CN106875009A - A kind of chaotic control method based on artificial neural network - Google Patents
A kind of chaotic control method based on artificial neural network Download PDFInfo
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Abstract
A kind of chaotic control method based on artificial neural network proposed in the present invention, its main contents include：Lorentz oscillator, cai's circuit, artificial neural network (ANN), use ANN control chaotics, its process is, cai's circuit is first built on panel, the output shown on oscillograph is tested and obtain, the electronic circuit of ANN various pieces is redrawn with simulation analysis program, the output of ANN circuits is connected to cai's circuit, a part for circuit output feeds back to ANN again, correspondingly adjusts weight, and ANN is by study, the parameter of cai's circuit is adjusted, required output is given.The present invention obtains required output, there is provided the stability of control using artificial neural network (ANN) effectively control chaotic system from chaos system, realizes automation；Chaos system is controlled, and it is realized the function in other application.
Description
Technical field
The present invention relates to chaos controlling field, more particularly, to a kind of chaos controlling side based on artificial neural network
Method.
Background technology
In recent years, scientist and scholar etc. mixed between finding every subjects from the observation to chaos phenomenon and research steering
The mutual restricting relation and inner link of ignorant behavior, so as to seek common law and the system that a major class challenge is generally followed
Method.There is the application prospect of great researching value and someone due to chaos controlling in engineering technology, it has become non-
The recent studies on field of linear scientific application.Chaotic system control has many potential applications, such as heat transfer, and biosystem swashs
Photophysics, chemical reactor, biomedicine, economics, weather and secure communication, or even also show in scientific research and national defense and military
Increasingly consequence is shown.However, chaos controlling technology of today is still unstable.
The present invention proposes a kind of chaotic control method based on artificial neural network, and Cai Shi electricity is first built on panel
Road, tests and obtains the output shown on oscillograph, and the electronic circuit of ANN various pieces, ANN electricity are redrawn with simulation analysis program
The output on road is connected to cai's circuit, and a part for circuit output feeds back to ANN again, correspondingly adjusts weight, and ANN is by learning
Practise, adjust the parameter of cai's circuit, provide required output.The present invention is using artificial neural network (ANN) effectively control chaotic
System, obtains required output, there is provided the stability of control from chaos system, realizes automation；Chaos system is obtained
Control, allows it to realize the function in other application.
The content of the invention
For the unstable problem of chaos controlling, the present invention provides a kind of chaos controlling side based on artificial neural network
Method, its main contents include：
(1) Lorentz oscillator；
(2) cai's circuit；
(3) artificial neural network (ANN)；
(4) ANN control chaotics are used.
Wherein, the method for described artificial neural network (ANN) control chaotic, can be had using artificial neural network (ANN)
Effect control chaotic, obtains required output from chaos system, and the chaos system of stabilization can be caused using ANN；Realize this
The subject matter of expected result is the time needed for adjusting ANN weights, first manually one by one by adjusting the output resistance of Cai Shi,
Then automatically by feedback control system.
Further, described chaos, it is defined as the attribute of nonlinear dynamic system, when minimum in systems becomes
When change causes system action difference very big, the sensitive dependence to primary condition is shown；The confusion that chaos is ordered into, because
The influence that forecasting system behavior will be produced to the change in input is unable to, so chaos is uncertain.
Wherein, described Lorentz oscillator, three below ODE defines the chaos row of Lorentz oscillator
For：
Dx/dt=δ (y-x) (1)
Dy/dt=δ (ρ-z)-y (2)
Dz/dt=xy- β z (3)
Wherein, x, y and z define the state of system, and t is the time, and δ, ρ and β are systematic parameters.
Further, described chaotic behavior, usual system does not show any kind of chaotic behavior, but for its parameter
Some values, such as：β=8/3, δ=10, ρ=28, system is there may be chaos figure；
As logarithmic mapping equation (xn+1=μ xn(1+xn)) in μ when increasing above 3.3, another of chaos just occurs
Good example；Work as μ<When 3.3, system vibrates between two values of x (cycle -2 circulation)；Further increase μ, make system
Vibration (bifurcated/cycle -4 circulation) between being worth at four, if keeping increasing μ, period multiplication is by smaller of parameter μ
Every generation.
Wherein, described cai's circuit, cai's circuit is one of simplest chaos system；Use oscillograph, Ke Yiguan
The double rollings of chaos of cai's circuit establishment are observed, it can be by three equation Modelings：
C1dv1/ dt=(v2-v1)/R-g(v1) (4)
C2dv2/ dt=- (v2-v1)/R+I (5)
LdI/dt=-rI-v2 (6)
Wherein, v1And v2It is respectively C1And C2The voltage at two ends, g (v1) it is nonlinear resistance (equivalent to Cai Shi diodes)
Conductance, r is the resistance of inductance.
Wherein, described artificial neural network (ANN), ANN are a parts of artificial intelligence (AI), and it is based on biological neural
System；It is based on the feedback of the input and its output in some sense due to neutral net and changes or learn, flows through network
Information can influence the structure of ANN.
Further, the output of described artificial neuron is by following formula control：
Y=f (v) (7)
Wherein, f (v) is activation primitive,
V=w1x1+w1x1+…+wmxm+w0b0 (8)
Wherein, w0,w1,w2,…wmIt is weight, x1,x2,…xmIt is input, b0It is deviation；
In order to obtain some desired output yd, the output of neuron is propagated back to system, and obtain by adjusting weight
Obtain desired output；Activation primitive used herein is S type functions.
Wherein, described use ANN control chaotics, for the chaotic behavior for controlling cai's circuit to be presented, first in face
Cai's circuit is built on plate, the output shown on oscillograph is tested and obtain；
By adjusting the value of resistance R and C, chaotic behavior can be eliminated, and circuit is provided desired stabilization output, be used for
Respond the different choice of R and C.
Further, described structure cai's circuit, above-mentioned circuit is simulated with Matlab, uses available Cai Shi electricity
The program on road is its equation；By using the electronic circuit built on panel, then mixed using Matlab available programs
Walk randomly as rear, the electronic circuit (weight, summing function, activation primitive) of ANN various pieces is redrawn with simulation analysis program, then
It is all to be electrically connected to together；Finally, the output of the big circuits of ANN is connected to cai's circuit, and a part for cai's circuit output is anti-
ANN is fed to, weight is correspondingly adjusted；
Once all be electrically connected to together, it is possible to use different initial values is ANN weights, then ANN passes through study,
The parameter of cai's circuit is adjusted, required output is given.
Brief description of the drawings
Fig. 1 is a kind of system framework figure of the chaotic control method based on artificial neural network of the present invention.
Fig. 2 is a kind of cai's circuit of the chaotic control method based on artificial neural network of the present invention.
Fig. 3 is a kind of artificial neural network of the chaotic control method based on artificial neural network of the present invention.
Fig. 4 is a kind of neuron system of the chaotic control method based on artificial neural network of the present invention.
Specific embodiment
It should be noted that in the case where not conflicting, the feature in embodiment and embodiment in the application can phase
Mutually combine, the present invention is described in further detail with specific embodiment below in conjunction with the accompanying drawings.
Fig. 1 is a kind of system framework figure of the chaotic control method based on artificial neural network of the present invention.Mainly include Lip river
Human relations hereby oscillator, cai's circuit, artificial neural network (ANN), use ANN control chaotics.
Wherein, using artificial neural network (ANN) can effective control chaotic, required output is obtained from chaos system,
The chaos system of stabilization can be caused using ANN；The subject matter for realizing this expected result be adjust ANN weights needed for when
Between, first manually one by one by adjusting the output resistance of Cai Shi, then automatically by feedback control system.
Chaos is defined as the attribute of nonlinear dynamic system, when minimum change in systems causes system action difference
When very big, the sensitive dependence to primary condition is shown；The confusion that chaos is ordered into, will because being unable to forecasting system behavior
The influence produced to the change in input, so chaos is uncertain.
Wherein, three below ODE defines the chaotic behavior of Lorentz oscillator：
Dx/dt=δ (y-x) (1)
Dy/dt=δ (ρ-z)-y (2)
Dz/dt=xy- β z (3)
Wherein, x, y and z define the state of system, and t is the time, and δ, ρ and β are systematic parameters.
Usual system does not show any kind of chaotic behavior, but for some values of its parameter, such as：β=8/3, δ=
10, ρ=28, system is there may be chaos figure；
As logarithmic mapping equation (xn+1=μ xn(1+xn)) in μ when increasing above 3.3, another of chaos just occurs
Good example；Work as μ<When 3.3, system vibrates between two values of x (cycle -2 circulation)；Further increase μ, make system
Vibration (bifurcated/cycle -4 circulation) between being worth at four, if keeping increasing μ, period multiplication is by smaller of parameter μ
Every generation.
Wherein, using ANN control chaotics, for the chaotic behavior for controlling cai's circuit to be presented, the structure first on panel
Cai's circuit is built, the output shown on oscillograph is tested and obtain；
By adjusting the value of resistance R and C, chaotic behavior can be eliminated, and circuit is provided desired stabilization output, be used for
Respond the different choice of R and C.
Above-mentioned circuit is simulated with Matlab, the use of the program of available cai's circuit is its equation；By using
The electronic circuit built on panel, after then obtaining chaotic behavior using Matlab available programs, is redrawn with simulation analysis program
The electronic circuit (weight, summing function, activation primitive) of ANN various pieces, it is then all to be electrically connected to together；Finally, ANN
The output of big circuit is connected to cai's circuit, and a part for cai's circuit output feeds back to ANN, correspondingly adjusts weight；
Once all be electrically connected to together, it is possible to use different initial values is ANN weights, then ANN passes through study,
The parameter of cai's circuit is adjusted, required output is given.
Fig. 2 is a kind of cai's circuit of the chaotic control method based on artificial neural network of the present invention.Cai's circuit is most
One of simple chaos system；Use oscillograph, it can be observed that the double rollings of chaos that cai's circuit is created, it can be by three
Individual equation Modeling：
C1dv1/ dt=(v2-v1)/R-g(v1) (4)
C2dv2/ dt=- (v2-v1)/R+I (5)
LdI/dt=-rI-v2 (6)
Wherein, v1And v2It is respectively C1And C2The voltage at two ends, g (v1) it is nonlinear resistance (equivalent to Cai Shi diodes)
Conductance, r is the resistance of inductance.
Fig. 3 is a kind of artificial neural network of the chaotic control method based on artificial neural network of the present invention.Artificial neuron
Network (ANN) is a part of artificial intelligence (AI), and it is based on biological nervous system；Due to neutral net base in some sense
Change or learn in the feedback of the input and its output, flowing through the information of network can influence the structure of ANN.
Fig. 4 is a kind of neuron system of the chaotic control method based on artificial neural network of the present invention.Artificial neuron
Output by following formula control：
Y=f (v) (7)
Wherein, f (v) is activation primitive,
V=w1x1+w1x1+…+wmxm+w0b0 (8)
Wherein, w0,w1,w2,…wmIt is weight, x1,x2,…xmIt is input, b0It is deviation；
In order to obtain some desired output yd, the output of neuron is propagated back to system, and obtain by adjusting weight
Obtain desired output；Activation primitive used herein is S type functions.
For those skilled in the art, the present invention is not restricted to the details of above-described embodiment, without departing substantially from essence of the invention
In the case of god and scope, the present invention can be realized with other concrete forms.Additionally, those skilled in the art can be to this hair
Bright to carry out various changes and modification without departing from the spirit and scope of the present invention, these improvement also should be regarded as of the invention with modification
Protection domain.Therefore, appended claims are intended to be construed to include preferred embodiment and fall into all changes of the scope of the invention
More and modification.
Claims (10)
1. a kind of chaotic control method based on artificial neural network, it is characterised in that mainly include Lorentz oscillator ()；
Cai's circuit (two)；Artificial neural network (ANN) (three)；Use ANN control chaotics (four).
2. the method for artificial neural network (ANN) control chaotic being based on described in claims 1, it is characterised in that user
Artificial neural networks (ANN) can effective control chaotic, required output is obtained from chaos system, can cause stabilization using ANN
Chaos system；The subject matter for realizing this expected result is the time needed for adjusting ANN weights, is passed through one by one manually first
The output resistance of Cai Shi is adjusted, then automatically by feedback control system.
3. based on the chaos described in claims 1, it is characterised in that it is defined as the attribute of nonlinear dynamic system, when
When minimum change in systems causes system action difference very big, the sensitive dependence to primary condition is shown；Chaos
The confusion being ordered into, because being unable to the influence that forecasting system behavior will be produced to the change in input, chaos is can not be pre-
Survey.
4. based on the Lorentz oscillator () described in claims 2, it is characterised in that three below ODE is defined
The chaotic behavior of Lorentz oscillator：
Dx/dt=δ (y-x) (1)
Dy/dt=δ (ρ-z)-y (2)
Dz/dt=xy- β z (3)
Wherein, x, y and z define the state of system, and t is the time, and δ, ρ and β are systematic parameters.
5. based on the chaotic behavior described in claims 4, it is characterised in that usual system does not show any kind of chaos row
For, but for some values of its parameter, such as：β=8/3, δ=10, ρ=28, system is there may be chaos figure；
As logarithmic mapping equation (xn+1=μ xn(1+xn)) in μ when increasing above 3.3, another for just occurring chaos be good
Example；Work as μ<When 3.3, system vibrates between two values of x (cycle -2 circulation)；Further increase μ, make system four
Vibration (bifurcated/cycle -4 circulation) between individual value, if keeping increasing μ, period multiplication is by the relatively closely spaced of parameter μ hair
It is raw.
6. based on the cai's circuit (two) described in claims 3, it is characterised in that cai's circuit is simplest chaos system
One of；Use oscillograph, it can be observed that the double rollings of chaos that cai's circuit is created, it can be by three equation Modelings：
C1dv1/ dt=(v2-v1)/R-g(v1) (4)
C2dv2/ dt=- (v2-v1)/R+I (5)
LdI/dt=-rI-v2 (6)
Wherein, v1And v2It is respectively C1And C2The voltage at two ends, g (v1) be nonlinear resistance (equivalent to Cai Shi diodes) electricity
Lead, r is the resistance of inductance.
7. based on the artificial neural network (ANN) (three) described in claims 1, it is characterised in that ANN is artificial intelligence (AI)
A part, it be based on biological nervous system；It is based on the feedback of the input and its output in some sense due to neutral net
And change or learn, flowing through the information of network can influence the structure of ANN.
8. based on the artificial neural network output described in claims 7, it is characterised in that the output of artificial neuron is by following formula
Control：
Y=f (v) (7)
Wherein, f (v) is activation primitive,
V=w1x1+w1x1+…+wmxm+w0b0 (8)
Wherein, w0,w1,w2,…wmIt is weight, x1,x2,…xmIt is input, b0It is deviation；
In order to obtain some desired output yd, the output of neuron is propagated back to system, and expected by adjusting weight
Output；Activation primitive used herein is S type functions.
9. based on use ANN control chaotics (four) described in claims 1, it is characterised in that in order to control cai's circuit institute
The chaotic behavior of presentation, builds cai's circuit on panel first, tests and obtain the output shown on oscillograph；
By adjusting the value of resistance R and C, chaotic behavior can be eliminated, and circuit is provided desired stabilization output, for responding
The different choice of R and C.
10. based on the structure cai's circuit described in claims 9, it is characterised in that simulate above-mentioned circuit with Matlab,
The use of the program of available cai's circuit is its equation；By using the electronic circuit built on panel, then use
After Matlab available programs obtain chaotic behavior, (weight is asked to redraw the electronic circuit of ANN various pieces with simulation analysis program
And function, activation primitive), it is then all to be electrically connected to together；Finally, the output of the big circuits of ANN is connected to cai's circuit, Cai
A part for family name's circuit output feeds back to ANN, correspondingly adjusts weight；
Once all be electrically connected to together, it is possible to use different initial values is ANN weights, then ANN is by study, adjustment
The parameter of cai's circuit, provides required output.
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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107578097A (en) * | 2017-09-25 | 2018-01-12 | 胡明建 | A kind of design method of more threshold values polygamma function feedback artificial neurons |
| CN108256633A (en) * | 2018-02-06 | 2018-07-06 | 苏州体素信息科技有限公司 | A kind of method of test depth Stability of Neural Networks |
| CN109855766A (en) * | 2019-01-21 | 2019-06-07 | 浙江工业大学 | A kind of heat dissipation rate measurement method based on the hot light generation of optical microresonator |
| CN108153147B (en) * | 2017-12-27 | 2021-03-12 | 东北石油大学 | Passivity analysis method |
-
2017
- 2017-03-03 CN CN201710124947.7A patent/CN106875009A/en not_active Withdrawn
Non-Patent Citations (1)
| Title |
|---|
| DR. IBRAHIM IGHNEIWA等: "Using Artificial Neural Networks(ANN) to Control Chaos", 《ARXIV(HTTPS://ARXIV.ORG/ABS/1701.00754)》 * |
Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107578097A (en) * | 2017-09-25 | 2018-01-12 | 胡明建 | A kind of design method of more threshold values polygamma function feedback artificial neurons |
| CN108153147B (en) * | 2017-12-27 | 2021-03-12 | 东北石油大学 | Passivity analysis method |
| CN108256633A (en) * | 2018-02-06 | 2018-07-06 | 苏州体素信息科技有限公司 | A kind of method of test depth Stability of Neural Networks |
| CN109855766A (en) * | 2019-01-21 | 2019-06-07 | 浙江工业大学 | A kind of heat dissipation rate measurement method based on the hot light generation of optical microresonator |
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Application publication date: 20170620 |