Abstract
A sufficient condition for a reference trajectory \(\hat x\) lies on the boundary of the reachable set is proved using a new interpretation of known results on Volterra series. Some examples and relations with known results are given.
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References
Sussmann H.J. — „A sufficient condition for local controllability”, SIAM J. Control and Optimization 16 (1978), p. 790–802.
Sussmann H.J. — „A general theorem on local controllability”, SIAM J. on Control and Optimization 25 (1987), p. 158–194.
Bianchini R.M., Stefani G. — „Sufficient conditions of local controllability” in IEEE Proceedings, 25suth CDC, Athens 1986, p. 967–970.
Stefani G. — „On the minimum time problem” to appear in Proceedings of MTNS 1987.
Stefani G. — „On the local controllability of a scalar input control system” Theory and applications of nonlinear control systems, Byrnes and Lindquist eds, North Holland 1986, p. 167–179.
Kawski M. — „A necessary condition for local controllability” Proceedings of Conference on Diff. Geometry, S. Antonio 1986, AMS Contem. Math. series.
Bianchini R.M., Stefani G. — „Local controllability along a reference trajectory” in „Analysis and Optimization of Systems” Lectures Notes in Control and Information Sciences No. 83, Springer Verlag, p. 342–352.
Bianchini R.M., Stefani G. — „A high order maximum principle” to appear in Proceedings of MTNS 1987.
Bianchini R.M. & Stefani G. — „A high order maximum principle and controllability” Quaderni dell'Istituto Matematico U. Dini no.12 1986/87, Firenze.
Bacciotti A. — „Aspetti topologici del problema del tempo minimo” in „Convegno internazionale su equazioni differenziali ordinarie ed equazioni funzionali” R. Conti, G. Sestini, G. Villari ed.s (1978), p. 423–432.
Bianchini R.M. & Stefani G. — „Normal local controllability of order one” Int. J. Control, 39 (1984) p. 701–714.
Lesiak C., Krener J.A. — „The existence and uniqueness of Volterra series for non-linear systems” IEEE Transaction on Automatic Control AC23 (1978) p. 1090–1095.
Fliess M. — „Functionelles causales non lineairs et indeterminees non commutatives” Bull. Soc Math. France 109 (1981) p.3–40.
Crouch P., Lamnabhi-Lagarrigue F. — „Algebraic and multiple integral identities” Preprint.
Lamnabhi-Lagarrigue F. — „Series de Volterra et commande optimale singuliere” These d'Etat Université Paris XI
Lamnabhi-Lagarrigue F., Stefani G. — „Singular optimal problems: on the necessary conditions of optimality” Preprint.
Godbillon C. — „Géométrie différentielle et mécanique analytique” Collection Méthodes Herman, Paris 1969.
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© 1988 Springer-Verlag
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Stefani, G. (1988). A sufficient condition for extremality. In: Bensoussan, A., Lions, J.L. (eds) Analysis and Optimization of Systems. Lecture Notes in Control and Information Sciences, vol 111. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0042221
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DOI: https://doi.org/10.1007/BFb0042221
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