Passive fuzzy control for uncertain nonlinear stochastic inverted pendulum robot system

This paper presents a passive fuzzy controller design method for stabilizing the uncertain nonlinear stochastic inverted pendulum robot system. Through Takagi-Sugeno (T-S) fuzzy modeling approach, the complex nonlinear properties can be described by combining several linear sub-systems and determined membership functions. The Ito stochastic differential equation is employed to represent dynamics of systems in this paper. Applying the modeling approach, the T-S fuzzy model with multiplicative noise can be built for describing the nonlinear stochastic system. Besides, the uncertainties of the controlled system are considered in this paper for dealing with molding errors and varying parameters. Hence, the robust control problem is also discussed and investigated in this paper. Finally, the numerical simulations are proposed to show the effectiveness of the present design approach.