Abstract
Consider an n — dimensional control system modelled by the differential equations
where f is smooth and an admissible control u is a piecewise continuous function taking values in a given set U having nonempty interior in Rm . Denote by a(t,q) the set of all points attainable at time t by solutions of (1) corresponding to admissible controls and initiating from q at time 0 . Let u* be a given control which generates a reference trajectory φ with φ(0) = p . The system (1) is locally controllable along φ at p if for all ε > 0 ,φ(ε)is an interior point of a(ε,p) . Loosely speaking, this implies the ability to control the system to a full neighborhood of the reference trajectory over an arbitrarily small interval of time.
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This research was supported by the National Science Foundation under grant GP27957
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© 1973 D. Reidel Publishing Company, Dordrecht
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Hermes, H. (1973). On Necessary and Sufficient Conditions for Local Controllability Along a Reference Trajectory. In: Mayne, D.Q., Brockett, R.W. (eds) Geometric Methods in System Theory. NATO Advanced Study Institutes Series, vol 3. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-2675-8_7
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DOI: https://doi.org/10.1007/978-94-010-2675-8_7
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