On the extension of classical calculus of variations and optimal control to problems with discontinuous trajectories
作者： Aram Arutyunov , Dmitry Karamzin , Fernando Pereira , None
关键词: Extension (predicate logic) 、 Calculus of variations 、 Control (linguistics) 、 Type (model theory) 、 Calculus 、 Optimal control 、 Mathematics
摘要: In this article, we present a proper extension of the problems classical calculus variations and optimal control to case discontinuous trajectories. An appropriate impulsive problem is introduced as result such extension. Existence theorems are proved under assumptions Filippov type.
sci-hub.se 参考文章(8)
R. B. Vinter, F. M. F. L. Pereira, A Maximum Principle for Optimal Processes with Discontinuous Trajectories SIAM Journal on Control and Optimization. ,vol. 26, pp. 205- 229 ,(1988) , 10.1137/0326013
B. Sh. Mordukhovich, Existence of optimum controls (Appendix to the article by Gabasov and Kirillova, ?methods of optimum control?) Journal of Soviet Mathematics. ,vol. 7, pp. 850- 886 ,(1977) , 10.1007/BF01084357
Raymond W. Rishel, An Extended Pontryagin Principle for Control Systems whose Control Laws Contain Measures Journal of the Society for Industrial and Applied Mathematics Series A Control. ,vol. 3, pp. 191- 205 ,(1965) , 10.1137/0303016
Arthur Stoddart, Existence of optimal controls Pacific Journal of Mathematics. ,vol. 20, pp. 167- 177 ,(1967) , 10.2140/PJM.1967.20.167
A. V. Arutyunov, D. Yu. Karamzin, F. L. Pereira, On constrained impulsive control problems Journal of Mathematical Sciences. ,vol. 165, pp. 654- 688 ,(2010) , 10.1007/S10958-010-9834-Z
A. Arutyunov, D. Karamzin, F. Pereira, A Nondegenerate Maximum Principle for the Impulse Control Problem with State Constraints Siam Journal on Control and Optimization. ,vol. 43, pp. 1812- 1843 ,(2005) , 10.1137/S0363012903430068
D. Yu. Karamzin, Necessary conditions of the minimum in an impulse optimal control problem Journal of Mathematical Sciences. ,vol. 139, pp. 7087- 7150 ,(2006) , 10.1007/S10958-006-0408-Z
G. N. Silva, R. B. Vinter, Necessary Conditions for Optimal Impulsive Control Problems Siam Journal on Control and Optimization. ,vol. 35, pp. 1829- 1846 ,(1997) , 10.1137/S0363012995281857