Abstract:
The constancy of sign of the second variation of a nonlinear control system is investigated. Sufficient conditions for controllability of second order and also sufficient conditions for optimality with respect to fast action of the extremals of this system analogous to the Legendre–Jacobi conditions of the classical calculus of variation are obtained.
Bibliography: 6 titles.
\Bibitem{Sar80}
\by A.~V.~Sarychev
\paper The index of the second variation of a~control system
\jour Math. USSR-Sb.
\yr 1982
\vol 41
\issue 3
\pages 383--401
\mathnet{http://mi.mathnet.ru/eng/sm2813}
\crossref{https://doi.org/10.1070/SM1982v041n03ABEH002238}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=601890}
\zmath{https://zbmath.org/?q=an:0484.49012}
Linking options:
https://www.mathnet.ru/eng/sm2813
https://doi.org/10.1070/SM1982v041n03ABEH002238
https://www.mathnet.ru/eng/sm/v155/i3/p464
This publication is cited in the following 26 articles:
Bonnard B., Chyba M., Marriott J., “Singular Trajectories and the Contrast Imaging Problem in Nuclear Magnetic Resonance”, SIAM J. Control Optim., 51:2 (2013), 1325–1349
E. Trélat, “Optimal Control and Applications to Aerospace: Some Results and Challenges”, J Optim Theory Appl, 2012
Sachkov Yu.L., “Conjugate and Cut Time in the Sub-Riemannian Problem on the Group of Motions of a Plane”, ESAIM-Control Optimisation and Calculus of Variations, 16:4 (2010), 1018–1039
Bernard Bonnard, Nataliya Shcherbakova, Dominique Sugny, “The smooth continuation method in optimal control with an application to quantum systems”, ESAIM: COCV, 17:1 (2010), 267
Yacine Chitour, Frederic Jean, Emmanuel Trelat, “Singular Trajectories of Control-Affine Systems”, SIAM J Control Optim, 47:2 (2008), 1078
Sachkov, YL, “Conjugate points in the Euler elastic problem”, Journal of Dynamical and Control Systems, 14:3 (2008), 409
Bonnard B. Caillau J.-B. Trelat E., “Second Order Optimality Conditions in the Smooth Case and Applications in Optimal Control”, ESAIM-Control OPtim. Calc. Var., 13:2 (2007), 207–236
Y. Chitour, F. Jean, E. Trelat, Proceedings of the 44th IEEE Conference on Decision and Control, 2005, 940
B. Bonnard, J.-B. Caillau, E. Trelat, Proceedings of the 44th IEEE Conference on Decision and Control, 2005, 929
B. Bonnard, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601), 2004, 1364
Andrey Sarychev, “Time-Optimality of Bang-Bang Controls for Chained Systems”, IFAC Proceedings Volumes, 36:2 (2003), 123
Emmanuel Trélat, Lecture Notes in Control and Information Sciences, 273, Dynamics, Bifurcations, and Control, 2002, 89
Emmanuel Trélat, “Asymptotics of accessibility sets along an abnormal trajectory”, ESAIM: COCV, 6 (2001), 387
Citation in format AMSBIB
Contact us: