Hybrid rule interval variation (HRIV) method for stabilizing a class of nonlinear systems

HRIV (Hybrid Rule Interval Variation) method is presented, as a means of stabilizing a class of fuzzy control-based nonlinear systems. The HRIV method consists of two modes: I-mode (Minimum Approximation Error-based control) and R-mode (Rule Interval Variation-based control). In I-mode, sliding mode control is used to compensate for the minimum approximation error caused by heuristic characteristics of fuzzy logic control. In R-mode, RIV (Rule Interval Variation) method reduces the interval lengths of rules as the states converge to an equilibrium point. The HRIV method considers the analytic upper bound of the minimum approximation error and reduces its effect in the control input, which is considered to be advantageous compared with the previous results. To show effectiveness of the proposed method, a simulation experiment is conducted to stabilize a simple nonlinear system and a modified inverted pendulum system.