Parameter-Dependent Polynomial Fuzzy Control of Nonlinear Inverted Pendulum System

In this paper, a fuzzy control issue of the nonlinear inverted pendulum system is discussed via Sum-Of-Square (SOS) technology. For describing the system, a Parameter-Dependent Polynomial Fuzzy (PDPF) model is constructed by combining Takagi-Sugeno (T-S) fuzzy model, polynomial representation and Linear Parameter Varying (LPV) description. Based on Parallel Distributed Compensation (PDC) method and gain-scheduled scheme, a PDPF controller is established to guarantee the stability. However, stability issue of PDPF model is often more complex and difficult than one of the traditional Takagi-Sugeno fuzzy model since the nonconvex problem caused by the coupling of variables. To avoid the nonconvex term, a parameter-dependent polynomial Lyapunov function is adopted to derive the stability criterion. Besides, the convex combination is employed to eliminate the restriction of time-varying parameters. Thus, some sufficient conditions are derived into the SOS form and solved by the corresponding toolbox efficiently. Finally, some simulation results are provided to verify the proposed design method.