SVD-based reduction to MISO TS models

Bárányi, Péter; Yam, Yeung; Várkonyi-Kóczy, Annamária R.; Patton, Ron J.

doi:10.1109/tie.2002.807673

Cited by 39 publications

(11 citation statements)

References 37 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Theorem 1. Let the fuzzy control system consist of the TSK FLC defined in Section 2 and the nonlinear process with the state-space Equations (1), and let V : X → R, V ∈ C 1 , be a radially unbounded positive definite function such thatV k (x) ≤ 0, ∀ x ∈ X A k , k = 1, p. Let X S = {x ∈ X|V (x) = 0} and M = {0} be the largest invariant set in X S . Then all solutions will converge globally asymptotically to M as t → ∞.…”

Section: Stability Analysis Methodsmentioning

confidence: 99%

“…The inference engine is assisted by the complete rule base expressed as where u = [u 1 u 2 ] T and u k = [u k 1 u k 2 ], k = 1, 9, will be determined as follows on the basis of Theorem 1. This rule base can be extended by considering other inputs as well, and several rule interpolation techniques assisted by adequate operators in the inference engine must be applied [1,3,18,49]. …”

Section: Fuzzy Logic Controllermentioning

confidence: 99%

See 1 more Smart Citation

Stability analysis and design of a class of MIMO fuzzy control systems

Precup

Tomescu

Preitl

et al. 2013

Journal of Intelligent &Amp; Fuzzy Systems

View full text Add to dashboard Cite

This paper presents a new stability analysis method dedicated to a class of fuzzy control systems (FCSs) controlling multi input-multi output (MIMO) nonlinear processes by means of Takagi-Sugeno-Kang fuzzy logic controllers (FLCs). The stability analysis of the FCSs is carried out using LaSalle's global invariant set theorem by the separate stability analysis of each fuzzy rule in MIMO fuzzy control systems. Therefore the complexity of the stability analysis is reduced and the adding of new fuzzy rules can be conducted easily; this modification of FLC structure requires the fulfillment of only one of the conditions of the stability analysis theorem suggested in this paper. Another advantage of the stability analysis approach proposed in this paper is that the derivative of the Lyapunov function candidate must be only negative semi-definite in comparison with Lyapunov's stability theorem where it must be negative definite. The conservativeness of stability conditions is thus reduced, and this enables the convenient design of FLCs. The applicability and efficiency of the theoretical results are illustrated by numerical simulations for a representative MIMO process which deals with the level control in a three spherical tank system.

show abstract

Section: Stability Analysis Methodsmentioning

confidence: 99%

Section: Fuzzy Logic Controllermentioning

confidence: 99%

Stability analysis and design of a class of MIMO fuzzy control systems

Precup

Tomescu

Preitl

et al. 2013

Journal of Intelligent &Amp; Fuzzy Systems

View full text Add to dashboard Cite

show abstract

“…), (Sugeno, M. & Kang, G. (1988)) and (Takagi T. & Sugeno, M. (1985)) have attracted lots of attention during the last twenty years (e.g., see (Baranyi, P. (2003), Wang, H. O. (2001).…”

Section: Overview Of Identification and Estimation Of Fuzzy Systemsmentioning

confidence: 99%

Extended Kalman Filter for the Estimation and Fuzzy Optimal Control of Takagi-Sugeno Model

Jiménez¹,

Al‐Hadithi²,

Matı́a³

2011

Fuzzy Controllers, Theory and Applications

View full text Add to dashboard Cite

“…Using these correspondences one can predict future outputs caused by the not yet considered inputs. Several methods are used with this regard, e.g., learning [3], [4], decision trees [5]- [7], artificial neural networks [8], [9] fuzzy logic [10]- [12], Bayesian filtering and Boolean entity lattices [13], [14], ontologies at different levels [15] or intelligent agents [16]. All these methods represent strategies that transform the observations into a law.…”

Section: Introductionmentioning

confidence: 99%

A general formulation of abduction algorithms

Pozna

Precup

2012

2012 IEEE 3rd International Conference on Cognitive Infocommunications (CogInfoCom)

View full text Add to dashboard Cite

The paper offers a general formulation of abduction algorithms, referred to as minimum length solution algorithms, which are based on all observable states. The algorithms compute the necessary evidence to derive the correct hypothesis in minimum steps. A first version of algorithms is proposed such that to deal with situations when not all states are observable. The development of fuzzy inference systems is presented in order to apply the minimum length solution algorithms to sets of imprecise observations. I.INTRODUCTION Cognitive reasoning represents the particular case of reasoning based on incomplete information. It is accepted that reasoning means to process and infer the premise information into conclusions. Several forms of logic inference are used in this context; they include the deduction, the induction and the abduction. The deduction is characterized by setting the necessity of the consequence. Two conditions are needed in this context, the observation of the premise and the knowledge on the fact that the premise causes the consequences. The induction states a necessary relation between two observations, the premise and the consequence. This statement is supported by several observations which link together the premise and the consequences.The abduction assumes the causal relation between two events. The abduction is needed when the causes of an observation are unknown, and that is possible if a set of hypotheses is available. The quality of this assumption can be a subject to a certain strategy and the well acknowledged Occam's razor principle is suggested in this framework. A hypothesis is based on the assumption that a certain premise is related to a particular observation. Using the previous experience each hypothesis has a certain degree of truth named the plausibility. Usually, several hypotheses can be proposed for a particular observation. These hypotheses form the observation's set of possible explanations.The ignorance can be classified in terms of incompleteness, imprecision and uncertainty. The incompleteness is the subject of non monotonic logic, the imprecision is the subject of fuzzy logic, and the uncertainty is the subject of probability theory. The combination of imprecision and uncertainty becomes the subject of evidence theory [1] or of possibility theory [2].The induction process in the machine learning theory employs input-output correspondences that are known, and the query is to find the function (the law) according to this correspondences. Using these correspondences one can predict future outputs caused by the not yet

show abstract

SVD-based reduction to MISO TS models

Cited by 39 publications

References 37 publications

Stability analysis and design of a class of MIMO fuzzy control systems

Stability analysis and design of a class of MIMO fuzzy control systems

Extended Kalman Filter for the Estimation and Fuzzy Optimal Control of Takagi-Sugeno Model

A general formulation of abduction algorithms

Contact Info

Product

Resources

About