Invariance properties of time measurable differential inclusions and dynamic programming

Journal of Dynamical and Control Systems

Volumn 2, Issue 3, 1996, Pages 423-448

  Rapaport, A E ^a   Vinter, R B ^a  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

Differential inclusions; Hamilton Jacobi equation; Invariance properties; Measurable time dependency

Indexed keywords

DYNAMIC PROGRAMMING; OPTIMAL CONTROL SYSTEMS; PARTIAL DIFFERENTIAL EQUATIONS; SET THEORY; SYSTEM STABILITY;

DIFFERENTIAL INCLUSIONS; HAMILTON-JACOBI EQUATION; INVARIANCE PROPERTIES; MEASURABLE TIME DEPENDENCY;

INVARIANCE;

EID: 0030188812     PISSN: 10792724     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02269425     Document Type: Article

References (16)

1. F. H. Clarke, Y. S. Ledyaev, R. J. Stern, and P. R. Wolenski, Qualitative properties of trajectories of control systems: A survey. J. Dynam. Control Syst. 1 (1995), No. 1, 1-48.
2. J. P. Aubin, Viability theory. Birkhaüser, Boston, 1991.
3. H. Frankowska, M. Plaskacz, and T. Rzezuchowski, Measurable viability theorem and Hamilton-Jacobi-Bellman equations. J. Differ. Equ. (to appear).
4. H. Frankowska, Lower semicontinuous solutions of Hamilton-Jacobi-Bellman equations. SIAM J. Control and Optimiz. 31 (1993), No. 1, 257-272.
5. E. N. Barron and R. Jensen, Semicontinuous viscosity solutions for Hamilton-Jacobi equations with convex Hamiltonians. Commun. Partial Differ. Equ. 15 (1990), 1713-1742.
6. P. L. Lions and B. Perthame, Remarks on Hamilton-Jacobi equations with measurable time-dependent Hamiltonians. Nonlinear Anal. 11 (1987), No. 5, 613-621.
7. J. P. Aubin and A. Cellina, Differential inclusions. Springer, 1984.
8. J. M. C. Clark and R. B. Vinter, On the absolute continuity of set-valued maps (in preparation).
9. n. J. Math. Anal. Appl. 148 (1990), 202-212.
10. K. Deimling, Multivalued differential equations. Walter de Gruyter, 1992.
11. N. Dunford and J. T. Schwartz, Linear operators. Part I: General theory. Intersience, 1958.
12. A. Ornelas, Parametrization of Caratheodory multifunctions. Rend. Semin. Mat. Univ. Padova 83 (1990).
13. P. D. Loewen, Optimal control via nonsmooth analysis. CRM Proc. and Lecture Notes, University of Montréal, 1993.
14. J. P. Aubin and H. Frankowska, Set-valued analysis. Birkhaüser, Boston, 1991.
15. F. H. Clarke, Optimization and nonsmooth analysis. Wiley Interscience, New-York, 1983.
16. R. Vinter and P. Wolenski, Hamilton-Jacobi theory for optimal control problems with data measurable in time. SIAM J. Control and Optimiz. 28 (1990), No. 6, 1404-1419.