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Global integral sliding mode-based third-order strict-feedback chaos proportion projection synchronization method

An integral sliding mode and global technology, which is applied in the direction of instruments, adaptive control, control/regulation systems, etc., to achieve good robustness and speed improvement

Inactive Publication Date: 2019-02-12
NORTHEASTERN UNIV
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  • Summary
  • Abstract
  • Description
  • Claims
  • Application Information

AI Technical Summary

Problems solved by technology

Sliding mode control is divided into approaching mode and sliding mode. The ordinary sliding mode controller using linear sliding mode surface is only robust in sliding mode, but not robust in approaching mode.

Method used

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  • Global integral sliding mode-based third-order strict-feedback chaos proportion projection synchronization method
  • Global integral sliding mode-based third-order strict-feedback chaos proportion projection synchronization method
  • Global integral sliding mode-based third-order strict-feedback chaos proportion projection synchronization method

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specific Embodiment 1

[0058] The specific process is as Figure 8 As shown, step 1: establish the driving system and response system according to the state equation of the third-order strict feedback chaotic system, and establish the proportional projection synchronization error system;

[0059] The drive system and the response system are isomorphic systems, both of which are Arneodo chaotic systems. The state equation of the Arneodo chaotic system is

[0060]

[0061] Formula (14) is the driving system, and the initial state is set to x 1 (0)=2,x 2 (0)=-2,x 3 (0)=-2.

[0062] The response system is also an Arneodo chaotic system, and the state equation is:

[0063]

[0064] The controlled response system with modeling uncertainties and external disturbance signals is expressed as:

[0065]

[0066] Among them, the modeling uncertainty △f 2 (y) is set to △f 2 (y)=0.6cos(y 1 the y 2 ), due to |△f 2 (y)|≤d 1 , then d 1 =0.6, the external interference signal d(t) is set as d(t)=...

specific Embodiment 2

[0086] The specific process is as Figure 8 Shown:

[0087] Step 1: Establish the driving system and response system according to the state equation of the third-order strict feedback chaotic system, and establish the proportional projection synchronization error system;

[0088] The drive system and the response system are heterogeneous systems, the drive system is the Genesio-Tesi chaotic system, and the response system is the Arneodo chaotic system. The state equation of the Genesio-Tesi chaotic system is:

[0089]

[0090] Formula (17) is the driving system, and the initial state is set to x 1 (0)=2, x 2 (0)=-2,x 3 (0)=1.

[0091] The response system is an Arneodo chaotic system, and the controlled response system with modeling uncertainties and external disturbance signals is:

[0092]

[0093] Among them, the modeling uncertainty △f 2 (y) is set to △f 2 (y)=0.5cos(y 1 +y 2 ), due to |△f 2 (y)|≤d 1 , then d 1 =0.5, the external interference signal d(t) ...

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Abstract

The invention provides a global integral sliding mode-based third-order strict-feedback chaos proportion projection synchronization method. The method comprises the following steps: step 1, establishing a driving system and a response system according to a state equation of the third-order strict-feedback chaos system, and establishing a proportion projection synchronization error system; step 2,designing a global integral sliding mode surface and a self-adaptive exponential approaching law; and step 3, designing a global integral sliding mode controller to control the proportion projection synchronization error system, and forming a closed-loop system, wherein the closed-loop control system can realize proportion projection synchronization control of the driving system and the response system. Stability of the closed-loop system is demonstrated through Lyapunov stability theory. Proportion projection synchronization control of isomorphic or heterogeneous third-order singular feedbackchaos of different initial states is realized by using only the single global integral sliding mode controller in a case of modeling uncertainty and external disturbance signals. An experiment resultshows effectiveness of the method, and the method has very good robustness and reliability.

Description

technical field [0001] The invention belongs to the technical field of automatic control, and in particular relates to a third-order strict feedback chaos proportional projection synchronization method based on a global integral sliding mode. Background technique [0002] Chaos is the link connecting deterministic motion and random motion, and it exists widely in nature and human society. The control and synchronization of chaos is a research subject that has attracted much attention in the field of nonlinear science. Since Mainieri and Rehacek proposed the concept of projective synchronization, different types of chaotic synchronization phenomena have been unified. Third-order strict feedback chaos, such as Genesio-Tesi chaos and Arneodo chaos, only needs a single control input to achieve proportional projection synchronization, and has broad application prospects in secure communication. [0003] Sliding mode control has strong robustness to modeling uncertainty and exte...

Claims

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Application Information

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IPC IPC(8): G05B13/02
CPCG05B13/024
Inventor 赵海滨刘冲陆志国
Owner NORTHEASTERN UNIV
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