Necessary optimality conditions for differential-difference inclusions

Nonlinear Analysis, Theory, Methods and Applications

Volumn 35, Issue 3, 1999, Pages 307-322

  Minchenko, Leonidi ^a  

^a BELARUSIAN STATE UNIVERSITY OF INFORMATICS AND RADIOELECTRONICS   (Belarus)

Author keywords

Differential inclusion; Maximum principle; Multifunction; Optimal control

Indexed keywords

CLOSED LOOP CONTROL SYSTEMS; DIFFERENCE EQUATIONS; DIFFERENTIAL EQUATIONS; FUNCTIONS; MATRIX ALGEBRA; MAXIMUM PRINCIPLE; OPTIMAL CONTROL SYSTEMS; PROBLEM SOLVING; THEOREM PROVING;

DIFFERENTIAL DIFFERENCE INCLUSIONS; MULTIFUNCTION;

OPTIMIZATION;

EID: 0033078383     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(97)00630-5     Document Type: Article

References (20)

1. J.-P. Aubin, I. Ekeland, Applied Nonlinear Analysis, Wiley-Interscience, New York, 1984.
2. J.-P. Aubin, H. Frankowska, Set-Valued Analysis, Birkhäuser, Boston, 1990.
3. F.H. Clarke, Optimization and Nonsmooth Analysis, Wiley-Interscience, New York, 1983.
4. Clarke F.H. Optimal solutions to differential inclusions. J. Optim. Theory Appl. 19:1976;469-478.
5. Clarke F.H., Watkins G.G. Necessary conditions, controllability and the value function for differential-difference inclusions. Nonlinear Anal. Theory Meth. Appl. 10:1986;1155-1179.
6. Filippov A.F. Classical solutions of differential equations with multi-valued right-hand side. SIAM J. Control Optim. 5:1967;609-621.
7. Frankowska H. The maximum principle for an optimal solution to a differential inclusion with end points constraints. SIAM J. Control Optim. 25:1987;145-157.
8. Hiriart-Urruty J.-B. New concepts in nondifferential programming. Bull. Soc. Math. France Mem. 60:1979;57-85.
9. A.D. Ioffe, V.M. Tikhomirov, Theory of Extremal Problems, North-Holland, Amsterdam, 1979.
10. Kharatishvili G.L. Maximum principle in the theory of optimum time-delay processes. Dokl. Akad. Nauk USSR. 136:1961;39-42.
11. P.-J. Laurrent, Approximation et Optimization, Hermann, Paris, 1972.
12. Loewen P.D., Rockafellar R.T. Optimal control of unbounded differential inclusions. SIAM J. Control Optim. 32:1994;442-470.
13. Kaskosz B., Lojasiewicz S. Lagrange-type extremal trajectories in differential inclusions. Systems Control Lett. 19:1992;241-247.
14. Minchenko L.I. Optimal trajectories of differential inclusions in a problem with constraints on the ends of the trajectories. Differential Equations. 26:1990;1119-1126.
15. Minchenko L.I., Tesluk V.N. On controllability of convex processes with delay. J. Optim. Theory Appl. 86:1995;191-197.
16. Mordukhovich B. Discrete approximations and refined euler-lagrange conditions for nonconvex differential inclusions. SIAM J. Control Optim. 33:1995;882-915.
17. B. Mordukhovich, Approximation Methods in Problems of Optimization and Control, Nauka, Moscow, 1988. (Russian; English transl. Wiley-Interscience, to appear.).
18. Polovinkin E.S., Smirnov G.V. An approach to differentiation of multifunctions and necessary optimality conditions for differential inclusions. Differential Equations. 22:1986;660-668.
19. B.N. Pshenichnyi, Convex Analysis and Extremal Problems, Nauka, Moscow, 1980.
20. R.T. Rockafellar, Convex Analysis, Prinston University Press, Priston, New Jersey, 1970.