Needle variations and almost lower semicontinuous differential inclusions

Set-Valued Analysis

Volumn 10, Issue 2-3, 2002, Pages 233-285

  Sussmann, Héctor J ^a  

^a RUTGERS UNIVERSITY   (United States)

Author keywords

Almost lower semicontinuous differential inclusions; Needle variations

Indexed keywords

EID: 0141792105     PISSN: 09276947     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1016540217523     Document Type: Article

References (16)

1. Bressan, A.: On differential relations with lower continuous right-hand side. An existence theorem, J. Differential Equations 37 (1980), 89-97.
2. Bressan, A.: Solutions of lower semicontinuous differential inclusions on closed sets, Rend. Sem. Mat. Univ. Padova 69 (1983), 99-107.
3. Bressan, A.: Directionally continuous selections and differential inclusions, Funkcial. Ekvac. 31 (1988), 459-470.
4. Bressan, A.: On the qualitative theory of lower semicontinuous differential inclusions, J. Differential Equations 77 (1989), 379-391.
5. Bressan, A.: Upper and lower semicontinuous differential inclusions: A unified approach, In: H. J. Sussmann (ed.), Nonlinear Controllability and Optimal Control, M. Dekker Inc., New York, 1990, pp. 21-31.
6. Cambini, A. and Querci, S.: Equazione differenziale del primo ordine con secondo membro discontinuo rispetto all'incognita, Rend. Istit. Mat. Univ. Trieste 1 (1969), 89-97.
7. Pucci, A.: Sistemi di equazioni differenziali con secondo membro discontinuo rispetto all'incognita, Rend. Istit. Mat. Univ. Trieste 3 (1971), 75-80.
8. Pontryagin, L. S., Boltyanskii, V. G., Gamkrelidze, R. V. and Mischenko, E. F.: The Mathematical Theory of Optimal Processes, Wiley, New York, 1962.
9. Sussmann, H. J.: A strong version of the Łojasiewicz Maximum Principle, In: Nicolai H. Pavel (ed.), Optimal Control of Differential Equations, Athens, OH, 1993, Lecture Notes in Pure and Appl. Math. 160, Marcel Dekker Inc., New York, 1994, pp. 293-309.
10. Sussmann, H. J.: A strong maximum principle for systems of differential inclusions, In: Proc. 35th IEEE Conference on Decision and Control, Kobe, Japan, Dec. 1996, IEEE publications, New York, 1996, pp. 1809-1814.
11. Sussmann, H. J.: Multidifferential calculus: Chain rule, open mapping and transversal intersection theorems, In: W. W. Hager and P. M. Pardalos (eds), Optimal Control: Theory, Algorithms, and Applications, Kluwer Academic Publishers, 1998, pp. 436-487.
12. Sussmann, H. J.: Geometry and optimal control, In: J. Baillieul and J. C. Willems (eds), Mathematical Control Theory, Springer-Verlag, New York, 1998, pp. 140-198.
13. Sussmann, H. J.: Transversality conditions and a strong maximum principle for systems of differential inclusions, In: Proc. 37th IEEE Conference on Decision and Control, Tampa, FL, Dec. 1998, IEEE publications, 1998, pp. 1-6.
14. Sussmann, H. J.: A nonsmooth hybrid maximum principle, In: D. Aeyels, F. Lamnabhi-Lagarrigue and A. J. van der Schaft (eds), Stability and Stabilization of Nonlinear Systems, Ghent, Belgium, 1999, Lecture Notes in Control and Inform. Sci. 246, Springer-Verlag, 1999, pp. 325-354.
15. Sussmann, H. J.: Résultats récents sur les courbes optimales, In: Quelques aspects de la théorie du contrôle, Journée annuelle de la Société Mathématique de France, Paris, June 2000, pp. 1-50.
16. Sussmann, H. J.: New theories of set-valued differentials and new versions of the maximum principle of optimal control theory, In: A. Isidori, F. Lamnabhi-Lagarrigue and W. Respondek (eds), Nonlinear Control in the Year 2000, Springer-Verlag, 2000, pp. 487-526.