Observer-based robust preview tracking control for a class of continuous-time Lipschitz nonlinear systems

Xiao Yu; Yan Hua; Yanrong Lu; Xiao Yu; Yan Hua; Yanrong Lu

doi:10.3934/math.20241301

AIMS Mathematics

2024, Volume 9, Issue 10: 26741-26764. doi: 10.3934/math.20241301

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Research article

Observer-based robust preview tracking control for a class of continuous-time Lipschitz nonlinear systems

Xiao Yu ^{1
,
,},
Yan Hua ¹,
Yanrong Lu ²

1.
School of Science, Shandong Jianzhu University, Jinan 250101, China
2.
College of Electrical and Information Engineering, Lanzhou University of Technology, Lanzhou 730050, China

Received: 06 June 2024 Revised: 07 August 2024 Accepted: 26 August 2024 Published: 13 September 2024
MSC : 34H05, 93B52, 93C10

In this paper, a novel observer-based robust preview tracking controller design method is proposed for a class of continuous-time Lipschitz nonlinear systems with external disturbances and unknown states. First, a state observer is designed to reconstruct unknown system states. Second, using differentiation, the state lifting technique, the differential mean value theorem, and several ingenious mathematical manipulations, an augmented error system (AES) containing the previewable information of a reference signal is constructed, thereby transforming the tracking control problem into a robust $ H_{\infty} $ control problem. Based on linear parameter-varying (LPV) system theory, a sufficient condition for asymptotic stability of a closed-loop system with a robust $ H_{\infty} $ performance level is established in terms of the linear matrix inequality (LMI). Furthermore, a tracking controller, which includes observer-based feedback control, integral control, and preview feedforward compensation, is established for the original system. In particular, the tracking controller design is simplified by computing the observer and tracking controller gains simultaneously via only a one-step LMI algorithm. Finally, numerical simulation results demonstrate that the proposed controller leads to superior improvement in the output tracking performance compared with the existing methods.
- continuous-time Lipschitz nonlinear systems,
- preview control,
- tracking control,
- observer design,
- LMI
Citation: Xiao Yu, Yan Hua, Yanrong Lu. Observer-based robust preview tracking control for a class of continuous-time Lipschitz nonlinear systems[J]. AIMS Mathematics, 2024, 9(10): 26741-26764. doi: 10.3934/math.20241301

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Abstract

In this paper, a novel observer-based robust preview tracking controller design method is proposed for a class of continuous-time Lipschitz nonlinear systems with external disturbances and unknown states. First, a state observer is designed to reconstruct unknown system states. Second, using differentiation, the state lifting technique, the differential mean value theorem, and several ingenious mathematical manipulations, an augmented error system (AES) containing the previewable information of a reference signal is constructed, thereby transforming the tracking control problem into a robust $ H_{\infty} $ control problem. Based on linear parameter-varying (LPV) system theory, a sufficient condition for asymptotic stability of a closed-loop system with a robust $ H_{\infty} $ performance level is established in terms of the linear matrix inequality (LMI). Furthermore, a tracking controller, which includes observer-based feedback control, integral control, and preview feedforward compensation, is established for the original system. In particular, the tracking controller design is simplified by computing the observer and tracking controller gains simultaneously via only a one-step LMI algorithm. Finally, numerical simulation results demonstrate that the proposed controller leads to superior improvement in the output tracking performance compared with the existing methods.

References

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