Neuro-adaptive finite-time control of fractional-order nonlinear systems with multiple objective constraints

Lusong Ding; Weiwei Sun; Lusong Ding; Weiwei Sun

doi:10.3934/mmc.2023029

Mathematical Modelling and Control

2023, Volume 3, Issue 4: 355-369. doi: 10.3934/mmc.2023029

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Research article

Neuro-adaptive finite-time control of fractional-order nonlinear systems with multiple objective constraints

Lusong Ding ^1,2,
Weiwei Sun ^{1,2
,
,}

1.
Institute of Automation, Qufu Normal University, Qufu 273165, China
2.
School of Engineering, Qufu Normal University, Rizhao 276826, China

Received: 17 May 2023 Revised: 19 June 2023 Accepted: 17 July 2023 Published: 19 December 2023

This paper presents a neuro-adaptive finite-time control strategy for uncertain nonstrict-feedback fractional-order nonlinear systems with multiple-objective constraints. To stabilize the uncertain nonlinear fractional-order systems, neural networks (NNs) are employed to identify the unknown nonlinear functions, and dynamic surface control is used to avoid the computational complexity of the backstepping design procedure. The effect caused by the algebraic loop problem can be solved via establishing fractional-order adaptive laws. Introducing a new barrier function, the system output is always limited to the predefined time-varying acceptable range while effectively solving the multi-objective constraint problem. Utilizing fractional-order finite-time stability theory, a finite-time control scheme is constructed to drive the system output to the reference signal in finite time, which ensures better tracking performance. Two examples are given to illustrate the availability and superiority of the presented control scheme.
- fractional-order system,
- finite-time control,
- multiple-objective constraints,
- neuro-adaptive control
Citation: Lusong Ding, Weiwei Sun. Neuro-adaptive finite-time control of fractional-order nonlinear systems with multiple objective constraints[J]. Mathematical Modelling and Control, 2023, 3(4): 355-369. doi: 10.3934/mmc.2023029

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Abstract

This paper presents a neuro-adaptive finite-time control strategy for uncertain nonstrict-feedback fractional-order nonlinear systems with multiple-objective constraints. To stabilize the uncertain nonlinear fractional-order systems, neural networks (NNs) are employed to identify the unknown nonlinear functions, and dynamic surface control is used to avoid the computational complexity of the backstepping design procedure. The effect caused by the algebraic loop problem can be solved via establishing fractional-order adaptive laws. Introducing a new barrier function, the system output is always limited to the predefined time-varying acceptable range while effectively solving the multi-objective constraint problem. Utilizing fractional-order finite-time stability theory, a finite-time control scheme is constructed to drive the system output to the reference signal in finite time, which ensures better tracking performance. Two examples are given to illustrate the availability and superiority of the presented control scheme.

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