On the stability and control of continuous-time TSK fuzzy systems.

This paper introduces a new stability test and control design methodology for type-1 and type-2 continuous-time (CT) Takagi-Sugeno-Kang systems. Unlike methods based on a common Lyapunov function, our stability results apply for systems with unstable consequents, and our controllers can be designed for systems with unstabilizable consequents. The stability results are derived using the comparison principle with a discontinuous function and the upper right-hand derivative. The control results include CT fuzzy proportional controllers and fuzzy proportional-integral controllers that can be obtained by solving linear matrix inequalities. We provide several examples to demonstrate our stability testing and controller design and compare our results to available methods in the literature. Our results compare favorably with results available in the literature and provide stability tests and controllers where earlier approaches fail.

TSK fuzzy function approximators: design and accuracy analysis.

Fuzzy systems are excellent approximators of known functions or for the dynamic response of a physical system. We propose a new approach to approximate any known function by a Takagi-Sugeno-Kang fuzzy system with a guaranteed upper bound on the approximation error. The new approach is also used to approximately represent the behavior of a dynamic system from its input-output pairs using experimental data with known error bounds. We provide sufficient conditions for this class of fuzzy systems to be universal approximators with specified error bounds. The new conditions require a smaller number of membership functions than all previously published conditions. We illustrate the new results and compare them to published error bounds through numerical examples.

Electro-tactile preference identification using fuzzy logic.

Electro-tactile based rehabilitation systems must be capable of self-tuning to suit the tactile preference of different users. However, tactile preference is difficult to assess in practice. We propose a Takagi-Sugeno-Kang (TSK) fuzzy logic modeling and control approach for the on-line assessment of tactile preference. The method relies on real-time measurements of voltage and power absorbed by the fingertip. Our results show that the fuzzy logic approach successfully models user tactile preference. We are currently developing an electro-tactile based Braille display (E-Braille) for assisting the Blind and Visually Impaired (BVI) that exploits our fuzzy model.