A new adaptive control scheme for uncertain nonlinear systems with quantized input signal

Xing, Lantao; Chen, Wen; Su, Hongye; Cai, Jianping; Wang, Lei

doi:10.1016/j.jfranklin.2015.06.020

Cited by 61 publications

(49 citation statements)

References 21 publications

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“…The sector bound approach and the hyperbolic tangent function property are used to deal with the quantization error, and an output feedback controller is designed to guarantee the stability of the uncertain nonlinear quantized system. This result extends the existing state feedback quantized controls to the output feedback control of nonlinear systems with unknown output functions and unknown control directions (see Section 5).…”

Section: Introductionsupporting

confidence: 57%

Global output feedback control for nonlinear cascade systems with unknown output functions and unknown control directions

Wang

Sun

2020

Intl J Robust & Nonlinear

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Summary This paper investigates the output feedback control for the uncertain nonlinear system with the integral input‐to‐state stable (iISS) cascade subsystem, which allow not only the unknown control direction but also the unknown output function. The unknown output function only needs to have a generalized derivative (which may not be derivable), and the upper and lower bounds of the generalized derivative need not to be known. To deal with the challenge raised by the unknown output function and the unknown control direction, we choose a special Nussbaum function with a faster growth rate to ensure the integrability for the derivative of the selected Lyapunov function. Then, a dynamic output feedback controller is designed to drive the system states to the origin while keeping the boundedness for all other closed‐loop signals. Moreover, via some appropriate transformations, the proposed control scheme is extended to deal with more general uncertain nonlinear cascade systems with quantized input signals. Finally, two simulation examples are given to show the effectiveness of the control scheme.

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Section: Introductionsupporting

confidence: 57%

Global output feedback control for nonlinear cascade systems with unknown output functions and unknown control directions

Wang

Sun

2020

Intl J Robust & Nonlinear

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“…Based on the backstepping technique and the sector bound approach, some important results on quantised feedback control problem for strict feedback nonlinear system have achieved (see e.g. Liu et al, 2012a;Xing et al, 2015;Zhou et al, 2014). However, all these results only considered the case of a single quantiser.…”

Section: Remark 32mentioning

confidence: 99%

“…Much attention has been paid to the design of quantised controller for linear and nonlinear systems, among which some important achievements can be found (see e.g. Brackett & liberzon, 2000;Elia & Mitter, 2001;Fu & Xie, 2005;Liberzon, 2003;Liberzon & Nešić, 2007;Liu, Jiang, & Hill, 2012a, 2012bXing, Wen, Su, Liu, & Cai, 2015;Xing, Wen, Su, Liu, Cai, & Wang, 2015, 2016Zhou, Wen, & Yang, 2014). Indeed, it was proved in Elia and Mitter (2001) that the coarsest quantiser that quadratically stabilises a single-input linear discrete time-invariant system is logarithmic.…”

Section: Introductionmentioning

confidence: 99%

“…However, to obtain the stability conditions, it required the system nonlinearities to satisfy global Lipschitz conditions with known Lipschitz constants and their partial derivatives to be bounded. The paper, Xing et al (2015), proposed a new robust backstepping approach for uncertain nonlinear system with input quantised and relaxed the stability conditions in Zhou et al (2014).…”

Section: Introductionmentioning

confidence: 99%

“…Although some corresponding works on quantised feedback nonlinear systems have been presented (see e.g. Liu et al, 2012aLiu et al, , 2012bXing et al, 2015;Zhou et al, 2014), most of them are only developed for the case of a single quantiser. The corresponding results for input and output quantised feedback nonlinear systems are relatively few, due to the fact that it is more difficult in nonlinear analysis to cope with the quantisation errors caused by both input and output quantisations.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Global state feedback stabilisation for a class of high-order nonlinear systems with quantised input and state

Lin

Zhang

2016

International Journal of Systems Science

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KEYWORDSHomogeneous domination approach; sector bound approach; logarithmic quantiser; quantised controller computed from quantised state ABSTRACTIn this paper, we aim at addressing the problem of global state feedback stabilisation for a class of high-order nonlinear systems with quantised input and state. The nonlinear functions of the system are bounded by both low-order and high-order terms multiplied by a polynomial-type incremental rate. With the combination of homogeneous domination approach and sector bound approach, a quantised controller computed from quantised state is constructed and a guideline is derived for selecting the parameters of the quantisers. Further, it is proved that, with the proposed scheme, the closed-loop system is globally asymptotically stable.

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Event‐triggered adaptive tracking control for a class of uncertain stochastic nonlinear systems with Markov jumping parameters

2018

Adaptive Control & Signal

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SummaryThis paper aims to investigate the problem of event‐triggered adaptive tracking control for a class of stochastic nonlinear systems with Markov jumping parameters. Since the stochastic system contains unknown parameters, the assumption of the stochastic input‐to‐state stability is a difficult task to check. To overcome the design difficulty, mode‐dependent adaptive controllers and the event‐triggered strategy are designed simultaneously with the help of backstepping technique. The stochastic input‐to‐state stability assumption is avoided by adding correction terms in controller to compensate the measurement errors. The proposed control schemes guarantee that all signals in the closed‐loop system remain bounded in probability and the tracking error signals eventually converge to the compact set in the sense of mean quartic value. Finally, simulation results show the effectiveness of the proposed approach.

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A new adaptive control scheme for uncertain nonlinear systems with quantized input signal

Cited by 61 publications

References 21 publications

Global output feedback control for nonlinear cascade systems with unknown output functions and unknown control directions

Global output feedback control for nonlinear cascade systems with unknown output functions and unknown control directions

Global state feedback stabilisation for a class of high-order nonlinear systems with quantised input and state

Event‐triggered adaptive tracking control for a class of uncertain stochastic nonlinear systems with Markov jumping parameters

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