2003•Unpublished venueOpen access

Geometric local controllability: second-order conditions

R.M. Hirschorn, Andrew D. Lewis

Abstract

The notion of a control-affine system is abstracted to its geometric essence: an affine subbundle. The notions of control systems and controllability are presented, and general second-order conditions for local controllability are given. The conditions are notable in that their hypotheses involve only the affine subbundle, and objects directly related to it. In this way the conditions we give are guaranteed to be independent of feedback transformations.

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Key concepts: Controllability, Affine transformation, Network controllability, Mathematics, Order (exchange), Pure mathematics, Computer science, Control (management)