Global adaptive control for uncertain nonaffine nonlinear hysteretic systems

Liu, Yonghua; Huang, Liangpei; Xiao, Dongming; Guo, Yong

doi:10.1016/j.isatra.2015.06.010

Cited by 12 publications

(14 citation statements)

References 34 publications

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“…z 1 is bounded, hence x 1 , α 1 , g 1 are bounded. Assumption 1 and a previous work [51], state that x 2 is likewise bounded. Furthermore, z 2 is bounded, thereby implying that α 2 is bounded.…”

Section: From the (T-3)-(t-11) Controllers And The (T-12)-(t-15) Paramentioning

confidence: 98%

Adaptive Control for Pure-Feedback Nonlinear Systems Preceded by Asymmetric Hysteresis

2019

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An adaptive control scheme is proposed for a class of uncertain pure-feedback nonlinear systems preceded by asymmetric hysteresis nonlinearity. The asymmetric property is described by the modified Bouc-Wen model based on the proposed asymmetric factor. State variables in the controller design are directly replaced with nonaffine functions to address the control problem caused by nonaffine appearance. Moreover, the control method can handle systems with external disturbances and guarantee the global stability of all the signals in the closed-loop system. The feasibility of the control scheme is verified by a simulation example and experimental results.

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Section: From the (T-3)-(t-11) Controllers And The (T-12)-(t-15) Paramentioning

confidence: 98%

Adaptive Control for Pure-Feedback Nonlinear Systems Preceded by Asymmetric Hysteresis

2019

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“…Assumption 2 is more general compared to the literature. 13 An auxiliary integral system is introduced to solve the nonaffine input of systems (1)…”

Section: Systems and Problem Statementmentioning

confidence: 99%

Robust adaptive prescribed performance control for a class of nonlinear pure‐feedback systems

Jia

Wang

Zhou

2019

Intl J Robust & Nonlinear

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Summary An adaptive prescribed performance control design procedure for a class of nonlinear pure‐feedback systems with both unknown vector parameters and unmodeled dynamics is presented. The unmodeled dynamics lie within some bounded functions, which are assumed to be partially known. A state transformation and an auxiliary system are proposed to avoid using the cumbersome formula to handle the nonaffine structure. Simultaneously, a parameter‐type Lyapunov function and L function are designed to ensure the prescribed performance of the pure‐feedback system. As illustrated by examples, the proposed adaptive prescribed performance control scheme is shown to guarantee global uniform ultimate boundedness. At the same time, this method not only guarantees the prescribed performance of the system but also makes the tracking error asymptotically close to a certain value or stable.

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“…• Nonaffinity: However, there exist several nonlinear nonaffine systems in practice, such as chemical reactors, biochemical processes, some aircraft and pendulum dynamical models, and so on [1,10,12,19,20,23,25,26,44,50,56,58]. Due to the great efforts devoted by researchers, remarkable adaptive control approaches have been developed for non-affine systems [19,44,50,56]. It is worth noting that affine systems are a special case of non-affine systems [1,10,12].…”

Section: Introductionmentioning

confidence: 99%

“…It is worth noting that affine systems are a special case of non-affine systems [1,10,12]. In [10,19,20], it has been shown that the non-affine problem can be traditionally addressed by five approaches, namely: (1) approach based on Taylor series expansion, (2) approach based on implicit function theorem, (3) approach based on the mean value theorem, (4) approach based on differentiating the original system equation, and (5) approach based on a local inversion of the TakagiSugeno (TS) fuzzy affine model. Moreover, the knowledge of the sign of the control gain is required in [20,23] to facilitate the design of the adaptive controls for nonlinear non-affine systems.…”

Section: Introductionmentioning

confidence: 99%

“…Compared with the existing controls in [2,8,10,11,40,62], the adaptive fuzzy control laws presented in [47][48][49] have solved the tracking problem for nonlinear uncertain discrete-time systems with unknown control direction and input nonlinearities (such as dead zone, backlash-like hysteresis, and backlash), by using the reinforcement learning algorithm. • Uncertainty: In most practical situations, the systems under control are unknown or partially unknown [4,7,12,13,17,19,22,31,42,56,57,61]. These facts require specific control tools to deal with the controller design process, being one of the most extended ones the adaptive control paradigm.…”

Section: Introductionmentioning

confidence: 99%

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Observer-based adaptive neural network control for a class of MIMO uncertain nonlinear time-delay non-integer-order systems with asymmetric actuator saturation

Zouari

Boulkroune

Ibeas

et al. 2016

Neural Comput & Applic

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This paper focuses on the adaptive neural output feedback control of a class of uncertain multi-input-multioutput nonlinear time-delay non-integer-order systems with unmeasured states, unknown control direction, and unknown asymmetric saturation actuator. Thus, the mean value theorem and a Gaussian error function-based continuous differentiable model are used in the paper to describe the unknown asymmetric saturation actuator and to get an affine model in which the control input appears in a linear fashion, respectively. The design of the controller follows a number of steps. Firstly, based on the semigroup property of fractional-order derivative, the system is transformed into a normalized fractional-order system by means of a state transformation in order to facilitate the control design. Then, a simple linear state observer is constructed to estimate the unmeasured states of the transformed system. A neural network is incorporated to approximate the unknown nonlinear functions while a Nussbaum function is used to deal with the unknown control direction. In addition, the strictly positive real condition, the Razumikhin Lemma, the frequency-distributed model, and the Lyapunov method are utilized to derive the parameter adaptive laws and to perform the stability proof. The main advantages of this work are that:(1) it can handle systems with constant, time-varying, and distributed time-varying delays, (2) the considered class of systems is relatively large, (3) the number of adjustable parameters is reduced, (4) the tracking errors converge asymptotically to zero and all signals of the closed-loop system are bounded. Finally, some simulation examples are provided to demonstrate the validity and effectiveness of the proposed scheme.

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Global adaptive control for uncertain nonaffine nonlinear hysteretic systems

Cited by 12 publications

References 34 publications

Adaptive Control for Pure-Feedback Nonlinear Systems Preceded by Asymmetric Hysteresis

Adaptive Control for Pure-Feedback Nonlinear Systems Preceded by Asymmetric Hysteresis

Robust adaptive prescribed performance control for a class of nonlinear pure‐feedback systems

Observer-based adaptive neural network control for a class of MIMO uncertain nonlinear time-delay non-integer-order systems with asymmetric actuator saturation

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