L1-Induced Static Output Feedback Controller Design and Stability Analysis for Positive Polynomial Fuzzy Systems

Aiwen Meng; Hak-Keung Lam; Liang Hu; Fucai Liu

doi:10.1007/978-3-030-29933-0_4

L₁-Induced Static Output Feedback Controller Design and Stability Analysis for Positive Polynomial Fuzzy Systems

Aiwen Meng^*, Hak-Keung Lam, Liang Hu, Fucai Liu

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference paper › peer-review

2 Citations (Scopus)

156 Downloads (Pure)

Abstract

The aim of this paper is to study the control synthesis and stability and positivity analysis under L₁-induced performance for positive systems based on a polynomial fuzzy model. In this paper, not only the stability and positivity analysis are studied but also the L₁-induced performance is ensured by designing a static output feedback polynomial fuzzy controller for the positive polynomial fuzzy (PPF) system. In order to improve the flexibility of controller implementation, imperfectly matched premise concept under membership-function-dependent analysis technique is introduced. In addition, although the static output feedback control strategy is more popular when the system states are not completely measurable, a tricky problem that non-convex terms exist in stability and positivity conditions will follow. The nonsingular transformation technique which can transform the non-convex terms into convex ones successfully plays an important role to solve this puzzle. Based on Lyapunov stability theory, the convex positivity and stability conditions in terms of sum of squares (SOS) are obtained, which can guarantee the closed-loop systems to be positive and asymptotically stable under the L₁-induced performance. Finally, in order to test the effectiveness of the derived theory, we show an example in the simulation section.

Original language	English
Title of host publication	Advances in Computational Intelligence Systems
Subtitle of host publication	UKCI 2019. Contributions Presented at the 19th UK Workshop on Computational Intelligence, September 4-6, 2019, Portsmouth, UK
Editors	Zhaojie Ju, Longzhi Yang, Chenguang Yang, Dalin Zhou, Alexander Gegov
Publisher	Springer, Cham
Pages	41-52
Number of pages	12
Volume	1043
ISBN (Electronic)	978-3-030-29933-0
ISBN (Print)	978-3-030-29932-3
DOIs	https://doi.org/10.1007/978-3-030-29933-0_4
Publication status	Published - 2020
Event	19th Annual UK Workshop on Computational Intelligence, UKCI 2019 - Portsmouth, United Kingdom Duration: 4 Sept 2019 → 6 Sept 2019

Publication series

Name	Advances in Intelligent Systems and Computing
Volume	1043
ISSN (Print)	2194-5357
ISSN (Electronic)	2194-5365

Conference

Conference	19th Annual UK Workshop on Computational Intelligence, UKCI 2019
Country/Territory	United Kingdom
City	Portsmouth
Period	4/09/2019 → 6/09/2019

Keywords

L-induced performance
Positive polynomial fuzzy-model-based (PPFMB) control systems
Stability analysis
Static output feedback control
Sum of squares (SOS)

Access to Document

10.1007/978-3-030-29933-0_4

L1-Induced Static Output Feedback Controller Design and Stability Analysis for Positive Polynomial Fuzzy SystemsAccepted author manuscript, 644 KB

Cite this

Meng, A., Lam, H.-K., Hu, L., & Liu, F. (2020). L₁-Induced Static Output Feedback Controller Design and Stability Analysis for Positive Polynomial Fuzzy Systems. In Z. Ju, L. Yang, C. Yang, D. Zhou, & A. Gegov (Eds.), Advances in Computational Intelligence Systems: UKCI 2019. Contributions Presented at the 19th UK Workshop on Computational Intelligence, September 4-6, 2019, Portsmouth, UK (Vol. 1043, pp. 41-52). (Advances in Intelligent Systems and Computing; Vol. 1043). Springer, Cham. https://doi.org/10.1007/978-3-030-29933-0_4

Meng, Aiwen ; Lam, Hak-Keung ; Hu, Liang et al. / L₁-Induced Static Output Feedback Controller Design and Stability Analysis for Positive Polynomial Fuzzy Systems. Advances in Computational Intelligence Systems: UKCI 2019. Contributions Presented at the 19th UK Workshop on Computational Intelligence, September 4-6, 2019, Portsmouth, UK. editor / Zhaojie Ju ; Longzhi Yang ; Chenguang Yang ; Dalin Zhou ; Alexander Gegov. Vol. 1043 Springer, Cham, 2020. pp. 41-52 (Advances in Intelligent Systems and Computing).

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title = "L1-Induced Static Output Feedback Controller Design and Stability Analysis for Positive Polynomial Fuzzy Systems",

abstract = "The aim of this paper is to study the control synthesis and stability and positivity analysis under L1-induced performance for positive systems based on a polynomial fuzzy model. In this paper, not only the stability and positivity analysis are studied but also the L1-induced performance is ensured by designing a static output feedback polynomial fuzzy controller for the positive polynomial fuzzy (PPF) system. In order to improve the flexibility of controller implementation, imperfectly matched premise concept under membership-function-dependent analysis technique is introduced. In addition, although the static output feedback control strategy is more popular when the system states are not completely measurable, a tricky problem that non-convex terms exist in stability and positivity conditions will follow. The nonsingular transformation technique which can transform the non-convex terms into convex ones successfully plays an important role to solve this puzzle. Based on Lyapunov stability theory, the convex positivity and stability conditions in terms of sum of squares (SOS) are obtained, which can guarantee the closed-loop systems to be positive and asymptotically stable under the L1-induced performance. Finally, in order to test the effectiveness of the derived theory, we show an example in the simulation section.",

keywords = "L-induced performance, Positive polynomial fuzzy-model-based (PPFMB) control systems, Stability analysis, Static output feedback control, Sum of squares (SOS)",

author = "Aiwen Meng and Hak-Keung Lam and Liang Hu and Fucai Liu",

year = "2020",

doi = "10.1007/978-3-030-29933-0_4",

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editor = "Zhaojie Ju and Longzhi Yang and Chenguang Yang and Dalin Zhou and Alexander Gegov",

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Meng, A, Lam, H-K, Hu, L & Liu, F 2020, L₁-Induced Static Output Feedback Controller Design and Stability Analysis for Positive Polynomial Fuzzy Systems. in Z Ju, L Yang, C Yang, D Zhou & A Gegov (eds), Advances in Computational Intelligence Systems: UKCI 2019. Contributions Presented at the 19th UK Workshop on Computational Intelligence, September 4-6, 2019, Portsmouth, UK. vol. 1043, Advances in Intelligent Systems and Computing, vol. 1043, Springer, Cham, pp. 41-52, 19th Annual UK Workshop on Computational Intelligence, UKCI 2019, Portsmouth, United Kingdom, 4/09/2019. https://doi.org/10.1007/978-3-030-29933-0_4

L₁-Induced Static Output Feedback Controller Design and Stability Analysis for Positive Polynomial Fuzzy Systems. / Meng, Aiwen; Lam, Hak-Keung; Hu, Liang et al.
Advances in Computational Intelligence Systems: UKCI 2019. Contributions Presented at the 19th UK Workshop on Computational Intelligence, September 4-6, 2019, Portsmouth, UK. ed. / Zhaojie Ju; Longzhi Yang; Chenguang Yang; Dalin Zhou; Alexander Gegov. Vol. 1043 Springer, Cham, 2020. p. 41-52 (Advances in Intelligent Systems and Computing; Vol. 1043).

Research output: Chapter in Book/Report/Conference proceeding › Conference paper › peer-review

TY - CHAP

T1 - L1-Induced Static Output Feedback Controller Design and Stability Analysis for Positive Polynomial Fuzzy Systems

AU - Meng, Aiwen

AU - Lam, Hak-Keung

AU - Hu, Liang

AU - Liu, Fucai

PY - 2020

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N2 - The aim of this paper is to study the control synthesis and stability and positivity analysis under L1-induced performance for positive systems based on a polynomial fuzzy model. In this paper, not only the stability and positivity analysis are studied but also the L1-induced performance is ensured by designing a static output feedback polynomial fuzzy controller for the positive polynomial fuzzy (PPF) system. In order to improve the flexibility of controller implementation, imperfectly matched premise concept under membership-function-dependent analysis technique is introduced. In addition, although the static output feedback control strategy is more popular when the system states are not completely measurable, a tricky problem that non-convex terms exist in stability and positivity conditions will follow. The nonsingular transformation technique which can transform the non-convex terms into convex ones successfully plays an important role to solve this puzzle. Based on Lyapunov stability theory, the convex positivity and stability conditions in terms of sum of squares (SOS) are obtained, which can guarantee the closed-loop systems to be positive and asymptotically stable under the L1-induced performance. Finally, in order to test the effectiveness of the derived theory, we show an example in the simulation section.

AB - The aim of this paper is to study the control synthesis and stability and positivity analysis under L1-induced performance for positive systems based on a polynomial fuzzy model. In this paper, not only the stability and positivity analysis are studied but also the L1-induced performance is ensured by designing a static output feedback polynomial fuzzy controller for the positive polynomial fuzzy (PPF) system. In order to improve the flexibility of controller implementation, imperfectly matched premise concept under membership-function-dependent analysis technique is introduced. In addition, although the static output feedback control strategy is more popular when the system states are not completely measurable, a tricky problem that non-convex terms exist in stability and positivity conditions will follow. The nonsingular transformation technique which can transform the non-convex terms into convex ones successfully plays an important role to solve this puzzle. Based on Lyapunov stability theory, the convex positivity and stability conditions in terms of sum of squares (SOS) are obtained, which can guarantee the closed-loop systems to be positive and asymptotically stable under the L1-induced performance. Finally, in order to test the effectiveness of the derived theory, we show an example in the simulation section.

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Meng A, Lam HK, Hu L, Liu F. L₁-Induced Static Output Feedback Controller Design and Stability Analysis for Positive Polynomial Fuzzy Systems. In Ju Z, Yang L, Yang C, Zhou D, Gegov A, editors, Advances in Computational Intelligence Systems: UKCI 2019. Contributions Presented at the 19th UK Workshop on Computational Intelligence, September 4-6, 2019, Portsmouth, UK. Vol. 1043. Springer, Cham. 2020. p. 41-52. (Advances in Intelligent Systems and Computing). Epub 2019 Aug 30. doi: 10.1007/978-3-030-29933-0_4