A systematic approach to improve multiple Lyapunov function stability and stabilization conditions for fuzzy systems

In recent years, the study of systems subject to time-varying parameters has awakened the interest of many researchers. The gain scheduling control strategy guarantees a good performance for systems of this type and also is considered as the simplest to deal with problems of this nature. Moreover, the class of systems in which the state derivative signals are easier to obtain than the state signals, such as in the control for reducing vibrations in a mechanical system, has gained an important hole in control theory. Considering those ideas, we propose sufficient conditions via LMI for designing a gain scheduling controller using state derivative feedback. The D-stability methodology was used for improving the performance of the transitory response. Practical implementation in an active suspension system and comparison with other methods validates the efficiency of the proposed strategy.

show abstract

“…This lemma ensures relaxation of the set of LMIs due to the disassociation of matrices or reduction of control design of the number of LMIs [22].…”

Section: Finsler's Lemma An Lmi Formulationmentioning

confidence: 99%

Design of Gain Scheduling Control Using State Derivative Feedback

Llins

Assunção

Teixeira

et al. 2017

Mathematical Problems in Engineering

View full text Add to dashboard Cite

show abstract

“…A refinement based on slack variables can be found in [70], that gives, under some assumptions, parameter-dependent LMI problems.…”

Section: Non-quadratic Lyapunov Functionsmentioning

confidence: 99%

Fuzzy control turns 50: 10 years later

Guerra

Sala

Tanaka

2015

Fuzzy Sets and Systems

View full text Add to dashboard Cite

In 2015, we celebrate the 50th anniversary of Fuzzy Sets, ten years after the main milestones regarding its applications in fuzzy control in their 40th birthday were reviewed in FSS, see [1]. Ten years is at the same time a long period and short time thinking to the inner dynamics of research. This paper, presented for these 50 years of Fuzzy Sets is taking into account both thoughts. A first part presents a quick recap of the history of fuzzy control: from model-free design, based on human reasoning to quasi-LPV (Linear Parameter Varying) model-based control design via some milestones, and key applications. The second part shows where we arrived and what the improvements are since the milestone of the first 40 years. A last part is devoted to discussion and possible future research topics.

show abstract

“…For the source of double fuzzy summation, Pólya's theory [37,27] is exploited to offer progressively necessary and sufficient conditions which generalizes some earlier 25 works [26,10]. For the source of quadratic Lyapunov function, more general types of Lyapunov function candidates such as fuzzy Lyapunov function [29,5,24,18], piecewise linear Lyapunov function [11,12], switching Lyapunov function [32,21] and polynomial Lyapunov function [4,21] function-independent stability conditions, the membership-function-dependent approach is applied to make the stability conditions depend on membership functions such as using approximated membership functions [30,17], polynomial constraints [38], symbolic variables [39,22,23] and other techniques [3,20,16,18,7]. 35 Another task of the development of FMB control strategy is to extend it to solve control problems [40,33,42,55,43,8,15,25,54].…”

mentioning

confidence: 95%

Design of polynomial fuzzy observer–controller with membership functions using unmeasurable premise variables for nonlinear systems

Liu

Lam

Ban

et al. 2016

Information Sciences

View full text Add to dashboard Cite

In this paper, the stability of polynomial fuzzy-model-based (PFMB) observercontrol system is investigated via Lyapunov stability theory. The polynomial fuzzy observer with unmeasurable premise variables is designed to estimate the system states. Then the estimated system states are used for the state-feedback control of nonlinear systems. Although the consideration of the polynomial fuzzy model and unmeasurable premise variables enhances the applicability of the fuzzy-model-based (FMB) control strategy, it leads to non-convex stability conditions. Therefore, the refined completing square approach is proposed to derive convex stability conditions in the form of sum of squares (SOS) with less manually designed parameters. In addition, the membership functions of the polynomial observer-controller are optimized by the improved gradient descent method, which outperforms the widely applied parallel distributed compensation (PDC) approach according to a general performance index. Simulation examples are provided to verify the proposed design and optimization scheme.

show abstract

A systematic approach to improve multiple Lyapunov function stability and stabilization conditions for fuzzy systems

Cited by 274 publications

References 46 publications

Design of Gain Scheduling Control Using State Derivative Feedback

Design of Gain Scheduling Control Using State Derivative Feedback

Fuzzy control turns 50: 10 years later

Design of polynomial fuzzy observer–controller with membership functions using unmeasurable premise variables for nonlinear systems

Contact Info

Product

Resources

About