Menu: Home :: go to Journal :: switch to Russian :: switch to English
You are here: all Journals and Issues→ Journal→ Issue→ Article

ON INFINITE-HORIZON CONTROL PROBLEMS WITH LOCALLY LIPSHITZ CONTINUOUS VALUE FUNCTION

Annotation

The Pontryagin Maximum Principle is a necessary condition of optimality for infinite horizon control problems, however for these problems it can be degenerate. We announce that the Lipschitz continuity of the value function implies the normal form version of the Pontryagin Maximum Principle, moreover normal co-state arc becomes a gradient of value function.

Keywords

control problem; infinite horizon problem; necessary conditions of optimality; Pontryagin maximum principle; value function; shadow price; limiting gradient

Full-text in one file

Download

UDC

517.977.5

Pages

1507-1510

References

1. Halkin H. Necessary conditions for optimal control problems with infinite horizons // Econometrica. 1974. V. 42. P. 267-272. 2. Aseev S.M., Kryazhimskiy A.V. Printsip maksimuma Pontryagina i zadachi optimal'nogo ekonomicheskogo rosta // Tr. MIAN. 2007. T. 257. C. 3-271. 3. Pereira F.L., Silva G.N. Necessary conditions of optimality for state constrained infinite horizon differential inclusions // Decision and Control and European Control Conference (CDC-ECC). IEEE. 2011. P. 6717-6722. 4. Aubin J-P, Clarke F.H. Shadow Prices and Duality for a Class of Optimal Control Problems // SIAM J. Control Optim. 1979. V. 17 P. 567-586. 5. Sagara N. Value functions and transversality conditions for infinite-horizon optimal control problems // Set-Valued Var. Anal. 2010. V. 18. P. 1-28. 6. Seierstad A. Necessary conditions for nonsmooth, infinite-horizon optimal control problems // J. Optim. Theory Appl. 1999. V. 103. P. 201-230. 7. Aseev S.M., Besov K.O., Kryazhimskiy A.V. Zadachi optimal'nogo upravleniya na beskonechnom intervale vremeni v ekonomike // UMN. 2012. T. 67. № 2(404) S. 3-64. 8. Khlopin D.V. Necessity of vanishing shadow price in infinite horizon control problems // Journal of Dynamical and Control Systems. 2013. V. 19:4. P. 519-552. 9. Aseev S.M., Veliov V.M. Maximum principle for infinite-horizon optimal control problems under weak regularity assumptions // Tr. IMM UrO RAN. 2014. T. 20, № 3. S. 41-57. 10. Khlopin D.V. Necessity of limiting co-state arc in Bolza-type infinite horizon problem // Optimization. published online: 20 Oct 2014. (arXiv:1407.0498) 11. Michel P. On the transversality condition in infinite horizon optimal problems // Econometrica. 1982. V. 50. P. 975-984. 12. Ye J.J. Nonsmooth maximum principle for infinite-horizon problems // J. Optim. Theory Appl. 1993. V. 76. P. 485-500. 13. Khlopin D.V. O nevyrozhdennosti printsipa maksimuma v zadachakh upravleniya na beskonechnom promezhutke s lipshitsevoy funktsiey tseny // Tezisy dokladov II Mezhdunarodnogo seminara «Teoriya upravleniya i teoriya obobshchennykh resheniy uravneniy Gamil'tona-Yakobi» (CGS’2015), posvyashchennogo 70-letiyu so dnya rozhdeniya akademika A.I. Subbotina (Ekaterinburg, 1-3 aprelya 2015 goda), Ekaterinburg, IMM UrO RAN. C. 140-141. 14. Khlopin D.V. On Hamiltonian as limiting gradient in infinite horizon problem // arXiv preprint arXiv: 1503.00161 (2015). 15. Vinter R.B. Optimal Control. Boston: Birkh¨auser, 2000. 16. Subbotina N.N. The maximum principle and the superdifferential of the value function // Problems Control Inform. Theory. 18 (1989). № 3. P. 151–160. 17. Cannarsa P., Frankowska H. Some sharasterization of optimal trajestories in sontrol theory // SIAM J. Control and Optimization. 1991. V. 29. P. 1322-1347.

Received

2015-05-15

Section of issue

Scientific articles

Для корректной работы сайта используйте один из современных браузеров. Например, Firefox 55, Chrome 60 или более новые.