Design and Stability Analysis of Fuzzy Model-based Predictive Control – A Case Study

Blažič, Sašo; Škrjanc, Igor

doi:10.1007/s10846-007-9147-8

Cited by 55 publications

(27 citation statements)

References 23 publications

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“…For future development there are two perspective areas. First, to "fuzzify" the traffic simulation system, which would be able in certain measure to absorb some unexpected events and the system could become more robust with consecutive stability analysis (Blažič and Škrjanc, 2007). Another possibility of "fuzzification" is to apply an information retrieval system that attempts to find exact answers to user's questions expressed in linguistic form (Ortiz-Arroyo and Christensen, 2009), e.g.…”

Section: Experimental Results and Conclusionmentioning

confidence: 99%

Adaptation of fuzzy cognitive maps by migration algorithms

Vaščák

2012

Kybernetes

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Purpose -Conventional rule-based systems are insufficient for description of complex dynamic systems requiring nontrivial decision procedures. Fuzzy cognitive maps seem to be convenient to overcome these limitations. However, they lack ability of self-learning and therefore some adaptation approaches are needed. The purpose of this paper is both to show the use of fuzzy cognitive maps for such systems and to present migration algorithms as convenient adaptation means. Design/methodology/approach -Some problems of a complex dynamic system description by knowledge-based means are discussed. Fuzzy cognitive maps are presented as a possible way to solve these problems followed by description of migration algorithms as their adaptation means. Their use is clarified on an example of the so-called parking problem based on path planning using a graph search algorithm and a traffic simulation system. Findings -After series of simulations the reality of the proposed system and selected methods with their modifications was proved. It has shown the robustness of the presented solution under circumstances of uncertainty, too.Research limitations/implications -The paper points to stability investigation of the proposed approach introducing uncertainties into the traffic simulation system to take into account, e.g. unexpected events. Further, a possibility of developing a linguistic information retrieval system is mentioned. Practical implications -The proposed approach can find various implementations not only in planning tasks but also in robotic navigation and multi-agent applications in general. In addition, it suggests possibilities of knowledge-based systems, directly using human-like approaches, to areas of decision making under uncertainties and contradictories. Originality/value -An new modification of migration algorithms for adaptation of parameters for fuzzy cognitive maps is introduced and compared to other known self-learning methods. Further, the concept of a traffic simulation system for path planning is presented.

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Section: Experimental Results and Conclusionmentioning

confidence: 99%

Adaptation of fuzzy cognitive maps by migration algorithms

Vaščák

2012

Kybernetes

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“…Further research will be concentrated on new applications of the proposed algorithm to several classes of processes [4,5,7,8,9,17,20]. The complex applications require the computer-aided design of the Takagi-Sugeno fuzzy logic controllers employing the stability analysis algorithm proposed in this paper to strive for increased generality.…”

Section: Discussionmentioning

confidence: 99%

Fuzzy Logic Control System Stability Analysis Based on Lyapunov’s Direct Method

Precup

Tomescu

Preitl

2009

INT J COMPUT COMMUN

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A stability analysis method for nonlinear processes controlled by TakagiSugeno (T-S) fuzzy logic controllers (FLCs) is proposed. The stability analysis of these fuzzy logic control systems is done in terms of Lyapunov's direct method. The stability theorem presented here ensures sufficient conditions for the stability of the fuzzy logic control systems. The theorem enables the formulation of a new stability analysis algorithm that offers sufficient stability conditions for nonlinear processes controlled by a class of T-S FLCs. In addition, the paper includes an illustrative example that describes one application of this algorithm in the design of a stable fuzzy logic control system.

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“…Remark 4: Based on the nonsingular transformation matrix Γ, we can obtain convex stability conditions (18) and positivity conditions (20) which are linear in the decision variables h and Z j (y). Once there exist feasible h and Z j (y), λ can be obtained by (15) and the polynomial feedback gains K j (y) can be obtained by (16).…”

Section: A Basic Stability Analysis Of Static Output Feedback Ppfmb mentioning

confidence: 99%

“…In the past few decades, many researchers paid close attention to the fuzzy systems and a great deal of results have been obtained. In [18], the fuzzy-model-based predictive control was investigated and the stability analysis results were obtained. For discrete-time single-input singleoutput (SISO) systems, the work in [19] investigated the stable and convergent iterative feedback tuning of fuzzy controllers.…”

Section: Introductionmentioning

confidence: 99%

Static Output Feedback Stabilization of Positive Polynomial Fuzzy Systems

Meng

Lam

et al. 2018

IEEE Trans. Fuzzy Syst.

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Abstract-This paper deals with the static output feedback stabilization of positive polynomial fuzzy-model-based (PPFMB) control systems. The positive polynomial fuzzy model does not need to share the same premise membership functions with the static output feedback polynomial fuzzy controller. Unlike the state feedback control case, the static output feedback control usually leads to non-convex stability conditions. To circumvent the problem, an approach is employed to transform the nonconvex stability conditions into convex ones by introducing a nonsingular transformation matrix. Initially, the conditions guaranteeing the resultant closed-loop systems to be positive and asymptotically stable are obtained. Moreover, the divisional approximated membership functions which carry the local information of the membership functions are employed to facilitate the stability analysis and controller synthesis. The relaxed stability conditions in terms of sum of squares (SOS) are obtained based on Lyapunov stability theory. Finally, a simulation example is given to testify the validity of the analysis result.

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Design and Stability Analysis of Fuzzy Model-based Predictive Control – A Case Study

Cited by 55 publications

References 23 publications

Adaptation of fuzzy cognitive maps by migration algorithms

Adaptation of fuzzy cognitive maps by migration algorithms

Fuzzy Logic Control System Stability Analysis Based on Lyapunov’s Direct Method

Static Output Feedback Stabilization of Positive Polynomial Fuzzy Systems

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