CN114884648A - Secret communication method for input saturated uncertain fractional order chaotic system - Google Patents
Secret communication method for input saturated uncertain fractional order chaotic system Download PDFInfo
- Publication number
- CN114884648A CN114884648A CN202110159240.6A CN202110159240A CN114884648A CN 114884648 A CN114884648 A CN 114884648A CN 202110159240 A CN202110159240 A CN 202110159240A CN 114884648 A CN114884648 A CN 114884648A
- Authority
- CN
- China
- Prior art keywords
- input
- function
- uncertain
- fractional order
- saturation
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
- 230000000739 chaotic effect Effects 0.000 title claims abstract description 77
- 238000000034 method Methods 0.000 title claims abstract description 25
- 238000004891 communication Methods 0.000 title claims abstract description 22
- 229920006395 saturated elastomer Polymers 0.000 title claims description 23
- 230000001360 synchronised effect Effects 0.000 claims abstract description 36
- 230000005540 biological transmission Effects 0.000 claims abstract description 5
- 239000013598 vector Substances 0.000 claims description 34
- 238000012886 linear function Methods 0.000 claims description 13
- 240000007049 Juglans regia Species 0.000 claims description 11
- 239000000126 substance Substances 0.000 claims description 8
- 238000009499 grossing Methods 0.000 claims description 6
- 238000009738 saturating Methods 0.000 claims description 2
- 238000010276 construction Methods 0.000 claims 1
- 238000004088 simulation Methods 0.000 description 11
- 238000010586 diagram Methods 0.000 description 6
- 230000006978 adaptation Effects 0.000 description 2
- 230000010354 integration Effects 0.000 description 2
- 102100037651 AP-2 complex subunit sigma Human genes 0.000 description 1
- 101000806914 Homo sapiens AP-2 complex subunit sigma Proteins 0.000 description 1
- 230000003044 adaptive effect Effects 0.000 description 1
- 238000013459 approach Methods 0.000 description 1
- 238000013528 artificial neural network Methods 0.000 description 1
- 230000003247 decreasing effect Effects 0.000 description 1
- 238000009795 derivation Methods 0.000 description 1
- 230000000694 effects Effects 0.000 description 1
- 239000007788 liquid Substances 0.000 description 1
- 230000000750 progressive effect Effects 0.000 description 1
- 230000009897 systematic effect Effects 0.000 description 1
Images
Classifications
-
- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
- H04L9/001—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols using chaotic signals
-
- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L63/00—Network architectures or network communication protocols for network security
- H04L63/04—Network architectures or network communication protocols for network security for providing a confidential data exchange among entities communicating through data packet networks
- H04L63/0428—Network architectures or network communication protocols for network security for providing a confidential data exchange among entities communicating through data packet networks wherein the data content is protected, e.g. by encrypting or encapsulating the payload
-
- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
- H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
- H04L9/0861—Generation of secret information including derivation or calculation of cryptographic keys or passwords
Landscapes
- Engineering & Computer Science (AREA)
- Computer Security & Cryptography (AREA)
- Computer Networks & Wireless Communication (AREA)
- Signal Processing (AREA)
- Computer Hardware Design (AREA)
- Computing Systems (AREA)
- General Engineering & Computer Science (AREA)
- Complex Calculations (AREA)
Abstract
The invention discloses a secret communication method of an input saturation uncertain fractional order chaotic system, when a ciphertext input signal is transmitted, the fractional order chaotic driving system outputs a chaotic driving input signal and transmits the chaotic driving input signal through a first channel, the chaotic driving input signal generates a response output signal after passing through an input saturation uncertain synchronous controller and the fractional order chaotic response system, an encryption function masks the ciphertext input signal by using the chaotic driving input signal and generates a secret key, the secret key is transmitted to a decryption function through a second channel, and the decryption function decrypts according to the response output signal and the secret key to generate a decrypted ciphertext input signal. The invention realizes the transmission of the dual-channel ciphertext input signals and comprehensively considers the problems of unknown control direction and input saturation.
Description
Technical Field
The invention relates to the technical field of secret communication, in particular to a secret communication method of an input saturation uncertain fractional order chaotic system.
Background
In a general control design, a control direction generally needs to be known in advance, and when the control direction is uncertain, especially when a control coefficient is time-varying or slowly-varying, not only the problem of synchronous control of the chaotic system becomes very difficult, but also an originally stable system may lose stability. Therefore, the situation that the control direction is unknown is also a problem which must be considered by designers in terms of engineering practice.
In practice, almost all systems are limited by input saturation due to physical limitations and safety requirements. The control of the motor is limited by the magnitude of the input voltage, and the valve can only be varied between fully open and fully closed during control, which limits the flow of liquid therethrough. The control problem of input saturation systems has been a major concern in the control theory. There are roughly two approaches to dealing with the input saturation problem: one is to design the controller directly. The controller is designed to be bounded, thereby avoiding a saturation condition; secondly, when the actuator is saturated, an additionally designed anti-saturation compensator is adopted to compensate performance reduction when the system is saturated, namely anti-saturation control in the traditional sense, but the technical problem that the control direction is unknown is not considered in the above scheme, so that how to consider the input saturation problem on the basis that the control direction is unknown becomes a technical problem which needs to be solved urgently in the field.
Disclosure of Invention
Based on the above, the invention aims to provide a secret communication method of an input saturation uncertain fractional order chaotic system, so as to realize the consideration of the problems of unknown control direction and input saturation.
In order to achieve the above object, the present invention provides a secret communication method for inputting a saturated uncertain fractional order chaotic system, wherein the method comprises:
step S1: constructing a saturation constraint condition;
step S2: constructing a fractional order chaotic response system based on a saturation constraint condition;
step S3: constructing a fractional order chaotic driving system based on a saturation constraint condition;
step S4: constructing a fractional order error system equation according to the fractional order chaotic driving system and the fractional order chaotic response system;
step S5: constructing a boundary condition that the control direction is unknown and the input saturation is uncertain;
step S6: constructing an input saturation uncertain synchronization controller based on the boundary condition;
step S7: synchronous data transmission of ciphertext input signals; when a ciphertext input signal is transmitted, the fractional order chaotic driving system outputs a chaotic driving input signal and transmits the chaotic driving input signal through a first channel, the chaotic driving input signal generates a response output signal after passing through the input saturation uncertain synchronous controller and the fractional order chaotic response system, the encryption function masks the ciphertext input signal by using the chaotic driving input signal to generate a secret key and transmits the secret key to the decryption function through a second channel, and the decryption function decrypts according to the response output signal and the secret key to generate a decrypted ciphertext input signal.
Optionally, the saturation constraint is constructed by the following specific formula:
wherein u (v (t)) is a saturation constraint and u M For a known upper bound on the control input v (t), v is shorthand for v (t), h (v) is a smoothing function, d 1 (v) For a bounded function y ∈ R n In response to the state vector of the system, d 1 (t) is a bounded function, D 1 To be the bounded function upper bound, sat () is a saturation function.
Optionally, the fractional order chaotic response system is constructed based on the saturation constraint condition, and the specific formula is as follows:
wherein the content of the first and second substances,
a response system of the ith dimension component of the chaotic system, y belongs to R n Output signals for response of the system, g i (y)∈R n As a non-linear function vector of the i-th component, Δ g i (y) isComponent system uncertainty of i-th dimension, d i (t) external disturbances of the ith-dimensional component, b i Control coefficient for i-dimensional component, v i As control input for the ith dimension component, u i (v i ) As a saturation constraint for the i-dimensional component, d 1,i (v i ) As a bounded function of the ith dimension component, h (v) i ) The function is a smooth function of the ith dimension component, (i ═ 1,2, …, n), and n is a positive integer.
Optionally, the step of constructing a fractional order error system equation has a specific formula:
wherein, g i (y)∈R n A non-linear function vector being the component of dimension i, b i Is a control coefficient for the i-th dimensional component,
as a bounded function, W *T Phi (y) is a Gaussian base function as a weight coefficient,
as an error function, x is the chaotic driving input signal of the system, f i (x) As a function vector, h (v) i ) Is a smooth function, c is a positive integer, v i Control input for the i-dimensional component, ω i In order to be the weight, the weight is,
is the derivative of the control input.
Optionally, the constructing an input saturation uncertain synchronization controller based on the boundary condition specifically includes:
step S61: constructing an uncertain synchronization controller based on the uncertainty of the boundary condition;
step S62: constructing an input saturation synchronous controller based on the input saturation characteristics of the boundary conditions;
step S63: and determining an input saturation uncertain synchronous controller according to the uncertain synchronous controller and the input saturation synchronous controller.
Optionally, the uncertain synchronization controller is constructed based on the uncertainty of the boundary condition, and the specific formula is as follows:
wherein, the first and the second end of the pipe are connected with each other,
being a virtual controller, α i For uncertain synchronisation controllers, N (k) i ) Is a function of the Nussbaum,
is a weight vector, f i (x) For known or unknown non-linear function vectors, g i (y) is a known or unknown nonlinear function vector, [ phi ] (y) is a Gaussian basis function,
as an upper bound estimate, e i For the synchronization error component, ε the reconstruction error, c 1 Is a positive integer, k i The law is updated for gain.
Optionally, the input saturation synchronous controller is constructed based on the input saturation characteristics of the boundary condition, and the specific formula is as follows:
wherein N (ζ) is a smooth Nussbaum function,
gain, ω, being a smooth Nussbaum function i In order to input the saturated synchronous controller,
to a virtual control law, c 2 Is a constant number of i Is an intermediate variable, c is a constant, h (v) i ) For a bounded smoothing function, v i For control input, ζ is the state variable, α i For an uncertain synchronisation controller, n is a positive integer,
in order to be a weight estimation value,
as an upper bound estimate, h (v) i ) Is a smooth function, x j Is a state variable, y j Is a state variable, z i Is a defined amount of error.
Optionally, the method further comprises:
step S8: and verifying that the input saturation uncertain synchronous controller converges.
Optionally, the verifying that the input saturation uncertain synchronization controller converges specifically includes:
step S71: verifying the uncertain synchronization controller convergence;
step S72: verifying that the input saturating synchronous controller converges.
Optionally, the ciphertext input signal is at least one of a video, a voice, an image, a military command, and a data file.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
the invention discloses a secret communication method of an input saturation uncertain fractional order chaotic system, when a ciphertext input signal is transmitted, the fractional order chaotic driving system outputs a chaotic driving input signal and transmits the chaotic driving input signal through a first channel, the chaotic driving input signal generates a response output signal after passing through an input saturation uncertain synchronous controller and the fractional order chaotic response system, an encryption function masks the ciphertext input signal by using the chaotic driving input signal and generates a secret key, the secret key is transmitted to a decryption function through a second channel, and the decryption function decrypts according to the response output signal and the secret key to generate a decrypted ciphertext input signal. The invention realizes the transmission of the dual-channel ciphertext input signals and comprehensively considers the problems of unknown control direction and input saturation.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without creative efforts.
FIG. 1 is a flowchart of a secure communication method for inputting a saturated uncertain fractional order chaotic system according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of a two-channel chaotic secure communication SC according to an embodiment of the present invention;
FIG. 3 is a graph of a simulation plot of synchronous error according to an embodiment of the present invention;
FIG. 4 is a control input simulation graph according to an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention aims to provide a secret communication method of an input saturation uncertain fractional order chaotic system, which is used for simultaneously considering the problems of unknown control direction and input saturation.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
As shown in fig. 1, the present invention provides a secret communication method for inputting a saturated uncertain fractional order chaotic system, wherein the method comprises:
step S1: and constructing a saturation constraint.
Step S2: and constructing a fractional order chaotic response system based on a saturation constraint condition.
Step S3: and constructing a fractional order chaotic driving system based on a saturation constraint condition.
Step S4: and constructing a fractional order error system equation according to the fractional order chaotic driving system and the fractional order chaotic response system.
Step S5: and constructing a boundary condition that the input saturation of the unknown control direction is uncertain.
Step S6: and constructing an input saturation uncertain synchronization controller based on the boundary condition.
Step S7: and synchronous data transmission of the ciphertext input signal.
As shown in fig. 2, when a ciphertext input signal m (t) is transmitted, a fractional order chaotic driving system outputs a chaotic driving input signal and transmits the chaotic driving input signal through a first channel, the chaotic driving input signal generates a response output signal after passing through the input saturation uncertain synchronization controller and the fractional order chaotic response system, an encryption function masks the ciphertext input signal by using the chaotic driving input signal and generates a secret key, the encryption function transmits the secret key to a decryption function through a second channel, the decryption function decrypts the ciphertext input signal according to the response output signal and the secret key and generates a decrypted ciphertext input signal
The individual steps are discussed in detail below:
step S1: and constructing a saturation constraint.
When | v (t) | u M At this time, the control input v (t) has sharp corners and cannot be directly processed, so the saturation function is approximately expressed by the following smooth function:
then sat (v (t)) expressed by the formula (la) can be rewritten as follows:
wherein d is 1 (v) Sat (v (t)) -h (v) is a bounded function, the boundary condition of which can be obtained by the following formula,
|d 1 (v)|＝|sat(v(t))-h(v)|≤u M (1-tanh(1))＝D 1 ；
note that at 0 ≦ v ≦ u M In part, when | v | increases from 0 to u | M When d is greater than 1 (v) Is a boundary value of 1 Decreasing to 0, fig. 1 gives an asymptotic curve of the saturation function.
To sum up, a saturation constraint condition is constructed, and the specific formula is as follows:
wherein u (v (t)) is a saturation constraint and u M For a known upper bound on the control input v (t), v is shorthand for v (t), h (v) is a smoothing function, v (t) is the control input, d 1 (v) For a bounded function y ∈ R n In response to the state vector of the system, d 1 (t) is a bounded function, D 1 To be the bounded function upper bound, sat () is a saturation function.
Step S2: a fractional order chaotic response system is constructed based on a saturation constraint condition, and the specific formula is as follows:
wherein the content of the first and second substances,
a response system of the ith dimension component of the chaotic system, y belongs to R n Output signals for response of the system, g i (y)∈R n As a non-linear function vector of the i-th component, Δ g i (y) systematic uncertainty of the ith-dimensional componentCharacterization of d i (t) external disturbances of the ith-dimensional component, b i Control coefficient for i-dimensional component, v i As control input for the ith dimension component, u i (v i ) As a saturation constraint for the i-dimensional component, d 1,i (v i ) As a bounded function of the ith dimension component, h (v) i ) The function is a smooth function of the ith dimension component, (i ═ 1,2, …, n), and n is a positive integer.
Step S3: a fractional order chaotic driving system is constructed based on a saturation constraint condition, and the specific formula is as follows:
wherein the content of the first and second substances,
is a state variable, f i (x) Is expressed by a fractional order chaotic driving system function.
Step S4: constructing a fractional order error system equation, wherein the specific formula is as follows:
wherein, g i (y)∈R n A non-linear function vector being the component of dimension i, b i Is a control coefficient for the i-th dimensional component,
as a bounded function, W *T Phi (y) is a Gaussian basis function,
as an error function, x is the chaotic driving input signal of the system, f i (x) As a function vector, h (v) i ) Is a smooth function, c is a positive integer, v i Control input for the i-dimensional component, ω i In order to be the weight, the weight is,
it is obvious that
Is bounded, having its upper bound ρ, i.e.
Is v is i The derivative of (a) of (b),
is the derivative of the control input.
Step S5: constructing a boundary condition with uncertain input saturation of unknown control direction, which specifically comprises the following steps:
1. the system satisfies ISS (input-to-state).
2. d (t) bounded.
3. Control direction b i Bounded, let | b i |≤b m The sign is unknown, i.e. the control direction is unknown.
Step S6: constructing an input saturation uncertain synchronization controller based on the boundary condition, which specifically comprises the following steps:
step S61: constructing an uncertain synchronization controller based on the uncertainty of the boundary condition, wherein the specific formula is as follows:
wherein the content of the first and second substances,
being a virtual controller, α i For uncertain synchronisation controllers, N (k) i ) Is a function of the Nussbaum,
is a weight vector, f i (x) For known or unknown non-linear function vectors, g i (y) is a known or unknown non-linear function vector, [ phi ] (y) is a Gaussian basis function,
as an upper bound estimate, e i For the synchronization error component, ε the reconstruction error, c 1 Is a positive integer, k i The law is updated for gain.
Step S62: constructing an input saturation synchronous controller based on the input saturation characteristics of the boundary conditions, wherein the specific formula is as follows:
wherein N (ζ) is a smooth Nussbaum function,
gain, ω, being a smooth Nussbaum function i In order to input the saturated synchronous controller,
to a virtual control law, c 2 Is a constant number of i Is an intermediate variable, c is a constant, h (v) i ) For a bounded smoothing function, v i For control input, ζ is the state variable, α i For an uncertain synchronisation controller, n is a positive integer,
in order to be a weight estimation value,
as an upper bound estimate, h (v) i ) Is a smooth function, x j Is a state variable, y j Is a state variable, z i Is a defined amount of error.
Step S63: and determining an input saturation uncertain synchronous controller according to the uncertain synchronous controller and the input saturation synchronous controller.
Step S7: verifying convergence of an input saturation uncertain synchronous controller, specifically comprising:
step S71: verifying the convergence of the uncertain synchronization controller specifically comprises:
step S711: based on parameter adaptation law
Constructing a first Lyapunov function; wherein the content of the first and second substances,
for parameter adaptation law, gamma W Is a function vector, phi (y) is a Gaussian base function, lambda W In order to achieve the gain,
in order to be a weight vector, the weight vector,
for adaptive rates, F ρ As a function vector, λ ρ In order to achieve the gain,
is composed of
And (4) an upper bound.
Step S712: and (3) deriving the first Lyapunov function, wherein the specific formula is as follows:
wherein gamma is greater than 0, and selecting suitable parameters to make
g i (y) is a non-linear function vector,
derivative of the Lyapunov function, W *T Is a weight vector, phi (y) is a Gaussian basis function, b i Is a coefficient, f i (x) As a non-linear function vector, h (v) i ) In order to be a smooth function of the image,
in order to be a function of a bounded nature,
in order to be a weight estimation value,
being a function vector, Γ ρ In the form of a vector of the function,
to estimate the upper bound, b i Is a coefficient, α i Being a virtual controller, c 1 Is a positive integer, f i (x) Is a function vector, gamma is a gain, b m Is a gain, ρ is
The upper bound of (a) is,
for the estimated value, ε is the function vector, λ W For gain, phi (y) is a Gaussian base function, W * Is the weight vector error.
According to the formula, the derivative of the first Lyapunov function of the formula is smaller than the right-side parameter, so that the convergence of the uncertain synchronous controller of the chaotic system is verified.
Step S72: verifying the convergence of the input saturation synchronous controller, specifically comprising:
step S721: constructing a second Lyapunov function, wherein the specific formula is as follows:
wherein, V 2 Is the Lyapunov function, z i Is an error amount.
Step S722: and (3) derivation and integration are carried out on the second Lyapunov function, and the specific formula is as follows:
note the book
Then the finishing can be as follows:
wherein the content of the first and second substances,
is the derivative of the Lyapunov function,
is the derivative of the Lyapunov function, omega is a design parameter, xi is a coefficient,
in order to be a virtual control law,
is a positive integer and is a non-zero integer,
is a positive integer, N (ζ) is a Nussbaum function,
for the gain update law, λ W In order to achieve the gain,
to estimate, λ max To gain, Γ ρ To gain, Γ W Is a gain, W * Is a weight vector error, V 2 Is the Lyapunov function.
Integration over [0, t ] yields:
wherein, V 2 (t) is the Lyapunov function, V 2 (0) Lyapunov function when t is 0, N (k) i ) Is a Nussbaum function and tau is an integral variable.
As can be seen from the above formula, the above formula is smaller than the right-side parameter, so that the convergence of the input saturation synchronous controller of the chaotic system is verified.
Simulation analysis
The drive system model was chosen as the uncertain superLorenz system as follows:
the controlled response system is as follows:
the function uncertainty term and the external disturbance term in the equation are as follows:
the drive system is initially chosen to be x (0) ═ 1,1,1,1) T The initial value of the response system is selected to be (0.1,0.1,0.1,0.1) T ，Γ W ＝diag{1,…1}∈R l×l ，λ W ＝1，Γ ρ ＝0.8，λ ρ 1, l-20, σ -2, writing the central value of the neural network as the last section, c-2, c 1 ＝1，c 2 1, 0.01, to enhance the adjustability of the designed control method
Get kappa 1 ＝0.01，κ 2 ＝0.005，κ 3 ＝0.01，κ 3 ＝0.003，μ i ＝0.01,i＝1,2,3，uM＝30，
The simulation graph of the synchronization error is shown in FIG. 3, where (a) is the synchronization error e 1 Simulation curve diagram, (b) is synchronization error e 2 Simulation curve diagram, (c) is synchronization error e 3 Simulation curve diagram, (d) is synchronization error e 4 Simulating a curve graph; the simulation graph of the control input is shown in FIG. 4, where (a) is the control input u 1 Simulation curve diagram, (b) is control input u 2 Simulation curve graph, control input u 3 Simulation curve diagram, (d) is control input u 4 And (5) simulating a curve graph.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other.
The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core concept of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.
Claims (10)
1. A secret communication method for inputting a saturated uncertain fractional order chaotic system is characterized by comprising the following steps:
step S1: constructing a saturation constraint condition;
step S2: constructing a fractional order chaotic response system based on a saturation constraint condition;
step S3: constructing a fractional order chaotic driving system based on a saturation constraint condition;
step S4: constructing a fractional order error system equation according to the fractional order chaotic driving system and the fractional order chaotic response system;
step S5: constructing a boundary condition that the control direction is unknown and the input saturation is uncertain;
step S6: constructing an input saturation uncertain synchronization controller based on the boundary condition;
step S7: synchronous data transmission of ciphertext input signals; when a ciphertext input signal is transmitted, the fractional order chaotic driving system outputs a chaotic driving input signal and transmits the chaotic driving input signal through a first channel, the chaotic driving input signal generates a response output signal after passing through the input saturation uncertain synchronous controller and the fractional order chaotic response system, the encryption function masks the ciphertext input signal by using the chaotic driving input signal to generate a secret key and transmits the secret key to the decryption function through a second channel, and the decryption function decrypts according to the response output signal and the secret key to generate a decrypted ciphertext input signal.
2. The secret communication method of the input saturated uncertain fractional order chaotic system according to claim 1, wherein the construction of the saturation constraint condition has a specific formula:
wherein u (v (t)) is a saturation constraint and u M For a known upper bound on the control input v (t), v being short for v (t), h (v) being a smoothing function, d 1 (v) For a bounded function y ∈ R n In response to the state vector of the system, d 1 (t) is a bounded function, D 1 To be the bounded function upper bound, sat () is a saturation function.
3. The secret communication method for inputting the saturated uncertain fractional order chaotic system according to claim 1, wherein the fractional order chaotic response system is constructed based on the saturation constraint condition, and the specific formula is as follows:
wherein the content of the first and second substances,
a response system of the ith dimension component of the chaotic system, y belongs to R n Output signals for response of the system, g i (y)∈R n As a non-linear function vector of the i-th component, Δ g i (y) the ith dimension component system uncertainty, d i (t) external disturbances of the ith-dimensional component, b i Control coefficient for i-dimensional component, v i As control input for the ith dimension component, u i (v i ) As a saturation constraint for the i-dimensional component, d 1,i (v i ) A bounded function of the ith dimensional component, h (v) i ) Is a smooth function of the ith dimension component, (i ═ 1,2, …, n), and n is a positive integer.
4. The secret communication method of the input saturated uncertain fractional order chaotic system according to claim 1, wherein the fractional order error system equation is constructed by the following specific formula:
wherein, g i (y)∈R n A non-linear function vector being the component of dimension i, b i Is a control coefficient for the i-th dimensional component,
as a bounded function, W *T Phi (y) is a Gaussian base function as a weight coefficient,
as an error function, x is the chaotic driving input signal of the system, f i (x) As a function vector, h (v) i ) Is a smooth function, c is a positive integer, v i Control input for the i-dimensional component, ω i In order to be the weight, the weight is,
is the derivative of the control input.
5. The secret communication method of the input saturated uncertain fractional order chaotic system according to claim 1, wherein the constructing of the input saturated uncertain synchronous controller based on the boundary condition specifically comprises:
step S61: constructing an uncertain synchronization controller based on the uncertainty of the boundary condition;
step S62: constructing an input saturation synchronous controller based on the input saturation characteristics of the boundary conditions;
step S63: and determining an input saturation uncertain synchronous controller according to the uncertain synchronous controller and the input saturation synchronous controller.
6. The secret communication method of the input saturated uncertain fractional order chaotic system according to claim 5, wherein the uncertain synchronization controller is constructed based on the uncertainty of the boundary condition, and the specific formula is as follows:
wherein the content of the first and second substances,
being a virtual controller, α i For uncertain synchronisation controllers, N (k) i ) Is a function of the Nussbaum,
is a weight vector, f i (x) For known or unknown non-linear function vectors, g i (y) is a known or unknown non-linear function vector, [ phi ] (y) is a Gaussian basis function,
as an upper bound estimate, e i For the synchronization error component, ε the reconstruction error, c 1 Is a positive integer, k i Is the gain update law.
7. The secret communication method of the input saturated uncertain fractional order chaotic system as claimed in claim 5, wherein the input saturated synchronous controller is constructed based on the input saturation characteristics of the boundary condition, and the specific formula is as follows:
wherein N (ζ) is a smooth Nussbaum function,
gain, ω, being a smooth Nussbaum function i In order to input the saturated synchronous controller,
to a virtual control law, c 2 Is a constant number of i Is an intermediate variable, c is a constant, h (v) i ) For a bounded smoothing function, v i For control input, ζ is the state variable, α i For an uncertain synchronisation controller, n is a positive integer,
in order to be a weight estimation value,
as an upper bound estimate, h (v) i ) Is a smooth function, x j Is a state variable, y j Is a state variable, z i Is a defined amount of error.
8. The secret communication method of the input saturated uncertain fractional order chaotic system according to claim 1, further comprising:
step S8: and verifying that the input saturation uncertain synchronous controller converges.
9. The secret communication method of the input saturated uncertain fractional order chaotic system according to claim 8, wherein the verifying the convergence of the input saturated uncertain synchronous controller specifically comprises:
step S71: verifying the uncertain synchronization controller convergence;
step S72: verifying that the input saturating synchronous controller converges.
10. The secret communication method for inputting the saturated uncertain fractional order chaotic system of claim 1, wherein the ciphertext input signal is at least one of video, voice, image, military command and data file.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202110159240.6A CN114884648B (en) | 2021-02-05 | 2021-02-05 | Secret communication method of input saturation uncertainty fractional order chaotic system |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202110159240.6A CN114884648B (en) | 2021-02-05 | 2021-02-05 | Secret communication method of input saturation uncertainty fractional order chaotic system |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN114884648A true CN114884648A (en) | 2022-08-09 |
| CN114884648B CN114884648B (en) | 2024-01-26 |
Family
ID=82666802
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202110159240.6A Active CN114884648B (en) | 2021-02-05 | 2021-02-05 | Secret communication method of input saturation uncertainty fractional order chaotic system |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN114884648B (en) |
Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN116073982A (en) * | 2023-02-07 | 2023-05-05 | 中国人民解放军陆军工程大学 | Secret communication method and system for resisting DoS attack in limited time |
| CN116318610A (en) * | 2023-02-07 | 2023-06-23 | 中国人民解放军陆军工程大学 | Finite time secret communication method and system of variable fractional order chaotic system |
| CN117081110A (en) * | 2023-10-10 | 2023-11-17 | 国网湖北省电力有限公司 | Multi-machine parallel new energy virtual inertia oscillation suppression method and related device |
Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US7072469B1 (en) * | 1999-07-23 | 2006-07-04 | France Telecom | Devices for emitting or receiving signals encrypted by deterministic chaos, and a transmission system, in particular a radio transmission system, including such devices |
| CN106301757A (en) * | 2016-08-25 | 2017-01-04 | 王波 | A kind of chaotic secret communication system |
| US20170085367A1 (en) * | 2015-03-31 | 2017-03-23 | The Board Of Regents Of The University Of Texas System | Method and apparatus for hybrid encryption |
| CN109951269A (en) * | 2019-03-25 | 2019-06-28 | 安徽工业大学 | A kind of secret communication method of Parameter uncertainties time-lag chaos neural network |
| CN111294198A (en) * | 2020-04-01 | 2020-06-16 | 上海交通大学 | Self-adaptive encryption communication method based on chaotic system |
-
2021
- 2021-02-05 CN CN202110159240.6A patent/CN114884648B/en active Active
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US7072469B1 (en) * | 1999-07-23 | 2006-07-04 | France Telecom | Devices for emitting or receiving signals encrypted by deterministic chaos, and a transmission system, in particular a radio transmission system, including such devices |
| US20170085367A1 (en) * | 2015-03-31 | 2017-03-23 | The Board Of Regents Of The University Of Texas System | Method and apparatus for hybrid encryption |
| CN106301757A (en) * | 2016-08-25 | 2017-01-04 | 王波 | A kind of chaotic secret communication system |
| CN109951269A (en) * | 2019-03-25 | 2019-06-28 | 安徽工业大学 | A kind of secret communication method of Parameter uncertainties time-lag chaos neural network |
| CN111294198A (en) * | 2020-04-01 | 2020-06-16 | 上海交通大学 | Self-adaptive encryption communication method based on chaotic system |
Non-Patent Citations (3)
| Title |
|---|
| LI G D 等: "Double chaotic image encryption algorithm based on optimal sequence solution and fractional transform", VISUAL COMPUTER * |
| 严;韦庆阳;: "分数阶混沌系统耦合同步及混沌键控通信设计", 计算机技术与发展, no. 12 * |
| 汪乐乐;李国东;: "基于分数阶Fourier的双混沌加密算法", 计算机科学, no. 2 * |
Cited By (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN116073982A (en) * | 2023-02-07 | 2023-05-05 | 中国人民解放军陆军工程大学 | Secret communication method and system for resisting DoS attack in limited time |
| CN116318610A (en) * | 2023-02-07 | 2023-06-23 | 中国人民解放军陆军工程大学 | Finite time secret communication method and system of variable fractional order chaotic system |
| CN116318610B (en) * | 2023-02-07 | 2023-09-29 | 中国人民解放军陆军工程大学 | Finite time secret communication method and system of variable fractional order chaotic system |
| CN116073982B (en) * | 2023-02-07 | 2024-01-19 | 中国人民解放军陆军工程大学 | Secret communication method and system for resisting DoS attack in limited time |
| CN117081110A (en) * | 2023-10-10 | 2023-11-17 | 国网湖北省电力有限公司 | Multi-machine parallel new energy virtual inertia oscillation suppression method and related device |
| CN117081110B (en) * | 2023-10-10 | 2024-01-02 | 国网湖北省电力有限公司 | Multi-machine parallel new energy virtual inertia oscillation suppression method and related device |
Also Published As
| Publication number | Publication date |
|---|---|
| CN114884648B (en) | 2024-01-26 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN114884648A (en) | Secret communication method for input saturated uncertain fractional order chaotic system | |
| Ding et al. | Nonsingular terminal sliding mode control of nonlinear second‐order systems with input saturation | |
| Modares et al. | Optimal synchronization of heterogeneous nonlinear systems with unknown dynamics | |
| Atassi et al. | Separation results for the stabilization of nonlinear systems using different high-gain observer designs | |
| Bechlioulis et al. | Adaptive control with guaranteed transient and steady state tracking error bounds for strict feedback systems | |
| Jankovic | Control barrier functions for constrained control of linear systems with input delay | |
| Shi et al. | Robust model reference adaptive control based on linear matrix inequality | |
| Song et al. | Adaptive hybrid fuzzy output feedback control for fractional-order nonlinear systems with time-varying delays and input saturation | |
| Gibson et al. | Improved transient response in adaptive control using projection algorithms and closed loop reference models | |
| Cai et al. | Decentralized backstepping control for interconnected systems with non-triangular structural uncertainties | |
| Hetel et al. | Local stabilization of switched affine systems | |
| Zhang et al. | Combined feedback–feedforward tracking control for networked control systems with probabilistic delays | |
| Wu et al. | Decentralized adaptive fuzzy tracking control for a class of uncertain large-scale systems with actuator nonlinearities | |
| Qasem et al. | Hybrid iteration ADP algorithm to solve cooperative, optimal output regulation problem for continuous-time, linear, multiagent systems: Theory and application in islanded modern microgrids with IBRs | |
| Argha et al. | Novel frameworks for the design of fault‐tolerant control using optimal sliding‐mode control | |
| Schuster et al. | Plasma vertical stabilization with actuation constraints in the DIII-D tokamak | |
| Zhang et al. | Finite‐time cooperative attitude control for leader‐follower spacecraft with fixed‐time observer | |
| CN114938267A (en) | Secret communication method of gain-limited uncertain fractional order chaotic system | |
| Zhang et al. | Attitude stabilization of rigid spacecraft with disturbance generated by time varying uncertain exosystems | |
| Fridman et al. | Decomposition of the min–max multi‐model problem via integral sliding mode | |
| Ansarifar et al. | An adaptive-dynamic sliding mode controller for non-minimum phase systems | |
| Bian et al. | Data-driven robust optimal control design for uncertain cascaded systems using value iteration | |
| Huang et al. | Design of an adaptive terminal sliding‐function controller for nonlinear multivariable systems | |
| Yao et al. | Event-triggered fault-tolerant control for nonlinear systems with semi-Markov process | |
| Battistel et al. | Multivariable BMRAC extension to arbitrary relative degree using global robust exact differentiators |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |