Nonlinear guaranteed cost attitude control via dynamic gain design

This paper investigates the guaranteed cost attitude control problem of a rigid-body subject to parameter uncertainty problem. The traditional LQR and guaranteed cost control (GCC) methods rest on linear systems and then entail model linearization in the application of attitude control by assuming small-angle rotations, since rigid-body attitude systems are highly nonlinear. In contrast, the proposed method effectively accounts for the nonlinearities inherent in the attitude dynamics of the rigid-body and ensures the attitude system with asymptotic stability and a guaranteed cost index. A linear state-feedback controller of the classical proportional/derivative (PD) structure is provided, which is off-line designed by some linear matrix inequality (LMI) conditions. Moreover, by virtue of the dynamic gain technology, the conditions are of simple structure, which thereby are easy to solve and eligible to turn into some optimization problems for optimizing the cost index and/or controller gains. The optimization problems are tractable to handle computationally and thus the optimal solution can be ensured. The developed theoretical results are illustrated by simulations.