Polynomial Fuzzy Control of an Underactuated Robot Using Sum of Squares

This paper proposed the design of an underactuated robot controller based on polynomial fuzzy systems. First, we obtain the nonlinear state equations by the properties of the underactuated robot systems. Second, the polynomial fuzzy model can be constructed by the nonlinear state equations. We apply the strategy of parallel distributed compensation to design the nonlinear controller. To guarantee the stability of the underactuated robot system, the constraint conditions are derived using the polynomial Lyapunov function. Furthermore, the stability conditions are represented in terms of sum of squares of the polynomial fuzzy model. In order to improve the performance of control system, we use the SOSTOOL to design the polynomial fuzzy controller.