Multi-Objective Robust H-infinity Control of Spacecraft Rendezvous

Based on the relative motion dynamic model illustrated by C-W equations, the problem of robust Hinfin control for a class of spacecraft rendezvous systems is investigated, which contains parametric uncertainties, external disturbances and input constraints. An Hinfin state-feedback controller is designed via a Lyapunov approach, which guarantees the closed-loop system to meet the multi-objective design requirements. The existence conditions for admissible controllers are formulated in the form of linear matrix inequalities (LMIs), and the controller design is cast into a convex optimization problem subject to LMI constraints. An illustrative example is provided to show the effectiveness of the proposed control design method

Robust variance-constrained H∞ control for stochastic systems with multiplicative noises

This is the post print version of the article. The official published version can be obtained from the link below - Copyright 2007 Elsevier Ltd.In this paper, the robust variance-constrained H∞ control problem is considered for uncertain stochastic systems with multiplicative noises. The norm-bounded parametric uncertainties enter into both the system and output matrices. The purpose of the problem is to design a state feedback controller such that, for all admissible parameter uncertainties, (1) the closed-loop system is exponentially mean-square quadratically stable; (2) the individual steady-state variance satisfies given upper bound constraints; and (3) the prescribed noise attenuation level is guaranteed in an H∞ sense with respect to the additive noise disturbances. A general framework is established to solve the addressed multiobjective problem by using a linear matrix inequality (LMI) approach, where the required stability, the H∞ characterization and variance constraints are all easily enforced. Within such a framework, two additional optimization problems are formulated: one is to optimize the H∞ performance, and the other is to minimize the weighted sum of the system state variances. A numerical example is provided to illustrate the effectiveness of the proposed design algorithm.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Nuffield Foundation of the UK under Grant NAL/00630/G, and the Alexander von Humboldt Foundation of Germany