Stabilization of the quadruple inverted pendulum by variable universe adaptive fuzzy controller based on variable gain H ∞ regulator

In this paper, the variable universe adaptive fuzzy controller based on variable gain H_?? regulator (VGH_??R) is designed to stabilize a quadruple inverted pendulum. The VGH_??R is a novel robust gain-scheduling approach. By utilizing VGH_??R technique, a more precise real-time feedback gain matrix, which is changing with states, is obtained. Via the variable gain matrix 10 state variables of quadruple inverted pendulum are transformed into a kind of synthesis error (E) and synthesis rate of change of error (EC) at sampling time. Therefore, the dimension of the multivariable system is reduced and the variable universe adaptive fuzzy controller is built. Experiments illustrate the effectiveness of the proposed control scheme.