Agrachev, A. A.; Gamkrelidze, R. V. Local controllability for families of diffeomorphisms. (English) Zbl 0778.93003 Syst. Control Lett. 20, No. 1, 67-76 (1993). Summary: We study groups and semigroups which are generated by analytic families of diffeomorphisms. The central notion is that of local controllability of a family of diffeomorphisms at a given point of the state manifold, when generalizes the familiar notion of local controllability of control systems with continuous, as well as discrete time. Lie theory methods are used. We systematically exploit the so-called fast switching variations and properties of the jet spaces of curves on the state manifold. Cited in 6 Documents MSC: 93B05 Controllability Keywords:local controllability; Lie theory methods PDFBibTeX XMLCite \textit{A. A. Agrachev} and \textit{R. V. Gamkrelidze}, Syst. Control Lett. 20, No. 1, 67--76 (1993; Zbl 0778.93003) Full Text: DOI References: [1] Agrachev, A. A.; Gamkrelidze, R. V., Exponential representation of flows and chronological calculus, Math. USSR Sb., 107, 487-532 (1978), (in Russian) · Zbl 0408.34044 [2] Agrachev, A. A.; Gamkrelidze, R. V., Volterra series and substitution groups, Itogi Nauki, VINITI. Sovremennye Problemy Matematiki. Noveshie Dostijenia, 39, 3-40 (1991), (in Russian). English translation to appear in J. Soviet Math. · Zbl 0797.58073 [3] Agrachev, A. A.; Gamkrelidze, R. V.; Sarychev, A. V., Local invariants of smooth control systems, Acta Appl. Math., 14, 191-237 (1989) · Zbl 0681.49018 [4] Fliess, M.; Normand-Cyrot, D., A group-theoretic approach to discrete-time nonlinear controllability, (Proc. IEEE Conf. Decision and Control. Proc. IEEE Conf. Decision and Control, Albuquerque, NM (1981)) · Zbl 0498.93010 [5] Gamkrelidze, R. V.; Agrachev, A. A.; Vakhrameev, S. A., Ordinary differential equations on vector bundles and chronological calculus, Itogi Nauki, VINITI. Sovremennye Problemy Matematiki. Noveyshie Dostijenia, 35, 3-107 (1989), (in Russian). English translation in J. Soviet Math. · Zbl 0719.58033 [6] Kawski, M., Control variations with an increasing number of switchings, Bull. Amer. Math. Soc. (N.S.), 18, 149-152 (1988) · Zbl 0663.93006 [7] Sussmann, H. J., Lie brackets and local controllability: A sufficient condition for scalar-input systems, SIAM J. Control Optim., 21, 686-713 (1983) · Zbl 0523.49026 [8] Sussmann, H. J., A general theorem for local controllability, SIAM J. Control and Optim., 25, 158-194 (1987) · Zbl 0629.93012 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.