Free Access
Volume 4, 1999
Page(s) 377 - 403
Published online 15 August 2002
  1. A.A. Agrachev, Quadratic mappings in geometric control theory, in: Itogi Nauki i Tekhniki, Problemy Geometrii, VINITI, Acad. Nauk SSSR, Moscow 20 (1988) 11-205. English transl. in J. Soviet Math. 51 (1990) 2667-2734.
  2. A.A. Agrachev, The second-order optimality condition in the general nonlinear case. Matem. Sbornik 102 (1977) 551-568. English transl. in: Math. USSR Sbornik 31 (1977).
  3. A.A. Agrachev, Topology of quadratic mappings and Hessians of smooth mappings, in: Itogi Nauki i Tekhniki, Algebra, Topologia, Geometria; VINITI, Acad. Nauk SSSR 26 (1988) 85-124.
  4. A.A. Agrachev, B. Bonnard, M. Chyba and I. Kupka, Sub-Riemannian spheres in Martinet flat case. ESAIM: Contr., Optim. and Calc. Var. 2 (1997) 377-448.
  5. A.A. Agrachev and R.V. Gamkrelidze, Second-order optimality condition for the time-optimal problem. Matem. Sbornik 100 (1976) 610-643. English transl. in: Math. USSR Sbornik 29 (1976) 547-576.
  6. A.A. Agrachev and R.V. Gamkrelidze, Exponential representation of flows and chronological calculus. Matem. Sbornik 107 (1978) 467-532. English transl. in: Math. USSR Sbornik 35 (1979) 727-785.
  7. A.A. Agrachev, R.V. Gamkrelidze and A.V. Sarychev, Local invariants of smooth control systems. Acta Appl. Math. 14 (1989) 191-237. [CrossRef] [MathSciNet]
  8. A.A. Agrachev and A.V. Sarychev, On abnormal extremals for Lagrange variational problems. (summary). J. Mathematical Systems, Estimation and Control 5 (1995) 127-130. Complete version: J. Mathematical Systems, Estimation and Control 8 (1998) 87-118.
  9. A.A. Agrachev and A.V. Sarychev, Abnormal sub-Riemannian geodesics: Morse index and rigidity. Ann. Inst. H. Poincaré 13 (1996) 635-690.
  10. A.A. Agrachev and A.V. Sarychev, Strong minimality of abnormal geodesics for 2-distributions. J. Dynamical Control Systems 1 (1995) 139-176. [CrossRef] [MathSciNet]
  11. V.I. Arnol'd, A.N. Varchenko and S.M. Gusein-Zade, Singularities of differentiable maps 1 Birkhäuser, Boston (1985).
  12. P. Brunovsky, Existence of regular synthesis for general problems. J. Differential Equations 38 (1980) 317-343. [CrossRef] [MathSciNet]
  13. R.L. Bryant and L. Hsu, Rigidity of integral curves of rank 2 distributions. Invent. Math. 114 (1993) 435-461. [CrossRef] [MathSciNet]
  14. W-L. Chow, Über Systeme von linearen partiellen Differentialgleichungen erster ordnung. Match. Ann. 117, (1940/41) 98-105.
  15. A.F. Filippov, On certain questions in the theory of optimal control. Vestnik Moskov. Univ., Ser. Matem., Mekhan., Astron. 2 (1959) 25-32.
  16. A. Gabrielov, Projections of semianalytic sets. Funct. Anal Appl. 2 (1968) 282-291. [CrossRef]
  17. R.V. Gamkrelidze, Principles of optimal control theory. Plenum Press, New York (1978).
  18. Zhong Ge, Horizontal path space and Carnot-Caratheodory metric. Pacific J. Math. 161 (1993) 255-286. [MathSciNet]
  19. V.Ya. Gershkovich, Bilateral estimates for metrics, generated by completely nonholonomic distributions on Riemannian manifolds. Doklady AN SSSR 278 (1984) 1040-1044.
  20. B.S. Goh, Necessary conditions for singular extremals involving multiple control variables. SIAM J. Control 4 (1966) 716-731. [CrossRef] [MathSciNet]
  21. M. Goresky and R. MacPherson, Stratified Morse Theory. Springer-Verlag, N.Y. (1988) Ch.1.
  22. R. Hardt, Stratifications of real analytic maps and images. Inventiones Math. 28 (1975) 193-208. [CrossRef] [MathSciNet]
  23. G.W. Haynes and H. Hermes, Nonlinear Controllability via Lie Theory. SIAM J. Control 8 (1970) 450-460. [CrossRef] [MathSciNet]
  24. H. Hironaka, Subanalytic sets, Lecture Notes Istituto Matematico ``Leonida Tonelli'', Pisa, Italy (1973).
  25. H.J. Kelley, R. Kopp and H.G. Moyer, Singular Extremals, G. Leitman, Ed., Topics in Optimization, Academic Press, New York, N.Y. (1967) 63-101.
  26. A.J. Krener, The high-order maximum principle and its applications to singular extremals. SIAM J. Control and Optim. 15 (1977) 256-293. [CrossRef]
  27. W. Liu and H.J. Sussmann, Shortest paths for sub-Riemannian metrics on rank-2 distributions, Memoirs of AMS, No. 564 (1995).
  28. S. Lojasiewicz Jr. and H.J. Sussmann, Some examples of reachable sets and optimal cost functions that fail to be subanalytic. SIAM J. Control and Optim. 23 (1985) 584-598. [CrossRef] [MathSciNet]
  29. R. Montgomery, Geodesics, which do not satisfy geodesic equations, Preprint (1991).
  30. R. Montgomery, A survey on singular curves in sub-Riemannian geometry. J. Dynamical and Control Systems 1 (1995) 49-90. [CrossRef]
  31. P.K. Rashevsky, About connecting two points of a completely nonholonomic space by admissible curve. Uchen. Zap. Ped. Inst. Libknechta 2 (1938) 83-94.
  32. C.B. Rayner, The exponential map for the Lagrange problem on differentiable manifolds. Philos. Trans. Roy. Soc. London Ser. A, Math. Phys. Sci. 262 (1967) 299-344.
  33. J.P. Serre, Lie algebras and lie groups, Benjamin, New York (1965).
  34. H.J. Sussmann, Subanalytic sets and feedback control. J. Differential Equations 31 (1979) 31-52. [CrossRef] [MathSciNet]
  35. H.J. Sussmann, A cornucopia of four-dimensional abnormall sub-Riemannian minimizers, A. Bellaïche, J.-J. Risler, Eds., Sub-Riemannian Geometry, Birkhäuser, Basel (1996) 341-364.
  36. H.J. Sussmann, Optimal control and piecewise analyticity of the distance function. A. Ioffe, S. Reich, Eds., Pitman Research Notes in Mathematics, Longman Publishers (1992) 298-310.
  37. A.M. Vershik and V.Ya. Gershkovich, Nonholonomic dynamical systems, geometry of distributions and variational problems. V.I. Arnol'd, S.P. Novikov, Eds., Dynamical systems VII, Encyclopedia of Mathematical Sciences 16, Springer-Verlag, NY (1994).
  38. L.C. Young, Lectures on the calculus of variations and optimal control theory, Chelsea, New York (1980).

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