Adaptive Fuzzy Sliding Mode Control of Under-actuated Nonlinear Systems

A new extension of the conventional adaptive fuzzy sliding mode control (AFSMC) scheme, for the case of under-actuated and uncertain affine multiple-input multiple-output (MIMO) systems, is presented. In particular, the assumption for non-zero diagonal entries of the input gain matrix of the plant is relaxed. In other words, the control effect of one actuator can propagate from a subgroup of canonical state equations to the rest of equations in an indirect sense. The asymptotic stability of the proposed AFSM control method is proved using a Lyapunov-based methodology. The effectiveness of the proposed method for the case of under-actuated systems is investigated in the presence of plant uncertainties and disturbances, through simulation studies.