Adaptive fuzzy control for nonlinear systems with sampled data and time-varying input delay

Kunting Yu; Yongming Li; Kunting Yu; Yongming Li

doi:10.3934/math.2020153

AIMS Mathematics

2020, Volume 5, Issue 3: 2307-2325. doi: 10.3934/math.2020153

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Research article

Adaptive fuzzy control for nonlinear systems with sampled data and time-varying input delay

Kunting Yu ,
Yongming Li ^,

College of Science, Liaoning University of Technology, Jinzhou, Liaoning, 121001, P. R. China

Received: 09 January 2020 Accepted: 27 February 2020 Published: 03 March 2020
MSC : 93B52, 93C42

In this paper, an adaptive fuzzy backstepping control strategy is studied for nonlinear nonstrict feedback systems with sampled data and time-varying input delay. Considering the practical application of the proposed control strategy, a time-varying signal transmission delay is investigated. By using fuzzy logic systems to approximate the unknown nonlinear functions, a fuzzy estimator (FE) model is proposed to estimate the states of the nonlinear plant, which is mainly utilized to support information of estimation states for the adaptive fuzzy controller. In the proposed strategy, the constraint between the signal transmission delay and the time-varying input delay is given to ensure the stability of the closed-loop system, and the state vectors are transformed to address the problem of time-varying input delay. By using the backstepping control technique and the information of the FE model, an adaptive fuzzy backstepping controller is designed. The proposed control strategy can guarantee that all signals of the closed-loop system are semi-globally uniformly ultimately bounded. Ultimately, a numerical simulation example is provided to verify the effectiveness of the proposed control method and theory.
- adaptive fuzzy control,
- backstepping,
- non-strict feedback systems,
- time-varying input delay,
- sampled-data
Citation: Kunting Yu, Yongming Li. Adaptive fuzzy control for nonlinear systems with sampled data and time-varying input delay[J]. AIMS Mathematics, 2020, 5(3): 2307-2325. doi: 10.3934/math.2020153

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Abstract

In this paper, an adaptive fuzzy backstepping control strategy is studied for nonlinear nonstrict feedback systems with sampled data and time-varying input delay. Considering the practical application of the proposed control strategy, a time-varying signal transmission delay is investigated. By using fuzzy logic systems to approximate the unknown nonlinear functions, a fuzzy estimator (FE) model is proposed to estimate the states of the nonlinear plant, which is mainly utilized to support information of estimation states for the adaptive fuzzy controller. In the proposed strategy, the constraint between the signal transmission delay and the time-varying input delay is given to ensure the stability of the closed-loop system, and the state vectors are transformed to address the problem of time-varying input delay. By using the backstepping control technique and the information of the FE model, an adaptive fuzzy backstepping controller is designed. The proposed control strategy can guarantee that all signals of the closed-loop system are semi-globally uniformly ultimately bounded. Ultimately, a numerical simulation example is provided to verify the effectiveness of the proposed control method and theory.

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