Abstract
The dynamics of acrobots, two-link underactuated system, have strong nonlinearity, so that gain scheduling (GS) control is suitable for stabilizing the system in a wide range of operation. In this paper, GS controller design problems for the attitude control are reduced to solving polynomially parameter-dependent linear matrix inequalities (PDLMIs). The polynomially PDLMIs are relaxed by matrix sum of squares (SOS) polynomials to find feasible solutions. Several reduction techniques are adopted to reduce the amount of computation for solving the SOS problems while direct formulations are too computationally expensive to solve. For two attitude modes of the acrobot, the effectiveness of GS control is shown by experiments as well as nonlinear simulations.
