Robust Stabilization Control for High-order Sub-fully Actuated Systems

Motivated by a high-order fully actuated (HOFA) system approach, this paper proposes a robust stabilization control method for a class of high-order sub-fully actuated systems (SFASs) to stabilize the system while weakening the influence of unknown nonlinear uncertainties. In comparison to most existing methods, this paper investigates the case of SFASs, allowing more sophisticated and challenging control problems to be solved due to the presence of feasibility issues. Firstly, with the assistance of concepts including the feasible set, a model for a class of uncertain high-order SFASs is proposed, representing general dynamical systems subject to unknown nonlinear uncertainties. Then, the robust stabilization control law can be directly constructed by means of the sub-full-actuation feature, which ensures that the states eventually converge asymptotically to the origin and provides a considerable amount of design degrees of freedom to allow for possible additional requirements in the application. By limiting the initial values to a restricted region, the proposed method solves the feasibility problem, which is the key to the control of SFASs, and assures that the control law always makes sense. The permanent existence of the initial values satisfying the constraint ensures that the robust stabilization control problem of the SFASs is always solvable. Finally, the power of the introduced method is illustrated by the satellite attitude control problem.