Nonlinear H_∞ Attitude Control Using Modified Rodrigues Parameters

摘要

In this note, the suboptimal nonlinear H_∞ state feedback problem has been examined for rigid spacecraft attitude control. The attitude parameterization that has been adopted is the modified Rodrigues parameters (MRPs) and their shadow parameters. A linear combination of angular velocity and MRP feedback has been shown to provide a local solution to the problem, that is, one that is valid in the presence of a finite number of MRP switches. The local nature of the solution stems from the discontinuous nature of the Lyapunov function used to solve the Hamilton-Jacobi inequality. The proof of Theorem 1, the main result, has been constructive and establishes bounds on the gain parameters that solve the problem in terms of the desired L_2-gain, the control weighting parameters in the performance output, and the moments of inertia. If a Lyapunov function solution of the Hamilton-Jacobi inequality can be found that is continuous across the MRP switching boundary, then the result can be made a global solution to the problem. It is also worth noting that a linear feedback solution (although with MRP switching and hence a local solution) has been found for a problem with nonlinear dynamics.