Guaranteed Identification of Viscous Friction for a Nonlinear Inverted Pendulum through Interval Analysis and Set Inversion

This paper focuses on the guaranteed identification of viscous friction parameters for a nonlinear inverted pendulum. The method is based on the interval analysis (IA) and set-inversion tools to determine the set of all the feasible friction parameters from a prior domain of interest, i.e. initial interval vector or box, that are consistent with all the experimental and theoretical datasets including their uncertainties. The capabilities of our proposed guaranteed identification are compared with the more commonly used approach based on the least square method identification (LSMI), which is used especially to adjust the inertial and geometric parameters of our experimental plant. Both of them have been investigated through several experiments on a real inverted pendulum and simulations with uncertain ODEs via the DynIbex library.