Journal of Dynamical and Control Systems

, Volume 13, Issue 1, pp 69–93 | Cite as

Dynamic Coverage Optimal Control for Multiple Spacecraft Interferometric Imaging

  • Islam I. HusseinEmail author
  • Anthony M. Bloch


In this paper, we study and generalize a class of optimal control problems known in the literature as τ-elastic variational optimal control problems. In the τ-elastic optimal control, we want to minimize a cost function over trajectories that evolve on a Riemannian manifold and satisfy a second-order differential equation together with some smoothness and motion constraints. The cost function is a weighted sum of the squared norm of the acceleration and the squared norm of the velocity. Here, we generalize the τ-elastic variational problem to the dynamic coverage optimal control problem, which is a class of optimal control problems motivated by multiple spacecraft formation flying for imaging applications. The main novelty of this paper is an interesting connection between multiple spacecraft formation flying and the τ-elastic and coverage optimal control problems.

2000 Mathematics Subject Classification

34H05 49J40 49K15 93C15 

Key words and phrases

Optimal control geometric mechanics τ-elastic variational problem dynamic coverage optimal control multi-spacecraft imaging 


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Copyright information

© Springer Science+Business Media, LLC 2006

Authors and Affiliations

  1. 1.University of MichiganAnn ArborUSA

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