Robust nonlinear H_∞ output-feedback for spacecraft attitude control

We propose a computational scheme for solving the robust output-feedback H_∞ control problem, for a class of nonlinear systems with polynomial vector field. By converting the resulting Hamilton-Jacobi inequalities from rational forms to their equivalent polynomial forms, we overcome the non-convex nature and numerical difficulty. Using quadratic Lyapunov functions, both the robust state-feedback and robust output-feedback problems are reformulated as semi-definite optimization conditions, while locally tractable solutions can be obtained through sum of squares (SOS) programming. The methodology is implemented on a spacecraft attitude control problem, where presence of unmodelled dynamics are matched and unstructured.