CN111736457B - Self-adaptive synchronization method based on Mittag-Leffler stability - Google Patents
Self-adaptive synchronization method based on Mittag-Leffler stability Download PDFInfo
- Publication number
- CN111736457B CN111736457B CN201910229143.2A CN201910229143A CN111736457B CN 111736457 B CN111736457 B CN 111736457B CN 201910229143 A CN201910229143 A CN 201910229143A CN 111736457 B CN111736457 B CN 111736457B
- Authority
- CN
- China
- Prior art keywords
- chaotic
- fractional order
- adaptive
- error
- leffler
- 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.)
- Active
Links
- 238000000034 method Methods 0.000 title claims abstract description 34
- 230000000739 chaotic effect Effects 0.000 claims abstract description 59
- 230000003044 adaptive effect Effects 0.000 claims abstract description 32
- 230000004044 response Effects 0.000 claims abstract description 26
- 230000001360 synchronised effect Effects 0.000 claims description 25
- 230000009471 action Effects 0.000 claims description 9
- 101100001669 Emericella variicolor andD gene Proteins 0.000 claims description 3
- 238000013461 design Methods 0.000 claims description 3
- 230000007246 mechanism Effects 0.000 claims description 3
- 238000006467 substitution reaction Methods 0.000 abstract description 4
- 238000004088 simulation Methods 0.000 description 12
- 238000010587 phase diagram Methods 0.000 description 10
- 230000000737 periodic effect Effects 0.000 description 4
- 238000004422 calculation algorithm Methods 0.000 description 2
- 238000012937 correction Methods 0.000 description 2
- 238000005516 engineering process Methods 0.000 description 2
- 230000008569 process Effects 0.000 description 2
- 238000007792 addition Methods 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 238000004891 communication Methods 0.000 description 1
- 239000002131 composite material Substances 0.000 description 1
- 238000009795 derivation Methods 0.000 description 1
- 238000010586 diagram Methods 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 230000000750 progressive effect Effects 0.000 description 1
- 238000011160 research Methods 0.000 description 1
- 230000003595 spectral effect Effects 0.000 description 1
- 230000006641 stabilisation Effects 0.000 description 1
- 238000011105 stabilization Methods 0.000 description 1
Images
Classifications
-
- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
- G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
- G05B13/0205—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric not using a model or a simulator of the controlled system
- G05B13/024—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric not using a model or a simulator of the controlled system in which a parameter or coefficient is automatically adjusted to optimise the performance
Landscapes
- Engineering & Computer Science (AREA)
- Health & Medical Sciences (AREA)
- Artificial Intelligence (AREA)
- Computer Vision & Pattern Recognition (AREA)
- Evolutionary Computation (AREA)
- Medical Informatics (AREA)
- Software Systems (AREA)
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Automation & Control Theory (AREA)
- Feedback Control In General (AREA)
Abstract
The invention discloses a self-adaptive synchronization method based on Mittag-Leffler stability, which mainly comprises the following steps: (1) selecting two fractional order chaotic systems with different structures and unknown parameters as a driving system and a response system; (2) adjusting the state of a chaotic driving system and a chaotic response systemSystem e for obtaining fractional error by subtracting information amount 1 ，e 2 ，e 3 ，e 4 (ii) a (3) In a fractional order error system e 1 ，e 2 ，e 3 ，e 4 In (1), v is added separately 1 (t)、v 2 (t)、v 3 (t)、v 4 (t) a controller; (4) establishing adaptive law of estimation parameters, designing v 1 (t)、v 2 (t)、v 3 (t)、v 4 (t) an adaptive rate controller; (5) constructing a Lyapunov control function of the error system, and judging a fractional order error system e according to the Mittag-Leffler stability theory 1 ，e 2 ，e 3 ，e 4 The global asymptotic stability is realized, and the synchronization of the two chaotic systems under the condition of containing unknown parameters is realized. The invention solves the problem that the existing self-adaptive method aiming at the synchronization of the fractional order chaotic system can realize the synchronization control only by searching inequality substitution or constructing a complex sliding mode surface.
Description
Technical Field
The invention relates to a self-adaptive synchronization method based on Mittag-Leffler stability, belonging to the technical field of automatic control methods.
Background
Researches show that compared with an integer order chaotic system, the fractional order chaotic system has higher nonlinear characteristics and expanded power spectral density, so that the fractional order chaotic system has wide application prospects in the related scientific fields of secret communication and the like, and the chaotic synchronization control method is a key technology.
The existing chaotic self-Adaptive synchronization method mainly aims at integer order chaotic systems, the main reason is that a fractional order synchronous error system is fractional order, and the constructed Lyapunov function also needs to be controlled by means of a complex fractional order sliding mode control plane, such as the document 'Adaptive scaling mode synchronization for a class of fractional-order periodic systems with discrete functions' and the document 'Adaptive feedback control and synchronization of non-absolute periodic fractional order systems', or the document 'Adaptive feedback control and synchronization of non-absolute periodic fractional order systems' is searched for unequal substitution to realize progressive stabilization of the error system, such as the document 'Adaptive feedback control and synchronization of non-absolute periodic fractional order systems'. The two methods have complex realization process, low synchronization speed and difficult guarantee of control precision. For the different-structure fractional order chaotic system with uncertain parameters, a simple, quick and more universal synchronous control method is still lacked at present.
Disclosure of Invention
The invention aims to provide a self-adaptive synchronization method based on Mittag-Leffler stability, which combines self-adaptive control rate with Mittag-Leffler stability criterion and can effectively simplify the synchronization between a fractional order and different structure system and a chaotic system containing uncertain parameters.
The technical scheme adopted by the invention is as follows:
the self-adaptive synchronization method based on the stability of Mittag-Leffler is characterized by comprising the following steps of:
(1) adaptive synchronous chaos problem description
The driving system is a fractional order chaotic system and has the following form:
wherein x is 1 ，x 2 ，x 3 And x 4 Is a state variable, q is more than 0 and less than 1, a is an unknown parameter, and a is more than 0 because the chaotic system is a dissipative system.
The response system is a fractional order chaotic system and has the following form:
wherein, y 1 ，y 2 ，y 3 And y 4 Is a state variable, q is more than 0 and less than 1, a is an unknown parameter, and a is more than 0 because the chaotic system is a dissipative system.
Starting from a certain initial value and at a certain parameter a, the variable x * Free evolution under the action of R n Obtaining an orbit O (x) called as a desired orbit, taking a given system formula (i) for generating the orbit as a driving system, and introducing a control mechanism into the parameter a of the system formula (ii) by the chaotic adaptive control synchronization method to ensure that the orbit O (y) of the system formula (ii) starting from any initial value is evolved to follow the orbit O (x) of a response system, if so, the orbit O (x) is obtained Is provided with
And if yes, the response system and the response system are synchronized.
(2) The state information quantities of the chaotic driving system and the chaotic response system are differenced to obtain a fractional order error system e 1 ，e 2 ，e 3 ，e 4 In the form of:
(3) in a fractional order error system e 1 ，e 2 ，e 3 ，e 4 In (1), v is added separately 1 (t)、v 2 (t)、v 3 (t)、v 4 (t) a controller of the form:
(4) design v 1 (t)、v 2 (t)、v 3 (t)、v 4 (t) an adaptive rate controller of the form:
wherein the parameters
Is the estimation of the parameter a, and the adaptive law of the estimated parameter is:
(5) the Lyapunov control function is constructed for the error system (iv), and according to the stability theory of Mittag-Leffler, the error system (iv) is known to have a balance point e equal to 0 and
obtain a fractional order error system e 1 ，e 2 ，e 3 ，e 4 Is globally asymptotically stable, and the chaotic system (i) is synchronous with the chaotic system (ii).
In step (1), the Caputo definition is used herein, and specifically includes:
wherein C represents that the definition mode is Caputo fractional order definition, q is the order of a differential operator, n is the minimum integer larger than q, n-1 < q < n, t and q are the upper and lower limits of definite integral respectively, and Γ (-) is a Gamma function.
In the step (5), (a) a Lyapunov function is constructed:
wherein e ═ e 1 ,e 2 ,e 3 ,e 4 ] T ，
Parameter(s)
Is an estimate of the unknown parameter a.
(b) Introduction 1: using the properties of the Caputo derivative operator:
if x (t) ε R is a continuous differentiable function, then for any t ≧ b, the following relationship holds:
(c) According to theorem 1, the derivative of the Lyapunov function (viii) is:
(d) 2, leading: according to Mittag-Leffler stability theory:
recording the balance point of the nonlinear fractional order power system as x eq 0, D is a region including a far point, V (t, x (t)) [0, ∞) xD → R + Is a continuously differentiable function and satisfies:
wherein gamma (. cndot.) is a function of class K, x ∈ D and 0 < alpha < 1, then the equilibrium point x is eq 0 is globally stable.
(e) Since a > 0, and according to lemma 2, error system (iv) has equilibrium point e equal to 0 and
D q v is less than or equal to 0, i.e
So as to obtain a fractional order error system e 1 ，e 2 ，e 3 ，e 4 The global asymptotic stability is stable, and the chaotic system (i) containing uncertain parameters is synchronous with the chaotic system (ii).
Compared with the existing method, the method has the remarkable advantages and beneficial effects that:
the adaptive law of the estimated parameters in the control function is designed according to the adaptive theory, for a fractional order chaotic system containing unknown parameters, derivation of a fractional order error function is avoided by constructing a simple Lyapunov function, and the heterostructure synchronization of the two fractional order chaotic systems containing the unknown parameters is realized according to the property of a Caputo derivative operator and the fractional order Mittag-Leffler stability theory; the existing self-adaptive synchronization method mainly aims at an integer order chaotic system, and the existing self-adaptive synchronization method aiming at a fractional order chaotic system can realize synchronization only by searching a sliding mode surface or inequality substitution, so that the realization process is complex, the synchronization speed is low, and the control precision is low; the adaptive synchronization method based on Mittag-Leffler stability has strong universality, is simple in operation and few in control steps, and provides a new selection scheme for the fractional order chaotic system in the application of the actual engineering technology.
Drawings
FIG. 1 is a schematic diagram of the adaptive synchronization control principle of the chaotic system with unknown parameters of the adaptive synchronization method based on Mittag-Leffler stability of the present invention.
FIG. 2 is a phase diagram of the Matlab three-dimensional attractor projection of the adaptive synchronization method driving system (i) based on Mittag-Leffler stability of the present invention.
FIG. 3 is a Matlab three-dimensional attractor projection phase diagram of the adaptive synchronization method response system (ii) based on Mittag-Leffler stability of the present invention.
Fig. 4 is a Matlab dynamic modeling simulation function of the adaptive synchronization method based on the misttag-Leffler stability of the present invention, which acts on the error system (iii) at time t-0.
Wherein in FIG. 2(a) is x 1 -x 2 -x 3 Spatial projection phase diagram, x in FIG. 2(b) 1 -x 3 -x 4 And (4) spatially projecting a phase diagram.
Wherein in FIG. 3(a) is y 2 -y 3 -y 4 Spatial projection phase diagram, y in FIG. 3(b) 1 -y 2 -y 4 And (4) spatially projecting a phase diagram.
Wherein FIG. 4(a) is an adaptive synchronous controller e 1 And the time domain response curve of the error system is acted at the moment t-0.
Wherein FIG. 4(b) is an adaptive synchronous controller e 2 And the time domain response curve of the error system is acted at the moment t-0.
Wherein FIG. 4(c) is an adaptive synchronous controller e 3 And the time domain response curve of the error system is acted at the moment t-0.
Wherein FIG. 4(d) is an adaptive synchronous controller e 4 And the time domain response curve of the error system is acted at the moment t-0.
Detailed Description
The invention is described in further detail below with reference to the figures and the detailed description.
The self-adaptive synchronization method based on the Mittag-Leffler stability is implemented according to the following steps:
taking the fraction order q as 0.8 and the system parameter a 1 ＝a 2 When 1, then:
the self-adaptive synchronization method based on the stability of Mittag-Leffler is characterized by comprising the following steps of:
and (1) self-adaptive synchronous chaotic problem description.
The driving system is a fractional order chaotic system and has the following form:
wherein x is 1 ，x 2 ，x 3 And x 4 And q is a fractional order, q is more than 0 and less than 1, and a is an unknown parameter.
And (3) performing numerical simulation on the system (i) by using matlab software, verifying that the chaotic behavior exists in the system, wherein the simulation algorithm adopts a prediction-correction method, the initial simulation value of the system is (1,2,2 and 3), the simulation step length h is 0.01, and the number N of simulation points is 4000.
FIG. 2(a) shows x of the drive system (i) 1 -x 2 -x 3 And (3) a space projection phase diagram, wherein the motion trajectory of the system (i) is a typical double-scroll-shaped attractor in a limited space, and the system (i) is a chaotic system.
FIG. 2 (b)) X of the drive system (i) is shown 1 -x 3 -x 4 Phase diagram of spatial projection, it can be seen that system (i) is at x 1 -x 3 -x 4 The space motion orbit is infinitely folded, twisted and stretched, has self-similarity, and indicates that the system (i) is a chaotic system.
The response system is a fractional order chaotic system and has the following form:
wherein, y 1 ，y 2 ，y 3 And y 4 The chaotic system is a state variable, q is a fractional order, q is more than 0 and less than 1, a is an unknown parameter, and a is more than 0 because the chaotic system is a dissipative system.
And (3) performing numerical simulation on the system (ii) by using matlab software, verifying the chaotic behavior of the system, wherein the simulation algorithm adopts a prediction-correction method, the initial simulation value of the system is (1,2,2 and 3), the simulation step length h is 0.01, and the number N of simulation points is 4000.
FIG. 3(a) shows y for response system (ii) 2 -y 3 -y 4 And (3) a space projection phase diagram, wherein the motion trajectory of the system (ii) is a ring and a spiral line, has infinite depth in a limited space and has the characteristic of a chaotic attractor, and the system (ii) is a chaotic system.
FIG. 3(b) shows y of the response system (ii) 1 -y 2 -y 4 Phase diagram of the spatial projection, it can be seen that system (ii) is in y 1 -y 2 -y 4 The space motion orbit has infinite depth, never self-crosses, only occupies limited space, has an infinite nested complex structure, and indicates that the system (ii) is a chaotic system.
FIG. 1 shows an adaptive synchronous control schematic according to the invention, in which an error system e is determined from a drive system equation (i) and a response system equation (ii), starting from a certain initial value for a state variable x and at a defined parameter a * Free evolution under the action of R n Obtaining an orbit O (x) which is called a desired orbit; establishing a composite system, and responding under the condition of meeting a certain self-adaptive control lawThe parameter a of the system formula (ii) introduces a control mechanism to make the orbit O (y) of the response system starting from an arbitrary initial value follow the orbit O (x) of the driving system, if any
And if yes, the response system and the driving system are synchronized.
Step (2) the state information quantities of the chaos driving system formula (i) and the chaos response system (ii) are differenced to obtain a fractional order error system e 1 ，e 2 ，e 3 ，e 4 In the form of:
step (3) in fractional order error system e 1 ，e 2 ，e 3 ，e 4 In (1), v is added separately 1 (t)、v 2 (t)、v 3 (t)、v 4 (t) a controller of the form:
step (4) design v 1 (t)、v 2 (t)、v 3 (t)、v 4 (t) an adaptive rate controller of the form:
wherein the parameters
Is the estimation of the parameter a, and the adaptive law of the estimated parameter is:
step (5) for error system (iv) constructionThe Lyapunov control function shows that the error system (iv) has an equilibrium point e equal to 0 and
obtain a fractional order error system e 1 ，e 2 ，e 3 ，e 4 Is globally asymptotically stable, and the chaotic system (i) is synchronous with the chaotic system (ii).
In step (1), the Caputo definition is used herein, specifically:
wherein C represents the definition mode as Caputo fractional order, q is the order of a differential operator, n is the minimum integer larger than q, n-1 < q < n, t, a are the upper and lower limits of the definite integral respectively, and Γ (-) is a Gamma function.
In step (5), the Lyapunov function needs to be constructed first:
wherein e ═ e 1 ,e 2 ,e 3 ,e 4 ] T ，
Parameter(s)
Is an estimate of the unknown parameter a.
Next, lemma 1 is introduced: properties of the Caputo derivative operator:
if x (t) ε R is a continuous differentiable function, then for any t ≧ b, the following relationship holds:
again, according to lemma 1, the derivative of the Lyapunov function (viii) is:
then, theorem 2 is introduced: according to Mittag-Leffler stability theory:
recording the balance point of the nonlinear fractional order power system as x eq 0, D is a region including a far point, V (t, x (t)) [0, ∞) xD → R + Is a continuously differentiable function and satisfies:
wherein gamma (. cndot.) is a function of class K, x ∈ D and 0 < alpha < 1, then the equilibrium point x is eq 0 is globally stable.
Finally, since a > 0, and again according to lemma 2, error system (iv) has equilibrium point e equal to 0 and
D q v is less than or equal to 0, i.e
So as to obtain a fractional order error system e 1 ，e 2 ，e 3 ，e 4 Chaotic system (i) with stable global asymptotic and uncertain parameters and chaotic systemSystem (ii) synchronizes.
Dynamic modeling simulation is carried out on the synchronization method by adopting MATLABR2016a, and the simulation time T is sim ＝10s。
The simulation parameters are set as follows: the step length is changed, and the absolute error and the relative error are all 10 -3 λ is-1000, and the solver adopts ode15s, adaptive law initial value 
The fractional order q is 0.8, and the initial values of the drive system (i) and the response system (ii) are both (1,2,2, 3).
And enabling the synchronous controller (v) at the moment t is 0.
FIG. 4(a) shows e under the action of the synchronous controller (v) 1 The synchronization error curve, on the ordinate with a minimum scale of 0.01, the synchronization set-up time is approximately 0.5 s.
FIG. 4(b) shows e under the action of the synchronous controller (v) 2 Synchronous error curve, at minimum scale 2 × 10 -5 On the ordinate, the synchronization establishment time is approximately 0.2 s.
FIG. 4(c) shows e under the action of the synchronous controller (v) 3 Synchronous error curve with minimum scale ordinate of 0.5 × 10 -8 During the action of the controller, fluctuations in the error curve can be seen, but since the ordinate scale is very small, the fluctuations do not exceed 0.25 × 10 -8 The synchronization setup time of the system can still be considered to be approximately 0 s.
FIG. 4(d) shows e under the action of the synchronization controller (vi) 4 Synchronous error curve with minimum scale ordinate of 0.5 × 10 -8 Since the ordinate scale is extremely small, the synchronization establishment time of the system can be considered to be approximately 0 s.
It can be seen from the error system time domain graph of fig. 4 that, the fractional order based chaotic systems with different structures converge to 0 within 0.5s under the action of the adaptive synchronization method based on the misttag-Leffler stability, which proves the effectiveness of the adaptive synchronization method of the fractional order heterogeneous structure chaotic system provided by the present invention.
The adaptive synchronization method based on the Mittag-Leffler stability provided by the implementation of the present invention is described in detail above, and the above description is only a preferred example of the present invention and is not a limitation of the present invention, and the present invention is not limited to the above example, and variations, modifications, additions and substitutions that can be made by those skilled in the art within the spirit and scope of the present invention also belong to the protection scope of the present invention.
Claims (1)
1. The self-adaptive synchronization method based on the stability of Mittag-Leffler is characterized by comprising the following steps of:
(1) adaptive synchronous chaos problem description
The driving system is a fractional order chaotic system and has the following form:
wherein x is 1 ，x 2 ，x 3 And x 4 Is a state variable, q is a fractional order, q is more than 0 and less than 1, a is an unknown parameter, and a is more than 0 because the chaotic system is a dissipative system; the response system is a fractional order chaotic system and has the following form:
wherein, y 1 ，y 2 ，y 3 And y 4 Is a state variable, q is a fractional order, q is more than 0 and less than 1, a is an unknown parameter, and a is more than 0 because the chaotic system is a dissipative system;
starting from a certain initial value and at a certain parameter a, the state variable x * Free evolution under the action of R n Obtaining an orbit O (x) called as an expected orbit, wherein a given system formula (i) for generating the orbit is a driving system, and the chaos self-adaptive control synchronization method introduces a control mechanism into a parameter a of a system formula (ii) so that the system formula (ii) evolves from an orbit O (y) starting from any initial value to follow the orbit O (x) of a response system; if there is 
If yes, the driving system and the response system are said to be synchronous;
(2) the state information quantities of the chaotic driving system (i) and the chaotic response system (ii) are differenced to obtain a fractional order error system e 1 ，e 2 ，e 3 ，e 4 In the form of:
(3) in a fractional order error system e 1 ，e 2 ，e 3 ，e 4 In (1), v is added separately 1 (t)、v 2 (t)、v 3 (t)、v 4 (t) a controller of the form:
(4) design v 1 (t)、v 2 (t)、v 3 (t)、v 4 (t) an adaptive rate controller of the form:
wherein the parameters
Is the estimation of the parameter a, and the adaptive law of the estimated parameter is:
(5) constructing a Lyapunov control function for the error system (iv) according to the Mittag-Leffler stability theory, and obtaining the Lyapunov by utilizing the property of a Caputo derivative operatorThe function is not negative, and an error system (iv) obtained by using the Mittag-Leffler stability theory has the balance point e equal to 0 and
thereby fractional order error system e 1 ，e 2 ，e 3 ，e 4 Is globally asymptotically stable, and the chaotic driving system (i) is synchronous with the chaotic response system (ii);
(5) in (a), constructing a Lyapunov control function:
wherein e ═ e 1 ,e 2 ,e 3 ,e 4 ] T ，
Parameter(s)
Is an estimate of the unknown parameter a;
(b) introduction 1: properties of the Caputo derivative operator:
if x (t) ε R is a continuous differentiable function, then for any t ≧ b, the following relationship holds:
(c) according to theorem 1, the derivative of the Lyapunov function (viii) is:
(d) 2, leading: according to Mittag-Leffler stability theory:
recording the balance point of the nonlinear fractional order power system as x eq D is a region containing the far point ═ 0Domain, V (t, x (t)) < 0, ∞ xD → R + Is a continuously differentiable function and satisfies:
wherein gamma (. cndot.) is a function of class K, x ∈ D and 0 < alpha < 1, then the equilibrium point x is eq 0 is globally stable;
(e) since a > 0, and according to lemma 2, error system (iv) has equilibrium point e equal to 0 and
D q v is less than or equal to 0, i.e
Obtain a fractional order error system e 1 ，e 2 ，e 3 ，e 4 The chaotic system is globally asymptotically stable, and a chaotic driving system (i) containing uncertain parameters is synchronous with a chaotic response system (ii);
in the step (1), the Caputo definition is adopted, and specifically:
wherein C represents the definition mode as Caputo fractional order, q is the order of a differential operator, n is the minimum integer larger than q, n-1 < q < n, t, a are the upper and lower limits of the definite integral respectively, and Γ (-) is a Gamma function.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910229143.2A CN111736457B (en) | 2019-03-25 | 2019-03-25 | Self-adaptive synchronization method based on Mittag-Leffler stability |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910229143.2A CN111736457B (en) | 2019-03-25 | 2019-03-25 | Self-adaptive synchronization method based on Mittag-Leffler stability |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN111736457A CN111736457A (en) | 2020-10-02 |
| CN111736457B true CN111736457B (en) | 2022-07-29 |
Family
ID=72645807
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201910229143.2A Active CN111736457B (en) | 2019-03-25 | 2019-03-25 | Self-adaptive synchronization method based on Mittag-Leffler stability |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN111736457B (en) |
Family Cites Families (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN1852089B (en) * | 2005-12-31 | 2012-01-18 | 华中科技大学 | System and method for generating analog-digital mixed chaos signals |
| CN102305926B (en) * | 2011-08-23 | 2013-03-13 | 南京航空航天大学 | Chaos radar signal source and signal production method and synchronization system |
| CN103217901A (en) * | 2013-01-31 | 2013-07-24 | 王少夫 | Chaotic system tracking control method |
| CN103152163A (en) * | 2013-03-25 | 2013-06-12 | 王少夫 | Fractional order hyper chaotic system and projection synchronization method thereof |
-
2019
- 2019-03-25 CN CN201910229143.2A patent/CN111736457B/en active Active
Also Published As
| Publication number | Publication date |
|---|---|
| CN111736457A (en) | 2020-10-02 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Hu et al. | Stabilization of switched systems via composite quadratic functions | |
| Yang et al. | Stability analysis and design of impulsive control systems with time delay | |
| Vincent | Chaos synchronization using active control and backstepping control: a comparative analysis | |
| CN111736457B (en) | Self-adaptive synchronization method based on Mittag-Leffler stability | |
| CN111736458B (en) | Adaptive synchronization method of fractional order heterogeneous structure chaotic system | |
| Ghadami et al. | Distributed H 2 control of multi-agent dynamic systems: Continuous-time case | |
| Park et al. | LMI optimization approach to synchronization of stochastic delayed discrete-time complex networks | |
| Mazenc et al. | Event-triggered control for systems with state delays using a positive systems approach | |
| Cherneva | Control of the chaotic processes in chaos shift keying communication system | |
| Dai et al. | A new three-dimensional chaotic system and its modified generalized projective synchronization | |
| Wu et al. | Improved delay-dependent absolute stability of Lur’e systems with time-delay | |
| Afzal et al. | Modeling and inverse complex generalized synchronization and parameter identification of non-identical nonlinear complex systems using adaptive integral sliding mode control | |
| Wu et al. | Generalized projective lag synchronization between different hyperchaotic systems with uncertain parameters | |
| CN101355448A (en) | Method and apparatus for comparing upload | |
| Henein et al. | Switched active control synchronization of three fractional order chaotic systems | |
| Griba et al. | Synchronization of chaotic systems: a survey study | |
| Suykens et al. | Impulsive control and synchronization of chaos | |
| Yelchuru et al. | Optimal controlled variable selection with structural constraints using miqp formulations | |
| Shu et al. | Control reconfiguration of dynamical systems for improved performance via reverse-and forward-engineering | |
| Cai et al. | Globally exponentially attractive set and synchronization of a novel three-dimensional chaotic finance system | |
| Ji et al. | Stability of equilibrium points for incommensurate fractional-order nonlinear systems | |
| Zhang et al. | Universal projective synchronization of two different hyperchaotic systems with unknown parameters | |
| CN108667016B (en) | Small interference stability domain boundary expansion method based on control parameter rolling optimization | |
| Zhu | Anti-synchronization of two different chaotic systems via optimal control with fully unknown parameters | |
| CN115800766B (en) | Model reference self-adaptive control method and device based on double active bridge converters |
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 | ||
| TR01 | Transfer of patent right | ||
| TR01 | Transfer of patent right |
Effective date of registration: 20240425 Address after: 230000 floor 1, building 2, phase I, e-commerce Park, Jinggang Road, Shushan Economic Development Zone, Hefei City, Anhui Province Patentee after: Dragon totem Technology (Hefei) Co.,Ltd. Country or region after: China Address before: 561000 No.25 Xueyuan Road, Xixiu District, Anshun City, Guizhou Province Patentee before: ANSHUN University Country or region before: China |