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A third-order strict feedback chaotic trajectory tracking method

A trajectory tracking and chaotic technology, which is applied in the direction of instruments, adaptive control, control/regulation systems, etc., can solve the problem of difficulty in trajectory tracking of the third-order strict feedback chaotic system, and overcome the influence of modeling uncertainty and external interference signals Effect

Inactive Publication Date: 2021-06-01
NORTHEASTERN UNIV LIAONING
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Problems solved by technology

Trajectory tracking of third-order strict feedback chaotic systems with different initial states is very difficult due to modeling uncertainties and external disturbance signals

Method used

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  • A third-order strict feedback chaotic trajectory tracking method
  • A third-order strict feedback chaotic trajectory tracking method
  • A third-order strict feedback chaotic trajectory tracking method

Examples

Experimental program
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Effect test

specific Embodiment 1

[0068] The third-order strict feedback chaotic system is Arneodo chaotic system. The state equation of the Arneodo system is:

[0069]

[0070] when parameter a 1 =-1, a 2 =-5.5, a 3 = 3.5, a 4 When = 1, the Arneodo system will appear chaotic phenomenon. A third-order strict feedback chaotic system with modeling uncertainties and external disturbance signals, the state equation is:

[0071]

[0072] Formula (14) is used as a third-order strict feedback chaotic system. The modeling uncertainty △f(x) is set as △f(y)=2sin(x 1 +x 2 ), the external interference signal d(t) is set as d(t)=3sin(3t). The initial state of the third-order strict feedback chaotic system is set to x 1 (0)=2, x 2 (0)=-2,x 3 (0)=2.5.

[0073] Arneodo chaotic system state variable x 1 The expected trajectory of x d =sin(t), state variable x 2 The expected trajectory of state variable x 3 The expected trajectory of The initial state of the desired trajectory is x d (0)=0,

[0074...

specific Embodiment 2

[0092] The third-order strict feedback chaotic system is Genesio-Tesi chaotic system. The state equation of the Genesio-Tesi system is:

[0093]

[0094] Among them, the parameters are a>0, b>0, c>0, and ab

[0095]

[0096]Formula (16) is used as a third-order strict feedback chaotic system. The modeling uncertainty △f(x) is set as △f(y)=2sin(3x 2 ), the external interference signal d(t) is set as d(t)=2cos(3t). The initial state of the third-order strict feedback chaotic system is set to x 1 (0)=-1,x 2 (0)=2.5, x 3 (0)=1.2.

[0097] Genesio-Tesi chaotic system state variable x 1 The expected trajectory of x d =sin(2t), state variable x 2 The expected trajectory of state variable x 3 The expected trajectory of The initial state of...

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Abstract

The present invention proposes a third-order strict feedback chaotic trajectory tracking method. The process includes: establishing a trajectory tracking error system according to the state equation and the expected trajectory of the third-order strict feedback chaotic system; designing a nonlinear global sliding mode surface and an adaptive exponential approach Law; design an adaptive global sliding mode controller, the single adaptive global sliding mode controller controls the trajectory tracking error system to form a closed-loop system, the closed-loop system can realize the trajectory tracking control of the third-order strict feedback chaotic system. The global sliding mode controller using the nonlinear global sliding mode surface is robust in both the approaching mode and the sliding mode. Combining the global sliding mode controller and the adaptive sliding mode controller, an adaptive global sliding mode controller is proposed. Modular controller only needs a single control input to achieve third-order strict feedback chaotic trajectory tracking control, and overcome the influence of modeling uncertainty and external interference signals.

Description

technical field [0001] The invention belongs to the technical field of automatic control, and in particular relates to a third-order strict feedback chaotic trajectory tracking method. Background technique [0002] Chaos is the link connecting deterministic motion and random motion, and it exists widely in nature and human society. The third-order strict feedback chaos can realize trajectory tracking with only a single input, and has broad application prospects in secure communication. Trajectory tracking of third-order strict feedback chaotic systems with different initial states is very difficult due to modeling uncertainties and external disturbance signals. [0003] Sliding mode control has strong robustness to modeling uncertainty and external disturbance signals, and has the advantages of fast response and easy implementation, and is widely used in the control of nonlinear systems. The global sliding mode controller using the nonlinear global sliding mode surface has...

Claims

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Application Information

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Patent Type & Authority Patents(China)
IPC IPC(8): G05B13/04
CPCG05B13/042
Inventor 赵海滨刘冲陆志国于清文颜世玉
Owner NORTHEASTERN UNIV LIAONING
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