Optimal Grey-Fuzzy Gain-Scheduler Design Using Taguchi-HGA Method

In this paper, the grey-fuzzy-gain-scheduling (GFGS) control scheme is proposed for making a nonlinear autonomous system to track a reference trajectory. The GFGS control scheme consists of two parts: the grey predictor and the fuzzy gain scheduling controller. An optimal combined method, i.e., Taguchi-hierarchical-genetic-algorithm (Taguchi-HGA), is presented in this paper to search for the optimal control parameters of both the grey predictor and the fuzzy gain scheduling controller (i.e., the sample size and grey constants of the grey predictor, the centers of the fuzzy regions, the left spread and the right spread of the membership functions, and the weighting matrices in the performance index of the linear quadratic regulator method) for guaranteeing stability and obtaining an optimal control performance. Computer simulations of a two-link robot arm example are performed to verify the effectiveness of the optimal GFGS control scheme designed by the Taguchi-HGA and to show that the optimal GFGS control scheme is superior to the existing optimal FGS (fuzzy-gain-scheduling) control scheme.