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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.