Semigeodesics and the minimal time function

 Access to full text

 Full (PDF)

1. [1] O. Alvarez, S. Koike and I. Nakayama, Uniqueness of lower semicontinuous viscosity solutions for the minimum time problem. SIAM J. Control Optim. 38 (2000) 470–481. Zbl0949.49020
2. [2] J.P. Aubin and A. Cellina, Differential inclusions. Springer-Verlag, New York (1984). Zbl0538.34007MR755330
3. [3] M. Bardi and I. Capuzzo-Dolcetta, Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations. With appendices by Maurizio Falcone and Pierpaolo Soravia. Birkhäuser Boston, Inc., Boston, MA (1997). Zbl0890.49011MR1484411
4. [4] E.N. Barron and R. Jensen, Semicontinuous viscosity solutions for Hamilton-Jacobi equations with convex Hamiltonians. Commun. Partial Differ. Equations 15 (1990) 1713–1742. Zbl0732.35014
5. [5] P. Cannarsa and C. Sinestrari, Convexity properties of the minimum time function. Calc. Var. 3 (1995) 273–298. Zbl0836.49013
6. [6] P. Cannarsa and C. Sinestrari, Semiconcave functions, Hamilton-Jacobi equations and optimal control problems. Birkhäuser Boston (2004). Zbl1095.49003MR2041617
7. [7] P. Cardaliaguet, M. Quincampoix and P. Saint-Pierre, Optimal times for constrained nonlinear control problems without local controllability. Appl. Math. Optim. 36 (1997) 21–42. Zbl0884.49002
8. [8] F.H. Clarke and Yu. Ledyaev, Mean value inequalities in Hilbert space. Trans. Amer. Math. Soc. 344 (1994) 307–324. Zbl0803.49018
9. [9] F.H. Clarke, Yu. Ledyaev, R. Stern and P. Wolenski, Qualitative properties of trajectories of control systems: A survey. J. Dynam. Control Syst. 1 (1995) 1–48. Zbl0951.49003
10. [10] F.H. Clarke, Yu. Ledyaev, R. Stern and P. Wolenski, Nonsmooth Analysis and Control Theory. Graduate Texts Math. 178 (1998). Springer-Verlag, New York. Zbl1047.49500MR1488695
11. [11] F.H. Clarke and C. Nour, The Hamilton-Jacobi equation of minimal time control. J. Convex Anal. 11 (2004) 413–436. Zbl1072.49018
12. [12] M.G. Crandall, H. Ishi and P.L. Lions, User’s guide to the viscosity solutions of second order partial differential equations. Bull. Amer. Math. Soc. 27 (1992) 1–67. Zbl0755.35015
13. [13] M.G. Crandall and P.L. Lions, Viscosity solutions of Hamilton-Jacobi equations. Trans. Amer. Math. Soc. 277 (1983) 1–42. Zbl0599.35024
14. [14] W.H. Fleming and H.M. Soner, Controlled Markov Processes and Viscosity Solutions. Springer-Verlag, New York (1993). Zbl0773.60070MR1199811
15. [15] H. Frankowska, Lower semicontinuous solutions of Hamilton-Jacobi-Bellman equations. SIAM J. Control Optim. 31 (1993) 257–272. Zbl0796.49024
16. [16] C. Nour, The Hamilton-Jacobi equation in optimal control: duality and geodesics. Ph.D. Thesis, Université Claude Bernard Lyon I (2003). 
17. [17] C. Nour, The bilateral minimal time function. J. Convex Anal., to appear. Zbl1112.49024MR2211804
18. [18] P. Soravia, Discontinuous viscosity solutions to Dirichlet problems for Hamilton-Jacobi equations with convex Hamiltonians. Comm. Partial Differ. Equ. 18 (1993) 1493–1514. Zbl0788.49028
19. [19] H.J. Sussmann, A general theorem on local controllability. SIAM J. Control Optim. 25 (1987) 158–133. Zbl0629.93012
20. [20] V.M. Veliov, Lipschitz continuity of the value function in optimal control. J. Optim. Theory Appl. 94 (1997) 335–363. Zbl0901.49022
21. [21] R.B. Vinter, Optimal control. Birkhäuser Boston, Inc., Boston, MA (2000). Zbl0952.49001MR1756410
22. [22] P. Wolenski and Y. Zhuang, Proximal analysis and the minimal time function. SIAM J. Control Optim. 36 (1998) 1048–1072. Zbl0930.49016