Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 83)
Local Controllabilifty Along a Reference Trajectory
Let (*) be a C∞ control system defined on a C∞ differential manifold, of the following typeSufficient conditions of local controllability along the trajectory t → exp tf0(x0) are aiven. These conditions are conditions on the Lie algebra generated by the vector fields f0, f1,...,fm in x0.
One of the conditions has been proved by Hermes and Sussmann independen-tly under the assumntion f0(x0) = 0.
KeywordsVector Field Local Controllability Reference Trajectory Analytic Vector Field Nilpotent Associative Algebra
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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- H. Sussmann, V. Jurdjevic, “Controllability of nonlinear systems”, J. Diff. Ea. 12 (1972), 95–116.Google Scholar
- H. Hermes, “Control systems which generate decomposable Lie alge-bras”, J. Diff. Eq. 44 (1982), 166–187.Google Scholar
- H. Sussmann, “A general theorem on local controllability”, to ap-pear.Google Scholar
- N.N. Petrov, “Local controllability of autonomous systems” (in rus-sian) Diff. Uravn. 4 (1968), 1218–1232.Google Scholar
- P.E. Crouch, C.I. Byrnes, “Local accessibility, local reachability and representations of compact groups”, to appear.Google Scholar
- R.M. Bianchini, G. Stefani, “Normal local controllability of order one”, Int. J. Control 39 (1984), 701–714.Google Scholar
- G. Stefani, “Local controllability of non linear systems: an exam-ple”, System & Control Letters 6 (1985).Google Scholar
- M. Fliess, “Fonctionelles causales non lineaires et indeterminees non commutatives”, Bull. Soc. Math. France, 109 (1981), 3–40.Google Scholar
- A.J. Krener, “A generalization of Chow’s theorem and Bang-Bang theorem to non linear control problems”, SIAM J. Control Opt. 12 (1974), 43–52.Google Scholar
- G. Stefani, “On local controllability of a scalar-input control system”, to appear in MTNS-85 7th Int. Symp. on the Mathematical Theory of Networks and systems, Stockholm 1985 (C. Byrnes, A. Lind-quist, eds.).Google Scholar
- H. Sussmann, “A general theorem on symmetries and local controlla-bility”, Proceedings of 24th CDC (1985).Google Scholar
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