system based on a gene network, which comprises the following modules:
the model building module is used for building an infection model of the driving model and the response model under the quorum sensing background respectively based on a quorum sensing system, wherein the quorum sensing system comprises the driving model and the response model;
the stability analysis module is used for carrying out stability analysis on the quorum sensing system based on the infection model constructed by the model construction module to obtain a plurality of free balance points, and judging the stability of the system through the free balance points;
the synchronous control module is used for adding a synovial membrane controller u (t) into the response model and adjusting parameters of the quorum sensing system according to the parameter self-adaptation law; the projection synchronous control method is adopted, the output signal of the driving model is used for driving the response model, and when the error function of the response system and the driving system reaches a stable state and the synchronous errors of the reaction approach to 0, namely the synchronous control method is adopted
Realizing the synchronous control of the gene network, and controlling the life activities of the cells based on the gene network after the synchronous control; wherein:
e＝[e1e2e3]T；
in the above first formula, e1＝V'-m1V,e2＝R'-m2R,e3＝N'-m3N, wherein mi∈R，i＝1,2,3,miNot equal to 0 is a scalar scale factor, e1、e2、e3V, V' respectively represent the number of susceptible host cells under the driving and response models; r, R' represents the number of infected cells under the driving and response models, respectively; n, N' represents the number of immune cells under the driving and response model;
in the second formula, t is the input signal of the driving model, τ is the delay parameter, b, β, c are constants taking positive values, c1,c2R is a design parameter greater than 0, s is a synovial surface in a synovial controller, and s ═ e3+c1e1+c2e2；
Which is an estimate of the error control parameter α, sign () is a sign function.
The synchronous control method and the synchronous control system based on the gene network have the following beneficial effects that:
1. the synchronization can enable people to better observe the stability and other performances of the quorum sensing system more quickly under the quorum sensing background, complete the synchronization control under a simple model and amplify various information exchange processes in the quorum sensing process;
2. the synchronous introduction of the gene into a quorum sensing system is another progress of human beings on biotechnology, and after further research, the gene can control the vital activities of cells, thereby having great significance to life science.
Drawings
The invention will be further described with reference to the accompanying drawings and examples, in which:
FIG. 1 is a flow chart of the implementation of a synchronous control method based on a gene network according to the embodiment 1 of the present invention;
FIG. 2 is a flow chart of the implementation of a synchronous control method based on a gene network according to the embodiment 2 of the present invention;
FIG. 3 is a structural diagram of a synchronous control system based on a gene network.
Detailed Description
For a more clear understanding of the technical features, objects and effects of the present invention, embodiments of the present invention will now be described in detail with reference to the accompanying drawings.
The synchronous and complete synchronization of a complex network is in fact a very ideal situation, and is not uncommon in objective reality. Generalized synchronization is easier to achieve in reality than full synchronization, and therefore, more researchers tend to study generalized synchronization. Projection Synchronization (PS) is the most representative of generalized synchronization, and means that the two system states after synchronization differ by a scaling factor α, and the synchronization type can be determined by the value of α.
However, for synchronous control in gene network quorum sensing, research is not much, control methods are complicated, and control of a controller cannot be completed quickly under a simple model because selection of a slide film surface tends to be complicated.
To overcome the disadvantages of the prior art, referring to embodiments 1 and 2, the present invention provides a synovial controller by which a proportional relationship between a driving model and a response model included under a quorum sensing system is controlled for projection synchronization in generalized synchronization, and a proportionality coefficient is random.
Example 1:
please refer to fig. 1, which is a flowchart illustrating a method for synchronous control based on a gene network according to embodiment 1 of the present invention, wherein the method for synchronous control based on a gene network includes the following steps:
s1, based on a quorum sensing system, the quorum sensing system comprises a driving model and a response model, and infection models of the driving model and the response model under a quorum sensing background are respectively constructed; wherein: when the input signals of the driving model and the response model are t and t', respectively, the mathematical expression of the driving and response models is defined as:
wherein the constant lambda is the generation rate of uninfected cells from the previous tissue, t and t ' are input signals of a driving and responding model respectively, V (t) and V (t ') are the numbers of susceptible host cells generated in the model based on the input signals t and t ', R (t) and R (t ') are the numbers of infected cells generated in the model based on the input signals t and t ', N (t) and N (t ') are the numbers of immune cells generated in the model based on the input signals t and t ', and the parameters lambda, a, b, c, d, β and rho are constants taking positive values;
derivation of "-" in the nonlinear system equation;
s2, based on the infection model constructed in the step S1, stability analysis is carried out on the quorum sensing system to obtain a plurality of free balance points, and when the system is judged to be stable through the free balance points, the next step is executed; when a balance point is obtained, the right side of the original quorum sensing system is zero to obtain three equations; the parameters R and N are expressed by the parameter V (refer to the second and third line formulas of the formula (a 3)), the value of V at the equilibrium point is solved according to the formula for solving the one-dimensional cubic equation, and the value of N and the value of R at the equilibrium point can be obtained after the parameter V is solved. Wherein the free balance point is derived by equations (a3) - (a 4):
in the formula (a4), for the sake of formula simplicity, take
M2Where ω is a complex number obtained according to the root equation, and where the parameters λ, a, b, c, d, β, ρ are defined in the preceding section, and where the equations (a3) - (a4) are:
M1＝ρcλ；
M3＝-ρcd+αβb；
in the formula (a3), the parameter V is the number of susceptible host cells generated when inputting signals to the driving and response model; r is the number of infected cells generated when the signal is input to the driving and response model; n is the number of immune cells generated when the signal is input to the driving and response model; in the formula (a4), V1、V2、V3The numbers of susceptible host cells at the three equilibrium points sought, respectively.
In the actual verification process, the method is calculated by the formula, and three balance points are possessed: positive balance point
And when the free balance point 1 and the free balance point 2 are in a negative frequency domain, the quorum sensing system is stable.
S3, adding a synovial membrane controller u (t) into the response model, and adjusting the control parameters of the quorum sensing system according to the parameter self-adaptation law; based on the projection synchronous control method, the output signal of the driving model is used for driving the response model, and when the error function of the response model and the driving model reaches a stable state and the synchronous error of the reaction approaches to 0, namely the synchronous control method is used for controlling the response model to be in a stable state
The synchronous control of the gene network is realized, and currently, the control of cell life activities can be carried out according to the synchronized gene network; wherein:
e＝[e1e2e3]T；(a5)
(a5) wherein u (t) is a mathematical representation of a synovial membrane controller; e.g. of the type1＝V′-m1V,e2＝R′-m2R,e3＝N′-m3N, wherein mi∈R，i＝1,2,3,miNot equal to 0 is a scalar scale factor, e1、e2、e3V, V' respectively represent the number of susceptible host cells under the driving and response models; r, R' represents the number of infected cells under the driving and response models, respectively; n, N' represents the number of immune cells under the driving and response model;
(a6) where t is the input signal of the driving model, τ is the delay parameter, b, β, c are constants taking positive values, c1,c2R is a first system design parameter greater than 0, s is a synovial surface in a synovial controller, and s is e3+c1e1+c2e2；
Which is an estimate of the error control parameter α, sign () is a sign function.
In the present step, when a synovial controller u (t) is added to the response model, the infection model of the response model is changed from (a2) to:
(a7) wherein at an input signal t' to the response model, uninfected cells die at a rate dV and become infected cells at a rate β VR, where β is a rate constant describing the infection process; infected cells die at the rate α R and are killed by immune cells at the rate ρ RN, which die at the rate bN.
The synchronous control technology is introduced into a quorum sensing system, wherein a single-dimensional synovial membrane controller is added to a response model, and under the action of a single-dimensional synchronous controller type and a parameter self-adaptation law type, the chaotic projection synchronous error system can be ensured to be asymptotically stable. It should be further noted that, when designing the sliding mode controller u (t) in step S3, the method includes the following steps:
s31, defining the error vector as e (t) α N2(t)-N1(t), the synovial controller was designed in its original form u (t) ═ ke (t), when the third row of the formula (a7) was rewritten as:
wherein N is1(t) and N2(t) the number of immune cells in the driver and response models, respectively; k is a system design parameter greater than 0;
s32, defining an error value: e.g. of the type1＝V′-m1V,e2＝R′-m2R,e3＝N′-m3N, wherein mi∈R(i＝1,2,3,miNot equal to 0) is a scalar scale factor; v, V' respectively represents the numbers of susceptible host cells defined under the driving and response models; r, R' respectively represents the number of infected cells defined under the driving and response model; n, N' represents the number of immune cells defined under the driving and response model;
in the current step, a projection synchronization control method is adopted, which comprises the following steps of:
wherein m is a scalar scale factor;
s33, simplifying the formula (a8), obtaining:
currently, the mathematical representation of the desired one-dimensional synovial membrane controller u (t) is further obtained as:
(a10) where t is the input signal of the driving model, τ is the delay parameter, b, β, c are constants taking positive values, c1、c2R is a system design parameter larger than 0, and the system design parameter is debugged according to experience in the later period; s is the synovial surface in the synovial controller, and s ═ e3+c1e1+c2e2；
Which is an estimate of the error control parameter α, sign () is a sign function.
In this embodiment, when synchronous stable control of a gene network is implemented, a single-dimensional controller designed based on the formula (a10) and under the action of a parameter adaptation law achieve corresponding technical effects; the mathematical expression of the parameter adaptation law L is as follows:
(a11) in the formula (I), the compound is shown in the specification,
γ1、γ2、γ3all are system design parameters, θ, greater than 01、θ2、θ3Are all vectors of control parameters of the system,
is thetaiI is 1,2, 3.
For chaotic synchronization error system, the single-dimensional synchronous controller type and the parameter adaptive law type designed under the embodimentUnder the action, the asymptotic stabilization of the chaotic projection synchronous error system can be realized, namely
Wherein e ═ e1e2e3]T。
Example 2:
based on example 1, when the amount of immune cells at time t depends on the amount at time t- τ, i.e. there is a time lag in the system, in order to accurately determine the stability of the system, in step S2, please refer to fig. 2, when performing the stability analysis of the system, on one hand, the time lag condition of critical stability of the system is calculated according to the nyquist stability criterion; on the other hand, the system stability is determined based on the obtained free balance point. In the process of time-lag condition judgment, the essential conditions of system stability are as follows: the number of open-loop right poles of the system is P, when omega is changed from-infinity to + ∞ona GH plane, the frequency characteristic curve GK (j omega) of the open-loop system and a closed curve formed by a mirror image of the open-loop frequency characteristic curve GK (j omega) are N circles (N >0) when the closed-loop frequency characteristic curve is clockwise surrounded by (-1, j0), N is less than 0 when the closed-loop frequency characteristic curve is counterclockwise surrounded by (-1, j0) points, the closed-loop frequency characteristic curve rotates by 360 degrees, namely is surrounded by one time, and the number Z of closed-loop right poles of the closed-loop: and Z is N + P. When Z is 0, the system is stable; when Z >0, the system is unstable.
Example 3:
on the basis of embodiment 1 or 2, the internal structure of the synchronous control system based on the gene network disclosed by the present invention refers to fig. 3, and the synchronous control system includes a model building module L1, a stability analysis module L2, and a synchronous control module L3:
the execution function of the model construction module L1 refers to step S1 described in embodiment 1, and the module is mainly used for constructing infection models of the driver model and the response model in the quorum sensing background;
please refer to step S2 described in embodiment 1 for the execution function of the stability analysis module L2, which is mainly used for performing stability analysis on the quorum sensing system by finding a free balance point; wherein:
the stability analysis module L2 further comprises a time-lag condition calculation module L21, when the quantity of immune cells at the time t depends on the quantity at the time t-tau, the time-lag condition of system critical stability is calculated according to the Nyquist stability criterion condition, and the system stability analysis is further carried out;
please refer to step S3 described in embodiment 1, the synchronous control module L3 is mainly used to implement synchronous control of the gene network by using a projection synchronous control method when adding a synovial membrane controller u (t) to the response model, and to control cell life activities based on the synchronized gene network.
Based on embodiments 1-3, the invention discloses a synchronous control method and system based on a gene network, and provides stability and synchronous control for the system aiming at a quorum sensing system in cellular immunity in a mathematical modeling mode. The synchronization can better observe the stability and other performances of the quorum sensing system in the quorum sensing background, and amplify various information exchange processes in the quorum sensing process. The synchronous introduction of the gene into a quorum sensing system is another progress of human beings on biotechnology, and after further research, the gene can control the vital activities of cells, thereby having great significance to life science.
While the present invention has been described with reference to the embodiments shown in the drawings, the present invention is not limited to the embodiments, which are illustrative and not restrictive, and it will be apparent to those skilled in the art that various changes and modifications can be made therein without departing from the spirit and scope of the invention as defined in the appended claims.
Claims (10)
1. A synchronous control method based on a gene network is characterized by comprising the following steps:
s1, based on a quorum sensing system, the quorum sensing system comprises a driving model and a response model, and infection models of the driving model and the response model under a quorum sensing background are respectively constructed;
s2, based on the infection model constructed in the step S1, stability analysis is carried out on the quorum sensing system to obtain a plurality of free balance points, and when the system is judged to be stable through the free balance points, the next step is executed;
s3, adding a synovial membrane controller u (t) into the response model, and adjusting the control parameters of the quorum sensing system according to the parameter self-adaptation law; the projection synchronous control method is adopted, the output signal of the driving model is used for driving the response model, and when the error function of the response system and the driving system reaches a stable state and the synchronous error of the reaction approaches to 0, namely the synchronous control method is adopted
Realizing the synchronous control of the gene network, and controlling the life activities of the cells based on the gene network after the synchronous control; wherein:
e＝[e1e2e3]T； (1)
(1) in the formula, e1＝V'-m1V,e2＝R'-m2R,e3＝N'-m3N, wherein mi∈R，i＝1,2,3,miNot equal to 0 is a scalar scale factor, e1、e2、e3V, V' respectively represent the numbers of susceptible host cells defined under the driving and response models; r, R' respectively represents the number of infected cells defined under the driving and response model; n, N' represents the number of immune cells defined under the driving and response model;
(2) where t is the input signal of the driving model, τ is the delay parameter, b, β, c are constants taking positive values, c1,c2R is a first system design parameter greater than 0, s is a synovial surface in a synovial controller, and s is e3+c1e1+c2e2；
Which is an estimate of the error control parameter α, sign () is a sign function.
2. The synchronous control method according to claim 1, wherein step S2 further comprises the step of generating a time lag when the number of immune cells generated at time t depends on the number at time t- τ;
in the current step, a time-lag condition of system critical stability is calculated according to a Nyquist stability criterion condition, and the system stability is judged by combining a free balance point.
3. The synchronous control method according to claim 2, wherein in step S1, the infection model of the driving model is:
in step S3, after adding the synovial controller u (t) to the response model, the infection model of the response model is:
wherein t and t ' are input signals of a driving and responding model respectively, V (t) and V (t ') are numbers of susceptible host cells generated in the model based on the input signals t and t ', R (t) and R (t ') are numbers of infected cells generated in the model based on the input signals t and t ', N (t) and N (t ') are numbers of immune cells generated in the model based on the input signals t and t ', and parameters lambda, a, b, c, d, β and rho are constants taking positive values;
derivation of "-" in the nonlinear system equation;
(3) in the first line of the calculation formulas in formulas (1) and (4), λ is the generation rate of infected cells from the precursor tissue when a signal is input to the model, and uninfected cells die at a rate dV and become infected cells at a rate β VR; in the second line of the calculation formula, when a signal is input to the model, β is a rate constant describing the infection process, and infected cells die at a rate aR and are killed by immune cells at a rate ρ RN; in the third line of the calculation formula, when a signal is input to the model, immune cells die at a rate bN;
the parameter t in the driving model is used as an input signal of the response model, and affects the output of the response model together with the signal t'.
4. The synchronous control method according to claim 3, wherein in step S3, the slip film controller u (t) is a one-dimensional controller;
the projection synchronization control method comprises the following steps of:
wherein m is a scalar scale factor; based on the formula (5), the steady state determination of the response model and the drive model is performed.
5. The synchronous control method according to claim 4, wherein in step S3, synchronous stable control of the gene network is realized under the action of the single-dimensional controller u (t) and the parameter adaptive law; the mathematical expression of the parameter adaptation law is as follows:
wherein the content of the first and second substances,
γ1、γ2、γ3second system design parameters, θ, each being greater than 01、θ2、θ3Are all systemsThe vector of control parameters is then used to control,
is thetaiI is 1,2, 3.
6. A synchronous control system based on a gene network is characterized by comprising the following modules:
the model building module is used for building an infection model of the driving model and the response model under the quorum sensing background respectively based on a quorum sensing system, wherein the quorum sensing system comprises the driving model and the response model;
the stability analysis module is used for carrying out stability analysis on the quorum sensing system based on the infection model constructed by the model construction module to obtain a plurality of free balance points, and judging the stability of the system through the free balance points;
the synchronous control module is used for adding a synovial membrane controller u (t) into the response model and adjusting parameters of the quorum sensing system according to the parameter self-adaptation law; the projection synchronous control method is adopted, the output signal of the driving model is used for driving the response model, and when the error function of the response system and the driving system reaches a stable state and the synchronous errors of the reaction approach to 0, namely the synchronous control method is adopted
Realizing the synchronous control of the gene network, and controlling the life activities of the cells based on the gene network after the synchronous control; wherein:
e＝[e1e2e3]T； (7)
(7) in the formula, e1＝V′-m1V,e2＝R′-m2R,e3＝N′-m3N, wherein mi∈R，i＝1,2,3,miNot equal to 0 is a scalar scale factor, e1、e2、e3Are all predeterminedError value of sense, V, V', indicates the number of susceptible host cells under the driving and response models, respectively; r, R' represents the number of infected cells under the driving and response models, respectively; n, N' represents the number of immune cells under the driving and response model;
(8) where t is the input signal of the driving model, τ is the delay parameter, b, β, c are constants taking positive values, c1,c2R is a third system design parameter greater than 0, s is a synovial surface in a synovial controller, and s ═ e3+c1e1+c2e2；
Which is an estimate of the error control parameter α, sign () is a sign function.
7. The synchronous control system of claim 6, wherein the stability analysis module further comprises a time lag condition calculation module; the time-lag condition calculation module is used for calculating the time lag of the system when the quantity of the immune cells at the t moment depends on the quantity at the t-tau moment; and calculating a time-lag condition of critical stability of the system according to the Nyquist stability criterion condition, and judging the stability of the system by combining a free balance point.
8. The synchronous control system of claim 7, wherein the infection model of the driving model in the model building module is:
in the synchronous control module, after adding the synovial membrane controller u (t) to the response model, the infection model of the response model is:
wherein t and t' are input signals of the driving and response models respectively; v (t) and V (t') are eachThe number of susceptible host cells generated based on input signals t and t ' in the model, R (t) and R (t ') are the number of infected cells generated based on the input signals t and t ' in the model respectively, N (t) and N (t ') are the number of immune cells generated based on the input signals t and t ' in the model respectively, and parameters lambda, a, b, c, d, β and rho are constants taking positive values;
derivation of "-" in the nonlinear system equation;
(9) in the first line of the calculation formulas in formulas (1) and (10), λ is the generation rate of infected cells from the precursor tissue when a signal is input to the model, and uninfected cells die at a rate dV and become infected cells at a rate β VR; in the second line of the calculation formula, when a signal is input to the model, β is a rate constant describing the infection process, and infected cells die at a rate aR and are killed by immune cells at a rate ρ RN; in the third line of the calculation formula, when a signal is input to the model, immune cells die at a rate bN;
the parameter t in the driving model is used as an input signal of the response model, and affects the output of the response model together with the signal t'.
9. The synchronous control system of claim 8, wherein in the synchronous control module, the slip film controller u (t) is a one-dimensional controller;
the projection synchronization control method comprises the following steps of:
wherein m is a scalar scale factor; the steady state determination of the response model and the drive model is performed based on equation (11).
10. The synchronous control system of claim 9, wherein the synchronous control module implements synchronous stable control of the gene network under the action of the single-dimensional controller u (t) and the parameter adaptive law; the mathematical expression of the parameter adaptation law is as follows:
wherein the content of the first and second substances,
γ1、γ2、γ3fourth System design parameters, θ, that are all greater than 01、θ2、θ3Are all control parameter vectors to be solved,
is thetaiI is 1,2, 3.
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112904730A (en) * | 2021-01-28 | 2021-06-04 | 中国地质大学（武汉） | Feedback control method, system, equipment and storage medium based on group induction |
| CN113219835A (en) * | 2021-05-19 | 2021-08-06 | 安徽大学 | Synchronous control method of complex network and application thereof in image encryption |
Citations (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20110276150A1 (en) * | 2010-05-10 | 2011-11-10 | Al-Duwaish Hussain N | Neural network optimizing sliding mode controller |
| CN105319972A (en) * | 2015-11-27 | 2016-02-10 | 燕山大学 | Remote operating robot fixed time control method based on rapid terminal sliding mode |
| CN105929693A (en) * | 2016-05-19 | 2016-09-07 | 沈阳工业大学 | Adaptive sliding-mode compensation synchronous control system of H type precision motion platform and method |
| CN106325068A (en) * | 2016-08-22 | 2017-01-11 | 哈尔滨理工大学 | Improved function projection method of complicated dynamic network |
| CN108459502A (en) * | 2018-02-11 | 2018-08-28 | 浙江工业大学 | A kind of Multi-arm robots synchronisation control means based on global sliding mode |
| CN108762093A (en) * | 2018-07-11 | 2018-11-06 | 东北大学 | A kind of same dimension chaos overall situation hybrid projection synchronous method improving POLE PLACEMENT USING |
| CN108845494A (en) * | 2018-08-29 | 2018-11-20 | 东北大学 | A kind of tight feedback chaos projective synchronization method of second order |
| CN108931917A (en) * | 2018-09-04 | 2018-12-04 | 东北大学 | A kind of tight feedback chaos projective synchronization method of three ranks |
-
2020
- 2020-05-27 CN CN202010460876.XA patent/CN111624881B/en not_active Expired - Fee Related
Patent Citations (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20110276150A1 (en) * | 2010-05-10 | 2011-11-10 | Al-Duwaish Hussain N | Neural network optimizing sliding mode controller |
| CN105319972A (en) * | 2015-11-27 | 2016-02-10 | 燕山大学 | Remote operating robot fixed time control method based on rapid terminal sliding mode |
| CN105929693A (en) * | 2016-05-19 | 2016-09-07 | 沈阳工业大学 | Adaptive sliding-mode compensation synchronous control system of H type precision motion platform and method |
| CN106325068A (en) * | 2016-08-22 | 2017-01-11 | 哈尔滨理工大学 | Improved function projection method of complicated dynamic network |
| CN108459502A (en) * | 2018-02-11 | 2018-08-28 | 浙江工业大学 | A kind of Multi-arm robots synchronisation control means based on global sliding mode |
| CN108762093A (en) * | 2018-07-11 | 2018-11-06 | 东北大学 | A kind of same dimension chaos overall situation hybrid projection synchronous method improving POLE PLACEMENT USING |
| CN108845494A (en) * | 2018-08-29 | 2018-11-20 | 东北大学 | A kind of tight feedback chaos projective synchronization method of second order |
| CN108931917A (en) * | 2018-09-04 | 2018-12-04 | 东北大学 | A kind of tight feedback chaos projective synchronization method of three ranks |
Non-Patent Citations (2)
| Title |
|---|
| ABHISHEK GARG，等: "Synchronous versus asynchronous modeling of gene regulatory networks", 《BIOINFORMATICS》 * |
| FENG LIU，等: "Synchronization of fractional-order gene regulatory network with delay", 《PROCEEDINGS OF THE 36TH CHINESE CONTROL CONFERENCE》 * |
Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112904730A (en) * | 2021-01-28 | 2021-06-04 | 中国地质大学（武汉） | Feedback control method, system, equipment and storage medium based on group induction |
| CN113219835A (en) * | 2021-05-19 | 2021-08-06 | 安徽大学 | Synchronous control method of complex network and application thereof in image encryption |
| CN113219835B (en) * | 2021-05-19 | 2022-04-08 | 安徽大学 | Synchronous control method of complex network and application thereof in image encryption |
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