Abstract

Control methods that guarantee stability in the presence of uncertainties are mandatory in space applications. Further, distributed control approaches are beneficial in terms of scalability and to achieve common goals, especially in multi-agent setups like formation control. This paper presents a combination of robust H ∞ control and distributed control using the consensus approach by deriving a distributed consensus-based generalized plant description that can be used in H ∞ synthesis. Special focus was set towards space applications, namely satellite formation flying. The presented results show the applicability of the developed distributed robust control method to a simple, though realistic space scenario, namely a spaceborne distributed telescope. By using this approach, an arbitrary number of satellites/agents can be controlled towards an arbitrary formation geometry. Because of the combination with robust H ∞ control, the presented method satisfies the high stability and robustness demands as found e.g., in space applications.

Highlights

  • The satellite formation flying (SFF) is an evolving research area leading to new applications in space.Various attempts have been undertaken to achieve distributed mission architectures reducing costs, development time, increasing failure safety and expanding possibilities for further mission concepts.Contributing to the improvement of telecommunications and Earth and deep space observation missions, the distribution of satellite systems flying in proximity using 3D formations has yet to prove itself valuable in real world applications

  • This paper presents a new approach of combining the fields of distributed control and robust control

  • The distributed consensus approach is related to classical H∞ robust control

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Summary

Introduction

The satellite formation flying (SFF) is an evolving research area leading to new applications in space. There have been different SFF missions demonstrating accurate stationkeeping of satellites like the Magnetospheric Multiscale Mission (MMS) mission from NASA [1] or autonomous acquisition and maintenance of a force free formation within the CanX-4 and 5 mission. Robust control methods can guarantee stability within a specific range of uncertainties, which is of special interest for space applications because of high safety demands due to the fact that single errors can lead to the failure of a whole mission (cf [11,12]).

Materials and Methods
Coordinate System
Linear Model of Satellite Dynamics
Graph Theory Fundamentals
Directed Graph
Reachability
Neighbor
Adjacency Matrix
Degree Matrix
Laplacian Matrix
Distributed Control
Connection to Graph Theory
General State-Space Representation of a Distributed LTI System
Decentralized and Distributed Control
Distributed Consensus Approach
Reference Tracking
Fixing Coordinate Origin to an Agent
Robust Control
Distributed Robust Control
Obtaining Generalized Plant for Single Agent
Computation of the CLTF
Obtaining the Generalized Plant for the Overall System
Wn a12
Results
Scenario Definition
Network Topology
Dynamically Decoupled State Definition
Distributed Robust Consensus Approach
Simulation Results
Discussion
Full Text
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