CN110601810A - Method for generating Rossler chaotic signal by controllable standard type global chaos inverse control - Google Patents

Abstract

A method for generating Rossler chaotic signals by controllable standard type global chaotic inverse control is realized in a full state space at a special view angle, different signals are generated by adjusting parameters in a certain range for the same Rossler chaotic signal, and the confidentiality is further improved.

Description

A method of generating Rossler chaotic signals by controllable standard global chaotic anti-control

technical field

The invention belongs to the technical field of secure communication, and particularly relates to a technology for generating Rossler chaotic signals from controllable standard chaotic anti-control at the transmitting end of a communication system.

Background technique

Chaos motion is a branch of nonlinear disciplines, but its scope has greatly exceeded the boundaries of traditional nonlinear disciplines, and has developed into a comprehensive, intersecting, and interdisciplinary branch of disciplines. It has greatly broadened people's understanding of nonlinearity. From the perspective of science, the understanding of nonlinear science is more profound.

Chaos has also been applied to secure communications. A typical application is chaotic modulation. The basic idea of chaotic modulation is to modulate the original signal and a chaotic signal together for transmission; while the receiver demodulates and separates the original signal according to the chaotic signal; the third party cannot know the dynamic characteristics of the chaotic signal because it does not know the dynamic characteristics of the chaotic signal. decrypt. As far as the technical solution discussed in this paper is concerned, the sender modulates the original signal into the Rossler chaotic signal, and the receiver performs appropriate signal processing to separate the original signal, which requires the sender to generate the corresponding Rossler chaotic signal, and the sender uses The well-known controllable standard type will improve the confidentiality of the sender itself.

The equations of the Rossler system are as follows

Where x=(x ₁ , x ₂ , x ₃ ) ^T is the state vector, and a, b and c are parameters. The balance of the system is

as well as

A total of two.

SUMMARY OF THE INVENTION

In order to overcome the disadvantage of poor confidentiality of the existing Rossler chaos technology, the present invention provides a method for generating Rossler chaos signals by controllable standard global chaotic anti-control with good confidentiality.

The technical scheme adopted by the present invention to solve its technical problems is:

A method for generating a Rossler chaotic signal by controlling standard global chaotic anti-control includes the following processes:

Suppose the controlled Rossler system has the following form:

where k ₁ and k ₂ are not all 0. The system drift vector field is

The input vector field is

Calculate Lie Derivatives

as well as

Since [k,ad _f k]=0, the two are involute; if

non-zero for exact feedback linearization; note is a quadratic polynomial with respect to x ₃ , Gu let

If for fixed parameters a and b, k ₁ and k ₂ can be found to ensure Δ<0, then There is no real solution for x ₃ , so the system can be globally feedback linearized; therefore, consider the following minimization problem

If there are k ₁ and k ₂ such that the minimum value of Δ<0 is less than 0, the feedback linearization can be achieved globally; usually a and b have the same sign and |a| is slightly smaller than |b|, both k ₁ and k can be found ₂ make _Δmin <0;

Now consider how to make transitions, design state transitions

in this state

Redesign state transitions

in this state

Description Select the following status

Accurate feedback linearization can be achieved, and the system equation in this coordinate system is

For convenience, the x state is still used on the right side of the equal sign of the third equation above, where

At the same time, the Rossler system obtained from the above formula is expressed as

3D single input controllable standard type is

Design Controller

v=α(x)

The y system and the z system become the same system, which realizes the anti-chaotic control; the sender sends a signal α(x) and can also send all three signals of the z state. For the former case, the receiver makes 3 for α(x). The second integral obtains the complete z state, and the integral operation endows the communication system with a certain anti-interference ability.

The present invention will provide a special method for generating Rossler chaos from controllable standard-type chaotic anti-control. The same Rossler chaotic signal will generate different signals through parameter adjustment within a certain range, which further improves the confidentiality ability. This method cannot be used for Rossler chaos under certain parameter settings.

The beneficial effects of the present invention are mainly manifested in: better confidentiality.

Description of drawings

Figure 1 is a schematic diagram of Rossler chaos.

Figure 2 is a schematic diagram of Rossler chaos through state transformation.

Figure 3 is a schematic diagram of the controllable standard type inverse control as Rossler chaos.

Fig. 4 is a control input diagram of the controllable standard type.

Detailed ways

The present invention will be further described below in conjunction with the accompanying drawings.

Referring to Figures 1 to 4, a method for generating a Rossler chaotic signal by controllable standard global chaotic anti-control includes the following processes:

Suppose the controlled Rossler system has the following form:

where k ₁ and k ₂ are not all 0. The system drift vector field is

The input vector field is

Calculate Lie Derivatives

as well as

Since [k,ad _f k]=0, the two are involute; if

If not 0, accurate feedback linearization is possible. notice is a quadratic polynomial with respect to x ₃ , Gu let

If for fixed parameters a and b, k ₁ and k ₂ can be found to ensure Δ<0, then There is no real solution for x ₃ , so the system can be feedback linearized globally. So, consider the following minimization problem

Feedback linearization can be achieved globally if there are k ₁ and k ₂ such that the minimum value of Δ<0 is less than 0. Let a=0.19 and b=0.21 and k ₁ =-2, search k ₂ to minimize Δ, find the smallest Δ _min =-0.358874 and k ₂ =-0.346279, indicating that global feedback linearization is possible. But when a=0.2 and b=0.2, search k ₁ and k ₂ to minimize Δ, and obtain Δ _min =0 and k ₁ =k ₂ =0, indicating that it is impossible to achieve global feedback linearization. The commonly used parameters of Rossler system a=0.15, b=0.2 and c=10, or a=0.095, b=0.1 and c=14, can realize global feedback linearization. Usually a and b have the same sign and |a| is slightly smaller than |b|, both k ₁ and k ₂ can be found to make _Δmin <0.

Now consider how to make transitions, design state transitions

in this state

Redesign state transitions

in this state

Description Select the following status

Accurate feedback linearization can be achieved. Since the general form is too complicated, only the state equations when a=0.19, b=0.21, c=5.7, k ₁ =-2 and k ₂ =-0.3 are given here. At this time, Δ<-0.3 can be globally feedback linear , the procedures and methods presented here are also applicable to all cases where global feedback linearization is possible. In this coordinate system, the system equation is

For convenience, the x-state is still used on the right side of the equal sign of the third equation above, where

At the same time, the above formula tells us that the Rossler system can be expressed as

3D single input controllable standard type is

Design Controller

v=α(x)

The y system and the z system become the same system, realizing the anti-chaotic control. The sender can send a signal α(x) or all 3 signals of the z state. For the former case, the receiver can integrate α(x) three times to obtain the complete z state. The integral operation gives the communication system a certain anti-interference ability.

_In order to verify this technology, the generalized synchronization from linear system to _Rossler system is simulated by using Matlab software. ,-3.0,-3.0) ^T of the Rossler system chaotic trajectory is shown in Figure 1; Figure 2 is the same trajectory in the y state, the corresponding initial value at this time is (-33.9495, 153.3466,-593.4234) ^T ; Figure 3 is the energy The initial value is (-33.9495, 153.3466, -593.4234) ^T of the system trajectory of the control standard type under the control variable v. Figure 2 is consistent with Figure 3, indicating that the chaotic anti-control has been realized; Figure 4 is the control input of the control standard type.

Claims (1)

1. A method for generating Rossler chaotic signals by controllable standard type global chaotic inverse control is characterized by comprising the following processes:

the controlled Rossler system is configured as follows:

wherein k is₁And k₂Not all are 0, the system drift vector field is

The input vector field is

Calculating lie derivatives

And

due to [ k, ad_fk]When the two are combined, the two are combined; if it is not

If not 0, the feedback linearization can be accurately carried out; it is noted thatTo relate to x₃Second order polynomial of

If for fixed parameters a and b, k can be found₁And k₂Ensure that delta is less than 0, thenWith respect to x₃No real solution exists, so that the system can be subjected to global feedback linearization; therefore, the following minimization is consideredProblem(s)

If there is k₁And k₂The minimum value of delta < 0 is smaller than 0, so that the feedback linearization can be realized globally; in general, a is the same sign as b and | a | is slightly less than | b |, k can be found₁And k₂Let a_min＜0；

Now consider how to make the transformations, the state transformations are designed

In this state

Redesign state transitions

In this state

The following states are selected

Can realize accurate feedback linearization, and the system equation is

Conveniently, the right side of the equal sign of the above-mentioned 3 rd equation still adopts the x state, wherein

Also represented by the Rossler system of the above formula

The 3-dimensional single-input energy control standard type is

Design controller

v＝α(x)

The y system and the z system are the same system, and chaotic inverse control is realized; the sending end sends a signal alpha (x) and can also send all 3 signals in the z state, the receiving end integrates alpha (x) for 3 times to obtain the complete z state in the former case, and the integration operation endows the communication system with certain anti-interference capability.