Fuzzy logic alternative membership function shape analysis with application to vehicular steering control in extreme situations

Imprecision has been a major concern to engineers for many years. One way to deal with the type of imprecision where the classes have no sharp transition from membership to non-membership is through fuzzy logic. While much research and work has been accomplished in the area of fuzzy logic control using triangular-shaped and trapezoidal-shaped membership functions, relatively little effort has been placed on the membership function's shape itself and its impact on overall system response, performance and stability. Thus, the four alternative membership function shapes of trapezoidal, Gaussian, sigmoidal and cubic spline will be compared to the triangular standard by attempting to mimic first-order, second-order, third-order, piecewise-linear and sinusoidal response functions. Zero-order Sugeno inference will be utilized in these rulebased, fuzzy systems. After identifying the "best" membership function, using defined criteria, its application to a three degree-of-freedom vehicular model will provide data to determine if system performance can be improved through the use of the alternative membership function shape alone.