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All issues Volume 50 / No 4 (July-August 2016) ESAIM: M2AN, 50 4 (2016) 1223-1240 References
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Issue
ESAIM: M2AN
Volume 50, Number 4, July-August 2016
Page(s) 1223 - 1240
DOI https://doi.org/10.1051/m2an/2015070
Published online 14 July 2016
  1. F. Ancona and A. Bressan, Patchy vector fields and asymptotic stabilization. ESAIM: COCV 4 (1999) 445–471. [CrossRef] [EDP Sciences] [Google Scholar]
  2. M. Bardi and M. Falcone, An approximation scheme for the minimum time function. SIAM J. Control Optim. 28 (1990) 950–965. [CrossRef] [MathSciNet] [Google Scholar]
  3. M. Bardi and I.C.-Dolcetta, Optimal control and viscosity solutions of Hamilton–Jacobi–Bellman equations. Systems and Control: Foundations and Applications. Birkhäuser, Boston (1997). [Google Scholar]
  4. M. Bardi, M. Falcone and P. Soravia, Numerical methods for pursuit-evasion games via viscosity solutions. In Stochastic and differential games. Birkhauser, Boston (1999) 105–175. [Google Scholar]
  5. G. Barles, Solutions de viscosité des équations de Hamilton-Jacobi. Vol. 17 of Math. Appl. Springer, Paris (1994). [Google Scholar]
  6. S. Cacace, E. Cristiani and M. Falcone, A local ordered upwind method for Hamilton–Jacobi and Isaacs equations. In Proc. of 18th IFAC World Congress (2011) 6800–6805. [Google Scholar]
  7. S. Cacace, E. Cristiani, M. Falcone and A. Picarelli, A patchy dynamic programming scheme for a class of Hamilton–Jacobi–Bellman equations. SIAM J. Sci. Comput. 34 (2012) A2625–A2649. [CrossRef] [Google Scholar]
  8. F. Camilli, M. Falcone, P. Lanucara and A. Seghini, A domain decomposition method for bellman equations. In Vol. 180, Domain Decomposition methods in Scientific and Engineering Computing. Contemp. Math. (1994) 477–483. [Google Scholar]
  9. P. Cannarsa and C. Sinestrari, Semiconcave functions, Hamilton–Jacobi equations, and optimal control. In Vol. 58 Progress Nonlin. Differ. Eq. Appl. Birkhäuser, Boston, MA (2004). [Google Scholar]
  10. E. Carlini, M. Falcone, N. Forcadel and R. Monneau, Convergence of a generalized fast-marching method for an eikonal equation with a velocity-changing sign. SIAM J. Numer. Anal. 46 (2008) 2920–2952. [CrossRef] [MathSciNet] [Google Scholar]
  11. M. Detrixhe, F. Gibou and C. Min, A parallel fast sweeping method for the eikonal equation. J. Comput. Phys. 237 (2013) 46–55. [CrossRef] [MathSciNet] [Google Scholar]
  12. I. Capuzzo Dolcetta and H. Ishii, Approximate solutions of the Bellman equation of deterministic control theory. Appl. Math. Optim. 11 (1984) 161–181. [CrossRef] [MathSciNet] [Google Scholar]
  13. R.J. Elliott and N.J. Kalton, The existence of value in differential games, Bull. Amer. Math. Soc. 78 (1972) 427–431. [CrossRef] [MathSciNet] [Google Scholar]
  14. M. Falcone, A numerical approach to the infinite horizon problem of deterministic control theory. Appl. Math. Optim. 15 (1987) 1–13. [CrossRef] [MathSciNet] [Google Scholar]
  15. M. Falcone and R. Ferretti, Convergence analysis for a class of high-order semi-Lagrangian advection schemes. SIAM J. Numer. Anal. 35 (1998) 909–940. [CrossRef] [MathSciNet] [Google Scholar]
  16. M. Falcone and R. Ferretti, Semi-Lagrangian Approximation Schemes for Linear and Hamilton–Jacobi Equations. Appl. Math. SIAM, Philadelphia (2014). [Google Scholar]
  17. A. Festa and R.B. Vinter, A decomposition technique for pursuit evasion games with many pursuers. 52nd IEEE Control and Decision Conference CDC (2013) 5797–5802. [Google Scholar]
  18. A. Festa and R.B. Vinter, Decomposition of differential games with multiple targets. J. Optim. Theory Appl. 169 (2016) 848–875. [CrossRef] [MathSciNet] [Google Scholar]
  19. C. Navasca and A.J. Krener, Patchy solutions of Hamilton–Jacobi-Bellman partial differential equations. In Vol. 364 of Modeling, Estimation and Control. Lect. Notes Control Inform. Sci., edited by A. Chiuso, A. Ferrante, and S. Pinzoni. Springer, Berlin (2007) 251–270. [Google Scholar]
  20. P. Soravia, Estimates of convergence of fully discrete schemes for the Isaacs equation of pursuit-evasion differential games via maximum principle. SIAM J. Control Optim. 36 (1998) 1–11. [CrossRef] [MathSciNet] [Google Scholar]
  21. M. Sun, Domain decomposition algorithms for solving hamilton–jacobi–bellman equations. Numer. Func. Anal. Optim. 14 (1993) 145–166. [CrossRef] [Google Scholar]
  22. A. Valli and A. Quarteroni, Domain decomposition methods for partial differential equations. Oxford University Press, Oxford (1999). [Google Scholar]
  23. R.B. Vinter, Optimal Control Theory. Birkhäuser, Boston Heidelberg (2000). [Google Scholar]
  24. H. Zhao, Parallel implementations of the fast sweeping method. J. Comput. Math. 25 (2007) 421–429. [MathSciNet] [Google Scholar]
  25. S. Zhou and W. Zhan, A new domain decomposition method for an hjb equation. J. Comput. Appl. Math. 159 (2003) 195–204. [CrossRef] [MathSciNet] [Google Scholar]

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