Control of nonlinear systems under dynamic constraints: A unified barrier function-based approach

Zhao, Kai; Song, Yongduan; Chen, C.L. Philip; Chen, Long

doi:10.1016/j.automatica.2020.109102

Cited by 166 publications

(70 citation statements)

References 33 publications

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“…Finally, although the method by Zhao et al 16 considered the constraints that could alternate positively and negatively, it works only for Scenario 1, whereas the proposed method works uniformly for all those cases.…”

Section: Resultsmentioning

confidence: 99%

“…Remark It is worth noting that Scenario 1 has been the main focus of most existing works, see for instance, References 5‐7,9,16, where the constraining boundaries considered are either constants and symmetric or at most time‐varying and asymmetric 5‐7,9 . The work by Tee et al 5 is among the first that explicitly considered asymmetrical and time‐varying output constraints, which, however, requires that the upper boundary be positive and that the ideal trajectory be within positive boundaries, which is rather restrictive in practice.…”

Section: Problem Formulation and Preliminariesmentioning

confidence: 99%

“…Although the time‐varying and asymmetric full‐state constraints are studied in Reference 9, the constraining boundaries need to be strictly positive, excluding the situation where the signs of upper and lower bounds alternate. The work by Zhao 16 is by far the first one that allows the lower and upper boundaries to be zero at some time instants, but the proposed control only works for Scenario 1 where such constraints must be always imposed during system operation. To our best knowledge, there is no feasible solution capable of uniformly dealing with aforementioned irregular constraints.…”

Section: Problem Formulation and Preliminariesmentioning

confidence: 99%

“…It is worth noting that the constraining lower boundary F 11 is sometimes positive and sometimes negative, or even zero periodically, rendering existing works inapplicable, 5,7‐9 and since the constraints are not imposed all the time during the system operation, the method by Zhao et al 16 is not applicable either.…”

Section: Simulationmentioning

confidence: 99%

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Unified tracking control under full‐state constraints imposed irregularly

Cui

Wang

Song

2021

Intl J Robust & Nonlinear

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It is nontrivial to address the control problem of nonlinear systems with irregular constraining conditions (where the constraints, possibly time‐varying, asymmetric and alternating positively and negatively, would occur or disappear in the middle of system operation). In this work, we present a control design framework for uncertain pure‐feedback systems under the aforementioned constraining conditions. By making use of auxiliary constraining boundaries, we analytically extend the originally imposed constraints over the entire time interval of system operation, with which we introduce a useful state transformation with unique features. It is such transformation that allows for the development of the control scheme capable of uniformly addressing a variety of constraints formed dynamically and imposed irregularly. It is shown that, for the scenarios where the constraints are partially or fully imposed or removed at any time instant during system operation, one only needs to reset the corresponding extended constraining boundaries in the control scheme instead of altering its structure. Both theoretical analysis and numerical simulation authenticate the effectiveness of the proposed method.

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Section: Resultsmentioning

confidence: 99%

Section: Problem Formulation and Preliminariesmentioning

confidence: 99%

Section: Problem Formulation and Preliminariesmentioning

confidence: 99%

Section: Simulationmentioning

confidence: 99%

See 2 more Smart Citations

Unified tracking control under full‐state constraints imposed irregularly

Cui

Wang

Song

2021

Intl J Robust & Nonlinear

Self Cite

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“…Moreover, it is worth mentioning that, under the BLF‐ or ABLF‐based controls, the problem of output constraint should be converted into the problem of error constraint, making the initial condition of output more rigorous (see the detailed analysis in Reference 43); IBLF 26

V = \int_{0}^{ž_{1}} \frac{σ k_{c 1}^{2}}{k_{c 1}^{2} - {(σ + y_{d})}^{2}} d σ,

where k c 1 is the constraining boundary of output. Although such function tackles the output constraint directly, it is only available for the symmetric case; Mapping Function ① 43,44

\begin{align} ζ & = \frac{x_{1}}{({\underline{ℱ}}_{1} + x_{1}) ({\overset{ℱ}{true}}_{1} prefix- x_{1})} . \end{align}

Such nonlinear transformation is employed to deal with the problem of output constraint, however, only some certain class of time‐varying asymmetric constraint can be handled, namely, the lower constraining function must be strictly negative and the upper constraining function must be strictly positive; Mapping Function ② 45,46

ζ = \log \frac{{\underline{ℱ}}_{1} + x_{1}}{{\overset{true‾}{ℱ}}_{1} - x_{1}} or ζ = \frac{x_{1} + {\underline{κ}}_{1}}{{\underline{ℱ}}_{1} + x_{1}} + x

…”

Section: Resultsmentioning

confidence: 99%

Adaptive asymptotic tracking control of constrained multi‐input multi‐output nonlinear systems via event‐triggered strategy

Lei

Zhao

Chen

2020

Intl J Robust & Nonlinear

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It is nontrivial to achieve adaptive asymptotic tracking control of multi‐input multi‐output (MIMO) nonlinear systems subject to asymmetric yet time‐varying output constraint and nonparametric uncertainties. The problem will become even challenging when the event‐triggered mechanism via controller‐to‐actuator channel is considered as it may impose additional design difficulty caused by the high‐order gain matrix. In this article, we present a new event‐based control solution by using the following steps. First, by constructing a new output‐dependent mapping function, not only the limit on constraining boundaries is not required but also the cases with and without constraint can be handled directly and uniformly without changing the control structure; Second, due to the introduction of event‐triggered rule, it is difficult (even impossible) to guarantee the positive definite property of the “virtual” high‐order gain matrix; Hence by imposing a reasonable condition on the original high‐order gain matrix, such difficulty in the event‐triggered control design is solved and the widely used assumption in most existing results of MIMO systems is removed; Furthermore, unlike the corresponding uniformly bounded tracking results, by employing an integrable function coping with nonparametric uncertainties, asymptotic tracking can be achieved. A simulation example is given to illustrate the effectiveness of the developed theoretical result.

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Finite‐Time Decentralized Adaptive Fuzzy Control for Non‐Triangular Form Large‐Scale Time‐Delay Systems With Full State Constraints

Jiao,

Li,

Zhang

2024

Adaptive Control & Signal

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This paper is concerned with the problem of finite‐time decentralized adaptive fuzzy fault tolerant control for a class of non‐triangular form large‐scale time delay systems with full state constraints. By using the fuzzy logic systems and domination approach, the unknown nonlinear functions are approximated and the non‐triangular form structure is tackled, respectively. The time‐varying barrier Lyapunov function (TBLF) is used to ensure that the full state constraints are satisfied. Based on the proposed TBLF and backstepping technique, an adaptive fuzzy fault‐tolerant control protocol is presented. It can assure that the errors converge to a small neighborhood of the origin in a finite time, the signals of the whole closed‐loop systems are bounded and the full state constraints are satisfied. Simulation example is presented to further demonstrate the effectiveness of the proposed approach.

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Control of nonlinear systems under dynamic constraints: A unified barrier function-based approach

Cited by 166 publications

References 33 publications

Unified tracking control under full‐state constraints imposed irregularly

Unified tracking control under full‐state constraints imposed irregularly

Adaptive asymptotic tracking control of constrained multi‐input multi‐output nonlinear systems via event‐triggered strategy

Finite‐Time Decentralized Adaptive Fuzzy Control for Non‐Triangular Form Large‐Scale Time‐Delay Systems With Full State Constraints

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