Stabilization of Interval Type-2 Polynomial-Fuzzy-Model-Based Control Systems

Xiao, Bo; Lam, Hak‐Keung; Li, Hongyi

doi:10.1109/tfuzz.2016.2554153

Cited by 98 publications

(56 citation statements)

References 34 publications

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“…Battery electric storage systems and wind power systems, which are connected to the power net by power electronic interface, are controllable. In mathematics, the frequency control method is equivalent to the tie-line bias control (TBC) method as a frequency control in electrical power systems in consideration of tie-line frequency [36][37][38][39]. For each subsystem, the block diagram is shown in Figure 2.…”

Section: Dynamic Model Of Power Gridmentioning

confidence: 99%

Frequency Regulation of Power Systems with Self-Triggered Control under the Consideration of Communication Costs

Zhu

Sun

et al. 2017

Applied Sciences

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Abstract:In control systems of power grids, conveying observations to controllers and obtaining control outputs depend greatly on communication and computation resources. Particularly for large-scale systems, the costs of computation and communication (cyber costs) should not be neglected. This paper proposes a self-triggered frequency control system for a power grid to reduce communication costs. An equation for obtaining the triggering time is derived, and an approximation method is proposed to reduce the computation cost of triggering time. In addition, the communication cost of frequency triggering is measured quantitatively and proportionally. The defined cost function considers both physical cost (electricity transmission cost) and communication cost (control signal transmission cost). The upper bound of cost is estimated. According to the estimated upper bound of cost, parameters of the controller are investigated by using the proposed optimization algorithm to guarantee the high performance of the system. Finally, the proposed self-triggered power system is simulated to verify its efficiency and effectiveness.

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Section: Dynamic Model Of Power Gridmentioning

confidence: 99%

Frequency Regulation of Power Systems with Self-Triggered Control under the Consideration of Communication Costs

Zhu

Sun

et al. 2017

Applied Sciences

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“…Since then, it has attracted great attention and many fruitful results have been presented in both theory and practice (see, e.g. [9][10][11][12][13][14][15]). One motivation for studying such a class of systems is that type-2 fuzzy sets are better in representing and capturing uncertainties [16,17], especially when the nonlinear plant inevitably suffers the parameter uncertainties while type-1 fuzzy sets do not contain uncertain information.…”

Section: Introductionmentioning

confidence: 99%

Control design for interval type‐2 polynomial fuzzy‐model‐based systems with time‐varying delay

Li¹,

Lam²,

Zhang

2017

IET Control Theory & Applications

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Citing this paper Please note that where the full-text provided on King's Research Portal is the Author Accepted Manuscript or Post-Print version this may differ from the final Published version. If citing, it is advised that you check and use the publisher's definitive version for pagination, volume/issue, and date of publication details. And where the final published version is provided on the Research Portal, if citing you are again advised to check the publisher's website for any subsequent corrections. General rightsCopyright and moral rights for the publications made accessible in the Research Portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognize and abide by the legal requirements associated with these rights.•Users may download and print one copy of any publication from the Research Portal for the purpose of private study or research.•You may not further distribute the material or use it for any profit-making activity or commercial gain •You may freely distribute the URL identifying the publication in the Research Portal Take down policy If you believe that this document breaches copyright please contact librarypure@kcl.ac.uk providing details, and we will remove access to the work immediately and investigate your claim. Abstract: In this paper, the problems of stabilization for interval type-2 polynomial fuzzy systems with time-varying delay and parameter uncertainties are investigated. The objective is to design a state-feedback interval type-2 polynomial fuzzy controller such that the closed-loop control system is asymptotically stable. The conditions for the existence of such a controller are delay dependent and membership function dependent in terms of sum-of-squares (SOS). Based on a basic lemma to deal with the delay terms, we formulate and solve the problem with more flexibility due to imperfect premise matching that the number of rules and premise membership functions are not necessary the same between the interval type-2 polynomial fuzzy model and interval type-2 polynomial fuzzy controller. Piecewise linear membership functions approximations enclosing the original lower and upper membership functions are employed to facilitate the stability analysis. A numerical example indicates the effectiveness of the derived results.

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“…Once uncertainties appear, the grades of membership will become uncertain in value leading to conservative stability conditions when uncertainty is not considered in the stability analysis. Recently, the T-S fuzzy model is extended to a more general polynomial fuzzy model [16][17][18][19]. The nonlinear plant can be represented more effectively because polynomials are allowed in the consequent part.…”

Section: Introductionmentioning

confidence: 99%

“…Yet, most of them focus on the control methodology and the stability analysis is approached by existing techniques. Furthermore, the T-S fuzzy model is the main stream on these work but the polynomial fuzzy model [19,37] is rarely considered in the literature. Although [19,37] investigated the stability analysis and tracking control of IT2 PFMB control systems, the method they used is on the basis of type-1 PFMB control system, i.e.…”

Section: Introductionmentioning

confidence: 99%

“…Furthermore, the T-S fuzzy model is the main stream on these work but the polynomial fuzzy model [19,37] is rarely considered in the literature. Although [19,37] investigated the stability analysis and tracking control of IT2 PFMB control systems, the method they used is on the basis of type-1 PFMB control system, i.e. approximating the IT2 membership functions by an embedded type-1 membership functions and considering the influences of the modeling errors between the embedded Type-1 membership functions and IT2 membership functions.…”

Section: Introductionmentioning

confidence: 99%

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Membership‐Function‐Dependent Stability Analysis of Interval Type‐2 Polynomial Fuzzy‐Model‐Base Control Systems

Song

Lam

Yang

2017

IET Control Theory & Applications

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Abstract:In this paper, the stability analysis for interval type-2 (IT2) polynomial fuzzy-model-based (PFMB) control system using the information of membership functions is investigated. In order to tackle uncertainties, IT2 membership functions are used in the IT2 polynomial fuzzy model and IT2 polynomial fuzzy controller. To improve the design flexibility and reduce the implementation costs, the IT2 polynomial fuzzy controller does not need to share the same premise membership functions nor the same number of rules with the IT2 polynomial fuzzy model. The stability of IT2 PFMB control system is investigated based on the Lyapunov stability theory and both sets of membership function independent (MFI) and membership function dependent (MFD) stability conditions are derived on the basis of the sum-of-squares (SOS) approach. To make the stability conditions membership function dependent, the boundary information of IT2 membership functions is used in the stability analysis. To extract richer information of IT2 membership functions, the operating domain is partitioned into sub-domains. In each sub-domain, the boundary information of IT2 membership functions and those of the upper and lower membership function are obtained. Furthermore, to further relax the conservativeness, a switching polynomial fuzzy controller, together with the informations obtained in each sub-domain, is employed in investigating the stability analysis. Numerical Examples and simulation results are given to demonstrate the validity of MFD and MFD switching methods.

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Stabilization of Interval Type-2 Polynomial-Fuzzy-Model-Based Control Systems

Cited by 98 publications

References 34 publications

Frequency Regulation of Power Systems with Self-Triggered Control under the Consideration of Communication Costs

Frequency Regulation of Power Systems with Self-Triggered Control under the Consideration of Communication Costs

Control design for interval type‐2 polynomial fuzzy‐model‐based systems with time‐varying delay

Membership‐Function‐Dependent Stability Analysis of Interval Type‐2 Polynomial Fuzzy‐Model‐Base Control Systems

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