Mixed H ∞ / H 2 gain-scheduled control for spacecraft rendezvous in elliptical orbits

Abstract

A mixed H_∞/H₂ gain-scheduled state-feedback control method is developed for trajectory tracking of spacecraft rendezvous in elliptical orbits. Since the tracking accuracy is vulnerable to exogenous disturbances, the mixed H_∞/H₂ control, which takes into consideration both worst-case disturbance-attenuation performance and tracking performance, is particularly attractive for trajectory tracking of spacecraft rendezvous. Owing to the fact that the dynamic model for elliptical-orbit rendezvous is time varying, the feedback gain matrix is formulated as a matrix fraction of parameter-dependent matrix. Parameter-dependent Lyapunov functions are adopted to reduce conservatism caused by fixed quadratic Lyapunov matrices, and slack matrices are introduced to avoid setting a common Lyapunov matrix for different performances. Then, the desired controller can be obtained through a convex optimization with linear matrix inequality constraints. Computer simulations show that the proposed method can (a) handle trajectory tracking of elliptical-orbit rendezvous effectively; (b) provide a balanced performance between disturbance-attenuation performance and tracking performance; and (c) yield results that are less conservative than those obtained through conventional methods.