CN111736458B - Adaptive synchronization method of fractional order heterogeneous structure chaotic system - Google Patents

Adaptive synchronization method of fractional order heterogeneous structure chaotic system Download PDF

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CN111736458B
CN111736458B CN201910229144.7A CN201910229144A CN111736458B CN 111736458 B CN111736458 B CN 111736458B CN 201910229144 A CN201910229144 A CN 201910229144A CN 111736458 B CN111736458 B CN 111736458B
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刘立才
杜传红
陈美玉
祝凤侠
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Abstract

Disclosure of the inventionA self-adaptive synchronization method of a fractional order heterogeneous structure chaotic system mainly comprises the following steps: (1) selecting two fractional order chaotic systems with different structures and determined parameters as a driving system and a response system; (2) system e for determining fractional order error1，e2，e3，e4(ii) a (3) In a fractional order error system e1，e2，e3，e4In (1), u is added separately1(t)、u2(t)、u3(t)、u4(t) a controller; (4) design u1(t)、u2(t)、u3(t)、u4(t) a controller and an adaptation law; (5) constructing a Lyapunov control function, and judging a fractional order error system e by utilizing the properties of a Caputo derivative operator and combining the Mittag-Leffler stability theory1，e2，e3，e4The method is asymptotically stable, and synchronous control of chaotic systems with different structures under the condition of determining parameters is realized. The invention can effectively control the fractional order chaotic system of the deterministic parameter, combines the constructed Lyapunov function with the fractional order Mittag-Leffler stability theory by designing the self-adaptive controller, effectively reduces the control complexity, shortens the synchronization time and is a control method with universality.

Description

Adaptive synchronization method of fractional order heterogeneous structure chaotic system
Technical Field
The invention relates to a synchronization method of a fractional order heterogeneous structure chaotic system, belonging to the technical field of automatic control methods.
Background
The nonlinear chaotic system has very rich dynamic characteristics, so that the nonlinear chaotic system is applied to various fields, such as the fields of meteorology, mechanics, secret communication and the like. The applications of the mixed secret communication and the related scientific fields have very wide prospects, and the chaotic synchronization is a key technology. Since the chaos synchronization concept proposed by Pecora and Carroll in the us naval laboratories of the last 90 s, many scholars proposed many effective synchronization methods, such as drive-response synchronization, active-passive synchronization, coupling synchronization, adaptive synchronization, projection synchronization, and sliding mode control synchronization.
The self-adaptive synchronization method is mostly applied to an integer order chaotic system because the constructed Lyapunov function is convenient for solving an integer order derivative for a synchronous error system, and the fractional order of the constructed Lyapunov function is difficult to calculate after the integral order derivative is solved for the constructed Lyapunov function because the synchronous error function is also fractional order for a fractional order system, and the two processing modes are shared. The document "Adaptive feedback control and Synchronization of non-iterative Fractional Order Systems" realizes Adaptive synchronous control of Fractional Order Systems by finding an inequality substitution mode, and the document "fine-time Synchronization between two complex-variable linear Systems with unsynchronized parameters non-iterative scaling mode control" and the document "Synchronization of discrete frame-Order Systems with discrete frame-Order Adaptive control" convert by constructing a sliding mode control plane, the mathematical operation processes of the two methods are complicated, and a more general Adaptive synchronous control method for Fractional Order Chaotic Systems is absent at present.
Disclosure of Invention
The invention aims to provide a self-adaptive synchronization method of a fractional order heterogeneous structure chaotic system, which can effectively simplify the synchronization among different fractional order chaotic systems.
The technical scheme adopted by the invention is as follows:
a self-adaptive synchronization method of a fractional order heterogeneous structure chaotic system is characterized by comprising the following steps:
(1) selecting two fractional order chaotic systems with different structures, determining the parameters of the two systems, and determining the state information quantity of the driving system to be x1，x2，x3，x4And the amount of response system state information is y1，y2，y3，y4；
(2) Obtaining a fractional order error system e according to the state information quantity of the chaotic driving system and the chaotic response system1，e2，e3，e4；
(3) In a fractional order error system e1，e2，e3，e4In (1), u is added separately1(t)、u2(t)、u3(t)、u4(t) a controller;
(4) design u1(t)、u2(t)、u3(t)、u4(t) controller andthe adaptive rate;
(5) constructing a Lyapunov control function according to the Mittag-Leffler stability theory, judging whether the derivative of the Lyapunov function is positive by using the property of a Caputo derivative operator, and obtaining a fractional order error system e according to the Mittag-Leffler stability theory1，e2，e3，e4The overall asymptotic stability is achieved, and synchronization of two chaotic systems with different structures under determined parameters is obtained.
In the step (1), the fractional calculus is determined as the fractional calculus defined by Caputo, which is specifically as follows:
Figure BDA0002006164900000011
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.
If q is of fractional order, a1For certain parameters of the system, the driving system is selected according to the definition of fractional calculus as follows:
Figure BDA0002006164900000021
if q is of fractional order, a2For certain parameters of the system, the response system is selected according to the definition of fractional calculus as follows:
Figure BDA0002006164900000022
in the step (2), the fractional order error system is as follows:
Figure BDA0002006164900000023
in the step (3), adding a controller u into the fractional order error system respectively1(t)、u2(t)、u3(t)、u4(t)：
Figure BDA0002006164900000024
The adaptive synchronization method for the fractional order heterogeneous structure chaotic system according to claim 1, wherein in the step (4), the controller is designed to:
Figure BDA0002006164900000031
wherein the parameters
Figure BDA0002006164900000032
Is to the parameter a1If λ is a parameter, the adaptive law of the estimated parameter is:
Figure BDA0002006164900000033
in the step (5), (a) theorem 1: according to Mittag-Leffler stability theory:
recording the balance point of the nonlinear fractional order power system as xeq0, D is a region including a far point, V (t, x (t)) [0, ∞) xD → R+Is a continuously differentiable function and satisfies:
Figure BDA0002006164900000034
wherein gamma (. cndot.) is a function of class K, x ∈ D and 0 < alpha < 1, then the equilibrium point x iseq0 is globally stable;
(b) constructing a Lyapunov control function by lemma 1:
Figure BDA0002006164900000035
wherein e ═ e1,e2,e3,e4]T，
Figure BDA0002006164900000036
Parameter(s)
Figure BDA0002006164900000037
Is a parameter a1Is estimated value of
(c) 2, leading: properties of Caputo derivative operator:
if x (t) ε R is a continuous differentiable function, then for any t ≧ b, the following relationship holds:
Figure BDA0002006164900000038
(d) when lambda is less than or equal to 0, DqV is less than or equal to 0, then there is lemma 1 and the error system (iv) has balance point e equal to 0 and
Figure BDA0002006164900000039
fractional order error system e1，e2，e3，e4The overall asymptotic stability is achieved, and synchronization of two chaotic systems with different structures under determined parameters is obtained.
Compared with the existing method, the method has the remarkable advantages and beneficial effects that:
the invention designs the adaptive law of the estimated parameters in the control function according to the adaptive theory, and for the fractional order chaotic system for determining the parameters, the fractional order Mittag-Leffler stability theory is utilized, the Lyapunov function is simply constructed, the derivation of the fractional order error function is avoided, and the different structure synchronization of the two fractional order chaotic systems is realized by utilizing the property of a Caputo derivative operator; the existing self-adaptive synchronization method mainly aims at an integer order chaotic system; the existing self-adaptive synchronization method for the fractional order chaotic system can realize synchronization only by searching a sliding mode surface or inequality substitution, the realization process is complex, and the control precision is low; the fractional order self-adaptive synchronous controller designed by the invention has strong universality and simple control steps, and lays a foundation for deeper theoretical research and actual engineering technology of the fractional order chaotic system.
Drawings
Fig. 1 is a Matlab two-dimensional attractor projection phase diagram of an adaptive synchronization method driving system (ii) of a fractional order heterogeneous structure chaotic system according to the present invention.
Fig. 2 is a Matlab two-dimensional attractor projection phase diagram of an adaptive synchronization method response system (iii) of the fractional order hetero-structure chaotic system of the present invention.
Fig. 3 is a Matlab dynamic modeling simulation function applied to an error system (v) at the time t being 0 by the adaptive synchronization method of the fractional order heterogeneous structure chaotic system of the present invention.
Wherein in FIG. 1(a) is x1-x2A plan phase diagram, in which x is shown in FIG. 1(b)2-x3Planar phase diagram.
Wherein in FIG. 2(a) is y1-y3A plan phase diagram, y in FIG. 2(b)1-y4Planar phase diagram.
Wherein FIG. 3(a) is an adaptive synchronous controller e1And the time domain response curve of the error system is acted at the moment t-0.
Wherein FIG. 3(b) is an adaptive synchronous controller e2And the time domain response curve of the error system is acted at the moment t-0.
Wherein FIG. 3(c) is an adaptive synchronous controller e3And the time domain response curve of the error system is acted at the moment t-0.
Wherein FIG. 3(d) is an adaptive synchronous controller e4And the time domain response curve of the error system is acted at the moment t-0.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and specific embodiments.
The invention discloses a self-adaptive synchronization method of a fractional order heterogeneous structure chaotic system, which is implemented according to the following steps:
taking the fraction order q as 0.8 and the system parameter a1＝a2When 1, then:
step (1), selecting a driving fractional order chaotic system as follows:
Figure BDA0002006164900000041
selecting a response system as follows:
Figure BDA0002006164900000042
and (3) performing numerical simulation on the system (ii) and the system (iii) 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 values of the two systems are (1,2,2 and 3), the simulation step length h is 0.01, and the number N of simulation points is 4000.
FIG. 1(a) shows system (ii) at x1-x2Planar attractor projection phase diagram at x1-x2In the phase space range of the plane (-25, 25) and (-40, 40), the motion trajectory of the system (ii) is a symmetrical double-scroll-shaped attractor, which indicates that the system (ii) is a chaotic system.
FIG. 1(b) shows system (ii) at x2-x3Planar attractor projection phase diagram at x2-x3In the phase space range of the plane (-40, 40) and the plane (20, 60), the motion trail of the system (ii) is a symmetric butterfly-shaped attractor, and the system (ii) is proved to be a chaotic system.
FIG. 2(a) shows system (iii) at y1-y3Planar attractor projection phase diagram at y1-y3In the plane (-20, 25) and (6, 24) phase space range, the motion trajectory of the system (iii) is a typical butterfly-shaped chaotic attractor, which shows that the chaotic behavior exists in the system (iii).
FIG. 2(b) shows system (iii) at y1-y4Planar attractor projection phase diagram at y1-y4Planes (-20, 20) and (-10, 10) have finite spatial extent, and the motion trajectories of system (iii) have self-similarity but never intersect, indicating that system (iii) is a chaotic system.
Step (2), the fractional order error system is:
Figure BDA0002006164900000051
and (3) respectively adding controllers into a fractional order error system:
Figure BDA0002006164900000052
step (4), theorem 1: the controller is designed as
Figure BDA0002006164900000053
Wherein the parameters
Figure BDA0002006164900000054
Is to the parameter a1And the adaptive law of the estimated parameters is as follows:
Figure BDA0002006164900000055
if the control parameter lambda is less than or equal to 0, the balance point e of the error system is equal to 0 and
Figure BDA0002006164900000056
the response system is globally asymptotically synchronized with the drive system, i.e. has an arbitrary initial value
Figure BDA0002006164900000057
And (3) proving that: substituting system (vi) into system (v) can result in:
Figure BDA0002006164900000061
the mis-differential mechanical system formula (I) and the response system parameter a2Irrelevant, as long as the error system is stable, the synchronization of the heterostructural chaotic systems with two different parameters can be realized.
Step (5), (a) theorem 1: according to Mittag-Leffler stability theory:
recording the balance point of the nonlinear fractional order power system as x eq0, D is the area containing the far point,
V(t,x(t)):[0,∞)×D→R+is a continuously differentiable function and satisfies:
Figure BDA0002006164900000062
wherein gamma (. cndot.) is a function of class K, x ∈ D and 0 < alpha < 1, then the equilibrium point x iseq0 is globally stable.
(b) With e1、e2、e3、e4And
Figure BDA0002006164900000063
constructing a Lyapunov control function for the variables as:
Figure BDA0002006164900000064
wherein e ═ e1,e2,e3,e4]T，
Figure BDA0002006164900000065
Parameter(s)
Figure BDA0002006164900000066
Is a parameter a1An estimate of (d).
(c) 2, leading: 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:
Figure BDA0002006164900000067
according to lemma 2, the derivative of the Lyapunov control function (ix) is:
Figure BDA0002006164900000068
Figure BDA0002006164900000069
Figure BDA00020061649000000610
Figure BDA00020061649000000611
from the stability theory of theorem 1, it can be seen that when λ is less than or equal to 0, DqV is less than or equal to 0, and the theorem 1 shows that the error system has a balance point e equal to 0 and
Figure BDA00020061649000000612
the error system (iv) is asymptotically stable, so that two different parameter heterostructural chaotic systems (ii) and (iii) are synchronized, and the nonlinear system is globally asymptotically stable.
After the syndrome is confirmed.
MATLAB R2016a is adopted to carry out dynamic modeling simulation on the synchronization method, and the simulation time Tsim＝10s。
The simulation parameters are set as follows: the step length is changed, and the absolute error and the relative error are all 10-3λ is-1000, and the solver adopts ode15s, adaptive law initial value
Figure BDA0002006164900000071
The fractional order q is 0.8, and the initial values of the drive system (ii) and the response system (iii) are both (1,2,2, 3).
FIG. 3(a) shows e under the action of the synchronization controller (vi)1Synchronization error curve, at minimum scale 10-4On the ordinate, the synchronization establishment time is approximately 0 s.
FIG. 3(b) shows e under the action of the synchronization controller (vi)2Synchronous error curve, at minimum scale 2 × 10-4On the ordinate, the synchronization establishment time is approximately 0.2 s.
FIG. 3(c) shows e under the action of the synchronization controller (vi)3The synchronization error curve, on the ordinate with a minimum scale of 0.05, the synchronization set-up time is approximately 0.2 s.
FIG. 3(d) shows e under the action of the synchronization controller (vi)4Synchronous error curve, 0.5X 10 at minimum scale-5On the ordinate, the synchronization establishment time is approximately 0.2 s.
It can be seen from the error system time domain graph of fig. 3 that the fractional order based chaotic systems with different structures converge to 0 within 0.2s under the action of the proposed adaptive law, which proves the effectiveness of the adaptive synchronization method of the fractional order hetero-structure chaotic system provided by the invention.
The above detailed description is only a preferred embodiment of the present invention, and the present invention is not limited to the above embodiment, and the present invention is also not limited to the above embodiment, and variations, modifications, additions and substitutions made by those skilled in the art within the spirit and scope of the present invention.

Claims (3)

1. A self-adaptive synchronization method of a fractional order heterogeneous structure chaotic system is characterized by comprising the following steps:
(1) selecting two fractional order chaotic systems with different structures, determining the parameters of the two systems, and determining the state information quantity of the driving system to be x1，x2，x3，x4And the amount of response system state information is y1，y2，y3，y4；
(2) Obtaining a fractional order error system e according to the state information quantity of the chaotic driving system and the chaotic response system1，e2，e3，e4；
(3) In a fractional order error system e1，e2，e3，e4In (1), u is added separately1(t)、u2(t)、u3(t)、u4(t) a controller:
Figure FDA0003600861650000011
wherein q is the order of the differential operator, a1 a2Determining parameters for a system
(4) Design u1(t)、u2(t)、u3(t)、u4(t) controller and adaptation rate:
Figure FDA0003600861650000012
wherein the parameters
Figure FDA0003600861650000013
Is to the parameter a1And the adaptive law of the estimated parameters is as follows:
Figure FDA0003600861650000014
wherein λ is a parameter;
(5) constructing a Lyapunov control function according to the Mittag-Leffler stability theory, judging that the derivative of the Lyapunov function is less than zero by using the property of a Caputo derivative operator, and judging a fractional order error system e according to the Mittag-Leffler stability theory1，e2，e3，e4The overall asymptotic stability is achieved, and synchronization of two chaotic systems with different structures under determined parameters is obtained;
(5) in (a), lemma 1: according to Mittag-Leffler stability theory:
recording the balance point of the nonlinear fractional order power system as xeq0, D is a region including a far point, V (t, x (t)) [0, ∞) xD → R+Is a continuously differentiable function and satisfies:
Figure FDA0003600861650000015
wherein gamma (. cndot.) is a function of class K, x ∈ D and 0 < alpha < 1, then the equilibrium point x iseq0 is globally stable;
(b) constructing a Lyapunov control function:
Figure FDA0003600861650000021
wherein e ═ e1,e2,e3,e4]T，
Figure FDA0003600861650000022
Parameter(s)
Figure FDA0003600861650000023
Is a parameter a1An estimated value of (d);
(c) 2, introduction: 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:
Figure FDA0003600861650000024
wherein, C represents that the definition mode is Caputo fractional order definition, q is the order of a differential operator, and a is the upper and lower limits of definite integral respectively;
(d) when λ is less than or equal to 0, DqV is less than or equal to 0, and the error system (iv) has the balance point e equal to 0 and
Figure FDA0003600861650000025
fractional order error system e1，e2，e3，e4The overall asymptotic stability is achieved, and synchronization of two chaotic systems with different structures under determined parameters is obtained.
2. The adaptive synchronization method of the fractional order heterogeneous structure chaotic system according to claim 1, wherein in the step (1), the cpu uto definition is adopted herein, and specifically:
Figure FDA0003600861650000026
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, a are the upper limit and the lower limit of definite integral respectively, and Gamma (·) is a Gamma function;
and then selecting a driving system according to the fractional calculus as follows:
Figure FDA0003600861650000027
wherein q is a fractional order, a1Determining parameters for the system;
the selection response system is as follows:
Figure FDA0003600861650000031
wherein q is a fractional order, a2Is a determined parameter of the system.
3. The adaptive synchronization method of the fractional order heterogeneous structure chaotic system according to claim 1, wherein in the step (2), the fractional order error system is obtained by:
Figure FDA0003600861650000032
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Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
EP1971070A1 (en) * 2005-12-31 2008-09-17 Huazhong University of Science and Technology A system and method for generating the analog-digital mixed chaotic signal, a encryption communication method thereof
CN102305926A (en) * 2011-08-23 2012-01-04 南京航空航天大学 Chaos radar signal source and chaos radar signal synchronization system
CN103152163A (en) * 2013-03-25 2013-06-12 王少夫 Fractional order hyper chaotic system and projection synchronization method thereof
CN103217901A (en) * 2013-01-31 2013-07-24 王少夫 Chaotic system tracking control method

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
EP1971070A1 (en) * 2005-12-31 2008-09-17 Huazhong University of Science and Technology A system and method for generating the analog-digital mixed chaotic signal, a encryption communication method thereof
CN102305926A (en) * 2011-08-23 2012-01-04 南京航空航天大学 Chaos radar signal source and chaos radar signal 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

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
张昭晗 等."分数阶时滞混沌系统的自适应模糊滑模同步".《郑州大学学报( 工学版)》.2011,第32卷(第6期),第117-120,125页. *

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