Multiple adaptive fuzzy Nussbaum-type functions design for stochastic nonlinear systems with fixed-time performance

Yang, Yongliang; Liu, Guilong; Li, Qing; Ahn, Choon Ki

doi:10.1016/j.fss.2023.108767

Cited by 5 publications

(2 citation statements)

References 52 publications

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“…By designing the virtual control signals (20), (34), (43) and (58), the adaptation law ( 21), ( 35), ( 44) and (59), the control law (52), for any z i (0), θi (t), all the signals remain SGUUB in probability, the tracking error converges to a region of the origin, the variable z j converges to Ω z , which satisfies…”

Section: Adaptive Fuzzy Tracking Control Designmentioning

confidence: 99%

“…In recent decades, nonlinear system control has received great concern from researchers due to its wide application; for instance, the optimization problem of prescribed performance tracking control was investigated for a class of strictly feedback nonlinear systems [18]; some new regressor-free adaptive controllers were proposed for cooperative robotic arms [19]. There always exist stochastic disturbances in practical physical plants [20]. The investigation of stochastic nonlinear systems has received considerable attention [21][22][23].…”

Section: Introduction and Related Work 1introductionmentioning

confidence: 99%

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Adaptive Fuzzy Backstepping Control for Itô-Type Nonlinear Switched Systems Subject to Unknown Hysteresis Input

Wan,

2024

Mathematics

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The adaptive fuzzy backstepping control problem is studied for Itô-type nonlinear switched systems subject to unknown hysteresis input. Compared with existing works, the unknown hysteresis and stochastic disturbances are considered in the pure-feedback switched systems. The mean value theorem tackles the non-affine functions. The backstepping technique introduces an auxiliary virtual controller. In addition, the Nussbaum function is employed to solve the difficulty caused by the unknown hysteresis under arbitrary switching. Based on a fuzzy logic system and backstepping technique, a new adaptive control proposal is obtained, which ensures that the system states satisfy semiglobally uniformly ultimately bounded (SGUUB) in probability and that the tracking error converges to a region of the origin. Finally, we provide two examples to show the validity of the presented scheme.

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Section: Adaptive Fuzzy Tracking Control Designmentioning

confidence: 99%

Section: Introduction and Related Work 1introductionmentioning

confidence: 99%

Adaptive Fuzzy Backstepping Control for Itô-Type Nonlinear Switched Systems Subject to Unknown Hysteresis Input

Wan,

2024

Mathematics

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Adaptive Robust Control of Nonlinear Constrained Stirred‐Tank Reactors via Self‐Organizing Fuzzy Neural Network

Cui,

Li,

2024

Adaptive Control & Signal

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This paper presents an adaptive robust constraint controller for a continuous stirred tank reactor (CSTR) system based on a self‐organizing fuzzy neural network (SOFNN). Due to the high complexity of the chemical reactions, the CSTR system contains many strong nonlinearities and uncertainties. This is the first time to introduce the SOFNN into the adaptive controller design of the CSTR system, which improves the adaptability to dynamic system changes through the adjustment of the fuzzy network structure. Meanwhile, the time‐varying integral barrier Lyapunov functions (TVIBLFs) are employed to ensure the dimensionless reactant concentration and mixture temperature within a reasonable scope, which can improve the stability and safety of the CSTR system. Based on Lyapunov stability analysis, all the signals in a closed‐loop system are ultimately bounded. Simulation results substantiate the efficacy of the proposed control scheme.

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Adaptive Nussbaum design using composite triggering condition for stochastic nonlinear systems with multiple unknown control directions

Liu,

Yang,

Ding

et al. 2024

Intl J Robust & Nonlinear

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The traditional Nussbaum‐type functions encounter challenges when extended to systems with multiple unknown control directions, as the coupling between the Nussbaum‐type function and Nussbaum‐type gain may lead to mutual elimination. To address this issue, a novel Nussbaum‐type function is introduced to handle multiple unknown control directions for stochastic systems. The stability of the proposed Nussbaum‐based design can be guaranteed using the Lyapunov analysis. To conserve computational resources, a static composite event‐triggered mechanism is integrated with intermittent feedback in the Nussbaum‐based design. In contrast to conventional event‐triggering mechanisms that depend solely on control signals, the presented design incorporates tracking errors into the event‐triggering conditions. Moreover, to further alleviate computational burdens, we further develop a dynamic composite event‐triggered mechanism. With the overall design scheme, bounded tracking errors and reduced computational burden can be ensured. Simulation examples validate the efficacy of the proposed adaptive Nussbaum composite event‐based robust control design.

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Multiple adaptive fuzzy Nussbaum-type functions design for stochastic nonlinear systems with fixed-time performance

Cited by 5 publications

References 52 publications

Adaptive Fuzzy Backstepping Control for Itô-Type Nonlinear Switched Systems Subject to Unknown Hysteresis Input

Adaptive Fuzzy Backstepping Control for Itô-Type Nonlinear Switched Systems Subject to Unknown Hysteresis Input

Adaptive Robust Control of Nonlinear Constrained Stirred‐Tank Reactors via Self‐Organizing Fuzzy Neural Network

Adaptive Nussbaum design using composite triggering condition for stochastic nonlinear systems with multiple unknown control directions

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