Design of an adaptive fuzzy model based controller for chaotic dynamics in Lorenz systems with uncertainty

Authors:
Chang-Woo Park;Chang-Hoon Lee;Mignon Park
Affiliations:
ICS Laboratory, Department of Electrical and Electronic Engineering, Yonsei University, 134 Shinchon-dong, Seodaemun-ku, Seoul, Republic of Korea;ICS Laboratory, Department of Electrical and Electronic Engineering, Yonsei University, 134 Shinchon-dong, Seodaemun-ku, Seoul, Republic of Korea;ICS Laboratory, Department of Electrical and Electronic Engineering, Yonsei University, 134 Shinchon-dong, Seodaemun-ku, Seoul, Republic of Korea
Venue:
Information Sciences—Informatics and Computer Science: An International Journal
Year:
2002

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Abstract

This paper presents the control methodology for uncertain chaotic dynamics of Lorenz systems. An adaptive fuzzy control (AFC) scheme based on well-known Takagi-Sugeno (T-S) fuzzy models for the MIMO plants is constructed. The developed control law and adaptive law guarantee the boundedness of all signals in the closed-loop system. In addition, the chaotic state tracks the state of the stable reference model (SRM) asymptotically with time for any bounded reference input signal. The proposed control is applied to control of an uncertain Lorenz system such as stabilization, synchronization and chaotic model following control (CMFC).