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Controllability revisited. (English) Zbl 0777.93005

Mathematical system theory, Festschr. Honor R. E. Kalman 60th Birthd., 463-474 (1991).
Summary: [For the entire collection see Zbl 0742.00029.]
Kalman’s controllability is extended to nonlinear dynamics via elementary differential field techniques. This generalization, which was first suggested by J.-F. Pommaret, is related to the notion of strong accessibility introduced by H. J. Sussmann and V. Jurdjevic [J. Diff. Equations 12, 95-116 (1972; Zbl 0242.49040)]. In the case of constant or time-varying linear systems, it comes down to a purely module-theoretic description. As a bonus of our methods we give a straightforward characterization of hidden modes and we also demonstrate that the controllability of a nonlinear dynamics is equivalent to the controllability of its tangent linearized dynamics.

MSC:

93B05 Controllability
93C10 Nonlinear systems in control theory
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