Finite-time adaptive prescribed performance DSC for pure feedback nonlinear systems with input quantization and unmodeled dynamics

Bin Hang; Weiwei Deng; Bin Hang; Weiwei Deng

doi:10.3934/math.2024332

AIMS Mathematics

2024, Volume 9, Issue 3: 6803-6831. doi: 10.3934/math.2024332

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Finite-time adaptive prescribed performance DSC for pure feedback nonlinear systems with input quantization and unmodeled dynamics

Bin Hang ¹,
Weiwei Deng ^{2
,
,}

1.
School of Automation, Northwestern Polytechnical University, Xi'an 710072, China
2.
College of Information Engineering, Yangzhou University, Yangzhou 225127, China

Received: 13 September 2023 Revised: 11 January 2024 Accepted: 29 January 2024 Published: 19 February 2024
MSC : 93A30, 93C10, 97N40

This paper presents a new prescribed performance-based finite-time adaptive tracking control scheme for a class of pure-feedback nonlinear systems with input quantization and dynamical uncertainties. To process the input signal, a new quantizer combining the advantages of a hysteresis quantizer and uniform quantizer has been used. Radial basis function neural networks have been utilized to approximate unknown nonlinear smooth functions. An auxiliary system has been employed to estimate unmodeled dynamics by producing a dynamic signal. By introducing a hyperbolic tangent function and performance function, the tracking error was made to fall within the prescribed time-varying constraints. Using modified dynamic surface control (DSC) technology and a finite-time control method, a novel finite-time controller has been designed, and the singularity problem of differentiating each virtual control scheme in the existing finite-time control scheme has been removed. Theoretical analysis shows that all signals in the closed-loop system are semi-globally practically finite-time stable, and that the tracking error converges to a prescribed time-varying region. Simulation results for two numerical examples have been provided to illustrate the validity of the proposed control method.
- prescribed performance,
- dynamic surface control,
- finite-time stability,
- unmodeled dynamics,
- input quantization
Citation: Bin Hang, Weiwei Deng. Finite-time adaptive prescribed performance DSC for pure feedback nonlinear systems with input quantization and unmodeled dynamics[J]. AIMS Mathematics, 2024, 9(3): 6803-6831. doi: 10.3934/math.2024332

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Abstract

This paper presents a new prescribed performance-based finite-time adaptive tracking control scheme for a class of pure-feedback nonlinear systems with input quantization and dynamical uncertainties. To process the input signal, a new quantizer combining the advantages of a hysteresis quantizer and uniform quantizer has been used. Radial basis function neural networks have been utilized to approximate unknown nonlinear smooth functions. An auxiliary system has been employed to estimate unmodeled dynamics by producing a dynamic signal. By introducing a hyperbolic tangent function and performance function, the tracking error was made to fall within the prescribed time-varying constraints. Using modified dynamic surface control (DSC) technology and a finite-time control method, a novel finite-time controller has been designed, and the singularity problem of differentiating each virtual control scheme in the existing finite-time control scheme has been removed. Theoretical analysis shows that all signals in the closed-loop system are semi-globally practically finite-time stable, and that the tracking error converges to a prescribed time-varying region. Simulation results for two numerical examples have been provided to illustrate the validity of the proposed control method.

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