Fuzzy Optimal Controller Design of Spatial Single Inverted Pendulum

The tensor product (TP) model transformation has not been applied to the spatial inverted pendulum systems due to the infeasible solution of the increasing number of LMIs. In this paper, we utilized the expansion of the Taylor series to transform the spatial inverted pendulum system into a quasi- LPV polynomial system with disturbances. A supervisory controller is designed for the spatial inverted pendulum system to effectively suppress disturbances. Finally, simulations are carried out with different tensor's sampling methods, such as local extremum optimization strategies and the hammersley sampling method.