Adaptive T-S fuzzy-neural modeling and control for general MIMO unknown nonaffine nonlinear systems using projection update laws.

*(English)*Zbl 1191.93073Summary: This paper describes a novel design of an on-line Takagi-Sugeno (T-S) fuzzy-neural controller for a class of general Multiple Input Multiple Output (MIMO) systems with unknown nonlinear functions and external disturbances. Instead of modeling the unknown systems directly, the T-S fuzzy-neural model approximates a virtual linearized system of a real system with modeling errors and external disturbances. Compared with previous approaches, the main contribution of this paper is an investigation of more general MIMO unknown systems using on-line adaptive T-S fuzzy-neural controllers. In this paper, we also use projection update laws, which generalize the projection algorithm, to tune the adjustable parameters. This prevents parameter drift and ensures that the parameter matrix is bounded away from singularity. We prove that the closed-loop system controlled by the proposed controller is robust stable and the effect of all the modeling errors and external disturbances on the tracking error can be attenuated. Finally, two examples covering four cases are simulated in order to confirm the effectiveness and applicability of the proposed approach in this paper.

##### MSC:

93C40 | Adaptive control/observation systems |

93C42 | Fuzzy control/observation systems |

93C10 | Nonlinear systems in control theory |

93D09 | Robust stability |

##### Keywords:

T-S fuzzy-neural model; on-line modeling; nonaffine nonlinear systems; projection update law
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\textit{W.-Y. Wang} et al., Automatica 46, No. 5, 852--863 (2010; Zbl 1191.93073)

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