Fuzzy Lookup Table Controller (FLTC) via Center Average De-fuzzifier (CAD) with a New Efficient Heaviside Search Algorithm (HSA) for Lookup Table Implementation

Abstract

This paper proposes an alternate interpretation of the traditional lookup table controller via the Center Average De-fuzzier (CAD) in Fuzzy Set Theory with a set of Disjoint Block Pulse Membership Functions (DBPMFs). Further, a new Heaviside Search Algorithm (HSA) is also proposed to implement the Fuzzy Lookup Table Controller (FLTC) in a more efficient way. The computation complexity of our new HSA is O (Σ R i), where R i is the number of membership functions for i th input variable in FLTC. Whereas the average computational complexity in traditional Linear Search Algorithm (LSA) is O ((П R i)/2). In comparison with LSA, the HSA also reduces the complexity of coding significantly in the same order as the comparison of computation complexities between HSA and LSA. The balancing of Inverted Pendulum System (IPS) is adopted as the benchmark to show the feasibility and efficiency of this new FLTC and HSA.