Nonlinear Output-Feedback H-Infinity Control for Spacecraft Attitude Control

In this paper, a novel computational scheme is proposed in order to solve the output-feedback H-infinity control problem for a class of nonlinear systems with polynomial vector field. By converting the Hamilton-Jacobi inequalities from rational expressions to equivalent polynomial expressions, the non-convex nature and the associated numerical difficulty are overcome. Using quadratic Lyapunov functions over an augmented state vector both the state-feedback and output-feedback problems are reformulated as semi-definite optimization problems, while locally tractable solutions can be obtained through sum of squares (SOS) programming. A numerical example shows that the proposed computational scheme results in a better disturbance attenuation closed-loop system, as compared to standard methods using classical quadratic Lyapunov functions. The novel methodology is applied in order to develop a robust spacecraft attitude regulator.