Adaptive fuzzy backstepping control for nonstrict feedback nonlinear systems with time-varying state constraints and backlash-like hysteresis
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The function c(v) is bounded by a positive constant c.
“The function c(t) is bounded, such that |c(v)| ≤ c with c being a positive constant.”
From Fixed-Time Adaptive Control for Nonstrict-Feedback Nonlinear Systems with Input Delay and Unknown Backlash-Like Hysteresis (2025) · cites this paper as [16]
The solution of the backlash-like hysteresis dynamics is u(v) = κv(t) + c(v).
“u(v) = κv(t) + c(v)”
From Fixed-Time Adaptive Control for Nonstrict-Feedback Nonlinear Systems with Input Delay and Unknown Backlash-Like Hysteresis (2025) · cites this paper as [16]
Several adaptive controllers have been introduced to specifically tackle the complexities associated with unknown backlash-like hysteresis.
“In response to this, several adaptive controllers have been introduced to specifically tackle the complexities associated with unknown backlash-like hysteresis [15][16][17].”
From Fixed-Time Adaptive Control for Nonstrict-Feedback Nonlinear Systems with Input Delay and Unknown Backlash-Like Hysteresis (2025) · cites this paper as [16]
This paper simultaneously considers the influence of both backlash-like hysteresis and input delay in nonstrict-feedback nonlinear systems.
“Unlike studies such as [16,17], which focus solely on backlash hysteresis, or [31,32], which primarily address input delay, this paper simultaneously considers the influence of both backlash-like hysteresis and input delay in nonstrict-feedback nonlinear systems.”
From Fixed-Time Adaptive Control for Nonstrict-Feedback Nonlinear Systems with Input Delay and Unknown Backlash-Like Hysteresis (2025) · cites this paper as [16]
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“…fixed time T to a neighborhood The system (1) is PFTS, with T bounded by Lemma 5 [32]: For real variables s and t , and any positive constants ρ , τ , and (cid:16) , the following inequality holds: Lemma 6 [33]: For any x , y ∈ R n that satisfy where l > 1, m > 1, n > 0, and ( l − 1 )( m − 1 ) = 1.”
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“Using the introduced mapping rule (6), system (1) is changed into the following system which is free from the constraints as follows:”
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“Recently, numerous scholars have incorporated the backlash-like hysteresis factor into their investigations on stochastic nonlinear systems [11], switched interconnected nonlinear systems [12] and non-strict feedback systems [13].”
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“The second comparative scheme (denoted as “CCS2” hereafter) is an existing barrier Lyapunov function-based constrained infinite-time adaptive fuzzy control scheme by following [28] in the absence of actuator hysteresis.”
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“Using (5) and (6), system (1) can be rewritten as:”
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“…2 /ς , we have Thus, the system (2.1) can be further rewritten as with u (v) being the input of the system subject to the backlash-like hysteresis of the actuator, and its dynamics are characterized by [16] where v represents hysteresis input, ω , κ , and (cid:8) are positive constants with κ ≥ c .”
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“Authors in Kong et al., 22 Sun et al. 30 Liu et al. 31,32 considered the effects of backlash-like hysteresis, but the enhancement of controller performance by PPTC is overlooked.”
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“(Liu et al., 2021) For any x , y 2 R n , the following inequality relationship holds where l > 1, m > 1, n > 0, and ð l (cid:2) 1 Þð m (cid:2) 1 Þ ¼ 1.”
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“…of state constraints, the barrier Lyapunov function (BLF) is widely applied, such that log-type BLF (Edalati et al., 2018; Liu & Tong, 2016; Yu et al. 2019), integral iBLF (Kim & Yoo, 2015; Liu et al., 2021a, 2021b) and tan-type BLF (Ma et al., 2022; Wang et al., 2021a, 2021b; Xia et al., 2019).”
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“(Liu et al., 2021) For any θ , q 2 R n , one has Lemma 3.”
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“Therefore, many scholars have dedicated to studying systems with hysteresis and have proposed many effective control algorithms (Bai et al., 2017; Liu et al., 2021; N. Xu et al., 2022; Z. Zhao et al.,2022; Z. Zhu et al., 2020).”
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“( [45]) The inequality relationship shown below is valid x y ≤ n a a ∥x∥ + 1 bnb ∥y∥ (2.”
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“Lemma 3 ([40]) .”
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“Traditional approaches to handling state constraints include barrier Lyapunov functions [32], model predictive control [33], and adaptive control methods incorporating feasibility conditions [34].”
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“In past decades, plenty of researches were conducted on uncertain nonlinear systems, designing various approximators to eliminate the influence brought by uncertainties, such as neural network [1]-[4], fuzzy network [5] , wavelet network [6], etc.”
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“To handle asymmetric time-varying state constraints, an asymmetric tan-type-based adaptive fuzzy control method was proposed in [18].”
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Adaptive Fuzzy Control for Structual Uncertain Non-Strict Feedback Systems
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- Authors
- Liu, Y., Zhu, Q., Zhao, N., & Wang, L.
- Affiliations
- Harbin Engineering University (CN)
- Corresponding author
- Zhu, Qidan
- Venue
- Information Sciences
- Publisher
- Elsevier BV
- Published
- 2021-10
- Volume
- 574
- Pages
- 606-624
- ISSN
- 0020-0255 (ISSN-L)
- OpenAlex
- W3184300438
- Cited by
- 53
- References
- 40
- Citations by year
- 2026: 5 · 2025: 8 · 2024: 15 · 2023: 11 · 2022: 12 · 2021: 2
- FWCI
- 4.45
- Type
- journal article
- Language
- en
- Open access
- closed
- Licence
- Locations
- Information Sciences (publishedVersion)
- Funders
- Fundamental Research Funds for the Central Universities (3072020CF0410)
- National Natural Science Foundation of China (61803116, 61673129)
- Topics
- Physical Sciences › Engineering › Control and Systems Engineering › Adaptive Control of Nonlinear Systems
- Physical Sciences › Engineering › Control and Systems Engineering › Stability and Control of Uncertain Systems
- Physical Sciences › Computer Science › Artificial Intelligence › Fuzzy Logic and Control Systems
- Keywords
- adaptive fuzzy control, backstepping control, nonstrict-feedback nonlinear systems, time-varying state constraints, backlash-like hysteresis, time-varying barrier Lyapunov function, tracking control, uniform ultimate boundedness, fuzzy basis functions
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