Robust adaptive prescribed performance dynamic surface control for uncertain nonlinear pure-feedback systems

Jia, Fujin; Yan, Xiao; Wang, Xuhuan; Lu, Junwei; Li, Yongmin

doi:10.1016/j.jfranklin.2019.12.006

Cited by 25 publications

(13 citation statements)

References 38 publications

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“…Lemma 2: For real numbers ℓ and any real number ϵ 0 greater than zero, the following inequality holds ((e.g. [29]).…”

Section: Systems and Fuzzy Internal Model Designmentioning

confidence: 99%

“…where θ 2 = θ 2 − ϑ 2 , and w 2 = ŵ 2 − w 2 , and ϑ 2 and w 2 are the estimation of θ 2 and ŵ 2 , respectively. From (29) and (30), the dynamic of V 2 is given as…”

Section: Controller Design Of Non-linear Systemsmentioning

confidence: 99%

“…Lemma For real numbers

ℓ

and any real number

ϵ_{0}

greater than zero, the following inequality holds ((e.g. [29]).

\begin{matrix} right left right left right left right left right left right left0.278em 2em 0.278em 2em 0.278em 2em 0.278em 2em 0.278em 2em 0.278em3pt \\ 0 \leq | ℓ | - ℓ \tanh (\frac{ℓ}{ϵ_{0}}) \leq δ_{0} ϵ_{0}, \end{matrix}

where

δ_{0}

satisfies

δ_{0} = e^{- false(δ_{0} + 1 false)}

, i.e.,

δ_{0} = 0.2785

.…”

Section: Systems and Fuzzy Internal Model Designmentioning

confidence: 99%

“…Although there are abundant results, the steady‐state property still depends on the SUUB control algorithms [28], and the PP functions can also only be relied on the exponential‐type symmetric functions. Therefore, previous PP control algorithms have limitations [29].…”

Section: Introductionmentioning

confidence: 99%

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Adaptive fuzzy output regulation of uncertain pure‐feedback non‐linear systems with prescribed performance

Jia

et al. 2020

IET Control Theory & Appl

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The output regulation problem for pure-feedback non-linear systems with prescribed performance (PP) driven by an external linear system with unknown parameter are investigated. First, an observer with a disturbance signal is designed to observe unmeasured system states. Secondly, fuzzy logic systems (FLS) are used to approximate unknown non-linear nonaffine functions. Thirdly, a fuzzy internal model is obtained to reject disturbance, and an adaptive fuzzy output feedback algorithm is proposed based on dynamic surface control (DSC) technique and backstepping method. Simultaneously, an L function is constructed so that the overall property (steady-state property and dynamic property) of the tracking error are constrained by PP functions. The results explain that the proposed control algorithm can make sure that all signals of the closed-loop system are semi-globally uniformly ultimately bounded (SUUB), and the tracking error is semi-globally PP uniformly ultimately bounded (SPPUUB). Finally, two examples are given to show the validity of the results.

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“…Lemma 2: For real numbers ℓ and any real number ϵ 0 greater than zero, the following inequality holds ((e.g. [29]).…”

Section: Systems and Fuzzy Internal Model Designmentioning

confidence: 99%

“…where θ 2 = θ 2 − ϑ 2 , and w 2 = ŵ 2 − w 2 , and ϑ 2 and w 2 are the estimation of θ 2 and ŵ 2 , respectively. From (29) and (30), the dynamic of V 2 is given as…”

Section: Controller Design Of Non-linear Systemsmentioning

confidence: 99%

“…Lemma For real numbers

ℓ

and any real number

ϵ_{0}

greater than zero, the following inequality holds ((e.g. [29]).

\begin{matrix} right left right left right left right left right left right left0.278em 2em 0.278em 2em 0.278em 2em 0.278em 2em 0.278em 2em 0.278em3pt \\ 0 \leq | ℓ | - ℓ \tanh (\frac{ℓ}{ϵ_{0}}) \leq δ_{0} ϵ_{0}, \end{matrix}

where

δ_{0}

satisfies

δ_{0} = e^{- false(δ_{0} + 1 false)}

, i.e.,

δ_{0} = 0.2785

.…”

Section: Systems and Fuzzy Internal Model Designmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Adaptive fuzzy output regulation of uncertain pure‐feedback non‐linear systems with prescribed performance

Jia

et al. 2020

IET Control Theory & Appl

Self Cite

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“…erefore, the prescribed performance control was proposed, which can satisfy preset transient and steady-state tracking performance in [34][35][36]. In particular, an adjustable finite-time prescribed performance function with fast convergence speed was adopted in [37,38], which ensures realtime adjustment of controller parameters cased by the tracking error.…”

Section: Introductionmentioning

confidence: 99%

Observer-Based Adaptive Fuzzy Predefined Performance Control of a Class of Nonlinear Pure-Feedback Systems with Input Delay

Zhang

2020

Complexity

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This paper presents a problem of observer-based adaptive fuzzy predefined performance control of a class of nonlinear pure-feedback systems with input delay and unknown control direction. Compared with the existing research, a novel predefined performance controller is proposed, which relaxes the assumption that the initial error is known. In addition, it is difficult to design the controllers due to input delay and nonaffine properties of the pure-feedback systems, which can be simplified by Pade approximation. Moreover, dynamic surface control and Nussbaum functions are applied to overcome the calculation explosion caused by repeated differentiations and unknown control direction, respectively. Based on the above methods, an adaptive fuzzy predefined performance controller is proposed, and it is proved that all the signals of a closed-loop system are semiglobally uniformly ultimately bounded (SGUUB). The tracking errors converge within a predefined range, while the observer estimation errors converge within a small zero region. Finally, the simulation results demonstrate the effectiveness of the proposed control system.

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Adaptive fuzzy finite‐time fault‐tolerant control design for nonlinear pure‐feedback systems with sensor faults

You

Shen

et al. 2023

Adaptive Control & Signal

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Summary This article investigates an adaptive fuzzy finite‐time fault‐tolerant control (FTC) scheme for nonlinear pure‐feedback systems (PFSs) with sensor faults. The pure‐feedback system in this article includes time‐varying fault factors and unknown nonlinear functions. Choose the time‐varying fault separation method to keep the fault parameters away from the actual state to avoid coupling problems. Using the mean‐value theorem (MVT) to handle the non‐affine functions in the system and effectively decouple the control input signals. The approximation capability of the fuzzy logic systems (FLSs) is utilized to handle the unknown functions in the system and combined with the backstepping techniques for the construction of the adaptive fault‐tolerant controller. Using Lyapunov theory to verify the stability of closed‐loop system. Finally, choose two simulation examples verified the validity of the control strategy.

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Robust adaptive prescribed performance dynamic surface control for uncertain nonlinear pure-feedback systems

Cited by 25 publications

References 38 publications

Adaptive fuzzy output regulation of uncertain pure‐feedback non‐linear systems with prescribed performance

Adaptive fuzzy output regulation of uncertain pure‐feedback non‐linear systems with prescribed performance

Observer-Based Adaptive Fuzzy Predefined Performance Control of a Class of Nonlinear Pure-Feedback Systems with Input Delay

Adaptive fuzzy finite‐time fault‐tolerant control design for nonlinear pure‐feedback systems with sensor faults

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