L∞ estimates on trajectories confined to a closed subset

Journal of Differential Equations

Volumn 252, Issue 2, 2012, Pages 1912-1933

  Bettiol, Piernicola ^a   Frankowska, Hélène ^b   Vinter, Richard B ^a  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

^b INSTITUT DE MATHÉMATIQUES DE JUSSIEU   (France)

Author keywords

Differential inclusions; Optimal control; Sensitivity; State constraints

Indexed keywords

EID: 80655146986     PISSN: 00220396     EISSN: 10902732     Source Type: Journal    
DOI: 10.1016/j.jde.2011.09.007     Document Type: Article

References (21)

1. Aubin J.-P., Frankowska H. Set-valued Analysis 1990, Birkhäuser Boston, Inc., Boston, Basel, Berlin.
2. Bettiol P., Cardaliaguet P., Quincampoix M. Zero-sum state constrained differential games: Existence of value for Bolza problem. Internat. J. Game Theory 2006, 34:495-527.
3. Bettiol P., Frankowska H. Regularity of solution maps of differential inclusions for systems under state constraints. J. Set-Valued Anal. 2007, 15(1):21-45.
4. 1,1 estimates and counter-examples. SIAM J. Control Optim. 2010, 48(7):4664-4679.
5. Bettiol P., Bressan A., Vinter R.B. Estimates for trajectories confined to a cone in Rn. SIAM J. Control Optim. 2011, 49(1):21-42.
6. Bettiol P., Vinter R.B. Sensitivity interpretations of the co-state variable for optimal control problems with state constraints. SIAM J. Control Optim. 2010, 48(5):3297-3317.
7. Bressan A., Facchi G. Trajectories of differential inclusions with state constraints. J. Differential Equations 2011, 250(4):2267-2281.
8. Clarke F.H. Optimization and Nonsmooth Analysis 1983, Wiley-Interscience, New York.
9. Clarke F.H., Rifford L., Stern R.J. Feedback in state constrained optimal control. ESAIM Control Optim. Calc. Var. 2002, 7:97-133.
10. Forcellini F., Rampazzo F. On nonconvex differential inclusions whose state is constrained in the closure of an open set, applications to dynamic programming. Differential Integral Equations 1999, 12(4):471-497.
11. Frankowska H., Plaskacz S., Rzezuchowski T. Measurable viability theorems and the Hamilton-Jacobi-Bellman equation. J. Differential Equations 1995, 116:265-305.
12. Frankowska H., Plaskacz S. A measurable upper semicontinuous viability theorem for tubes. J. Nonlinear Anal. TMA 1996, 26:565-582.
13. Frankowska H., Rampazzo F. Filippov's and Filippov-Wazewski's theorems on closed domains. J. Differential Equations 2000, 161:449-478.
14. Frankowska H., Vinter R.B. Existence of neighbouring feasible trajectories: Applications to dynamic programming for state constrained optimal control problems. J. Optim. Theory Appl. 2000, 104(1):21-40.
15. Rampazzo F., Vinter R.B. A theorem on existence of neighbouring trajectories satisfying a state constraint, with applications to optimal control. IMA J. Math. 1999, 16(4):335-351.
16. Rampazzo F., Vinter R.B. Degenerate optimal control problems with state constraints. SIAM J. Control Optim. 2000, 39(4):989-1007.
17. Rapaport A.E., Vinter R.B. Invariance properties of time measurable differential inclusions and dynamic programming. J. Dyn. Control Syst. 1996, 2(3):423-448.
18. Rockafellar R.T. Clarke's tangent cones and the boundaries of closed sets in Rn. Nonlinear Anal. 1979, 3(1):145-154.
19. Sagan H. Space-Filling Curves 1994, Springer-Verlag, New York.
20. Soner H.M. Optimal control problems with state-space constraints. SIAM J. Control Optim. 1986, 24:552-562. and 1110-1122.
21. Vinter R.B. Optimal Control 2000, Birkhäuser, Boston.