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Controlling Chaotic Systems Using Aggregated Linear Quadratic Regulator

Wang D., Ha P.

Przegląd Elektrotechniczny

2012

R. 88, nr 7b

336--340

A systematic design method for controlling chaotic systems is presented in this paper. The aggregated multiple local models are adopted to express chaotic systems. The Linear Quadratic Regulator (LQR) theory is proposed to design state feedback control system for each local model. Multi-model control strategy has come into being by combining of T-S fuzzy model and LQR. The global stability of closed loop control system can guarantee and it is illustrated with several chaotic systems as examples.

Zaproponowano projekt sterowania systemem chaotycznym. Zaadaptowano wypadkowe (aggregated) połączenie wielu lokalnych modeli do opisu system chaotycznego. Każdy lokalny model jest sterowany z wykorzystaniem teorii LQR – linear quadratic regulator.

On choosing the fuzziness parameter for identifying TS models with multidimensional membership functions

Kroll A.

Journal of Artificial Intelligence and Soft Computing Research

2011

Vol. 1, No. 4

283--300

Fuzzy clustering is a well-established method for identifying the structure/fuzzy partitioning of Takagi-Sugeno (TS) fuzzy models. The clustering algorithms require choosing the fuzziness parameter m. Prior work in the area of pattern recognition shows, that a suitable choice of m is application- dependent. Yet, the default of m=2 is commonly chosen. This paper examines the suitable choice of m for identifying TS models. The focus is on models that use the classifiers resulting from fuzzy clustering as multi-dimensional membership functions or their projection and approximation. At first, the differentiability and grouping properties of the fuzzy classifiers are analyzed to make a general recommendation of choosing m(1;3). Besides, the effect of the cluster number c on the classification fuzziness is examined. Finally, requirements that are specific to TS modeling are introduced, which narrow down the suitable range for m. Building on algorithm analysis and four case studies (function approximation, a vehicle engine and an axial compressor application for nonlinear regression), it is demonstrated that choosing m2(1;1.3) for local and m2(1;1.5) for global estimation will typically provide for good results.