Regularity of Solution Maps of Differential Inclusions Under State Constraints
Tóm tắt
Từ khóa
Tài liệu tham khảo
Arisawa, M., Lions, P.L.: Continuity of admissible trajectories for state constraints control problems. Discrete Contin. Dynam. Systems 2, 297–305 (1996)
Aubin, J.-P.: Viability Theory. Systems & Control: Foundations & Applications. Birkhäuser, Boston, (1991)
Aubin, J.-P., Cellina, A.: Differential Inclusions. Gründlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 264. Springer, Berlin Heidelberg New York (1984)
Aubin, J.-P., Ekeland, I.: Applied Nonlinear Analysis. Pure and Applied Mathematics. Wiley, New York (1984)
Aubin, J.-P., Frankowska, H.: Set-valued analysis. Systems & Control: Foundations & Applications. Birkhäuser, Boston (1990)
Bettiol, P., Cardaliaguet, P., Quincampoix, M.: Zero-sum state constrained differential games: Existence of value for Bolza problem. Int. J. Game Theory (to appear)
Cannarsa, P.M., Frankowska, H.: Some characterizations of optimal trajectories in control theory. SIAM J. Control Optim. 29, 1322–1347 (1991)
Capuzzo-Dolcetta, I., Lions, P.L.: Hamilton–Jacobi equations with state constraints. Trans. Amer. Math. Soc. 318, 643–687 (1990)
Cardaliaguet, P., Plaskacz, S.: Invariant solutions of differential games and Hamilton–Jacobi equations for time-measurable Hamiltonians. SIAM J. Control Optim. 38, 1501–1520 (2000)
Delfour, M.C., Zolesio, J.P.: Shape analysis via oriented distance functions. J. Funct. Anal. 123, 129–201 (1994)
Delfour, M.C., Zolesio, J.P.: Oriented distance function and its evolution equation for initial sets with thin boundary. SIAM J. Control Optim. 42, 2286–2304 (2004)
Fleming, W.H., Rishel, R.W.: Deterministic and Stochastic Optimal Control. Applications of Mathematics. Springer, Berlin Heidelberg New York (1975)
Frankowska, H.: Optimal trajectories associated to a solution of contingent Hamilton–Jacobi equations. Appl. Math. Optim. 19, 291–311 (1989)
Frankowska, H., Plaskacz, S., Rzezuchowski, T.: Measurable viability theorems and the Hamilton–Jacobi–Bellman equation. J. Differential Equations 116, 265–305 (1995)
Frankowska, H., Plaskacz, S.: A measurable upper semicontinuous viability theorem for tubes. Nonlinear Anal. JMA 26, 565–582 (1996)
Frankowska, H., Rampazzo, F.: Filippov's and Filippov–Wazewski's theorems on closed domains. J. Differential Equations 161, 449–478 (2000)
Loreti, P., Tessitore, M.E.: Approximation and regularity results on constrained viscosity solutions of Hamilton–Jacobi–Bellman equations. J. Math. Systems Estim. Control 4, 467–483 (1994)
Rockafellar, R.T.: Convex analysis. Princeton Mathematical Series, No. 28. Princeton University Press, Princeton, New Jersey (1970)