Small-Time Reachable Sets and Time-Optimal Feedback Control
This paper describes selected aspects of a direct geometric approach to time-optimal control. The underlying idea is to obtain a regular synthesis of time-optimal controls from a precise knowledge of the structure of the small-time reachable set for an extended system to which time has been adjoined as extra coordinate.
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- A. A. Agrachev and R. V. Gamkrelidze, Symplectic geometry for optimal control, in Nonlinear Controllability and Optimal Control(H. SUSSMANN, ed.), Marcel Dekker, 1990, pp. 263–277.Google Scholar
- N. BoURBAKl, Elements of Mathematics, Lie Groups and Lie Algebras, Chapters 1–3, Springer-Verlag, Berlin, 1989.Google Scholar
- N. JACOBSON, Lie Algebras, Dover, New York, 1979.Google Scholar
- I.A.K. KUPKA, The ubiquity of Fuller’s phenomenon, in Nonlinear Controllability and Optimal Control,(H. SUSSMANN, ed.), Marcel Dekker, New York, 1990, pp. 313–350.Google Scholar
- H. SCHATTLER, Conjugate points and intersections of bang-bang trajectories, Proceedings of the 28th IEEE Conference on Decision and Control, Tampa, Florida, (1989), pp. 1121–1126.Google Scholar
- H. SCHÄTTLER, A local feedback synthesis of time-optimal stabilizing controls indimension three,Mathematics of Control, Signals and Systems, Vol.4, (1991), pp.293–313.Google Scholar
- H. SCHATTLER, Extremal trajectories, small-time reachable sets and local feedback synthesis: a synopsis of the three-dimensional case, in Nonlinear Synthesis, Proceedings of the IIASA Conference on Nonlinear Synthesis, Sopron, Hungary, June 1989, (C. I. BYRNES, A. KURZHANSKY, eds.), Birkhauser, Boston, 1991, pp. 258–269.Google Scholar
- H. SCHATTLER AND M. JANKOVIC, A synthesis of time-optimal controls in the presence of saturated singular arcs, Forum Mathematicum.Google Scholar
- H. SUSSMANN, Lie brackets and real analyticity in control theory,in Mathematical Control Theory,Banach Center Publications, Vol.14, Polish Scientific Publishers, Warsaw, Poland, 1985, pp. 515–542.Google Scholar
- H. SUSSMANN, A product expansion for the Chen series, in Theory and Applications of Nonlinear Control Systems(C. BYRNES, A. LLNDQUIST, eds.) North-Holland, Amsterdam, 1986, pp. 323–335.Google Scholar
- H. SUSSMANN, Envelopes, conjugate points, and optimal bang-bang extremals, in Proceedings of the 1985 Paris Conference on Nonlinear Systems(M. FLIESS, M. HAZEWINKEL, eds.) Reidel Publishing, Dordrecht, 1987.Google Scholar
- H. SUSSMANN, Envelopes, high order optimality conditions and Lie brackets,Proceedings of the 28th IEEE Conference on Decision and Control, Tampa, Florida, (1989), pp. 1107–1112Google Scholar