TIME AND NORM OPTIMAL CONTROLS:A SURVEY OF RECENT RESULTS AND OPEN PROBLEMS
TIME AND NORM OPTIMAL CONTROLS:A SURVEY OF RECENT RESULTS AND OPEN PROBLEMS
摘要
We present in this paper a survey of recent results on the relation between time and norm optimality for linear systems and the infinite dimensional version of Pontryagin＇s maximum principle. In particular, we discuss optimality （or nonoptimality） of singular controls satisfying the maximum principle and smoothness of the costate in function of smoothness of the target.
We present in this paper a survey of recent results on the relation between time and norm optimality for linear systems and the infinite dimensional version of Pontryagin＇s maximum principle. In particular, we discuss optimality （or nonoptimality） of singular controls satisfying the maximum principle and smoothness of the costate in function of smoothness of the target.
参考文献24
-
1Bellman R E, Glicksberg I, Gross O A. On the "bang-bang" control problem. Quart Appl Math, 1956, 14:11-18.
-
2Bellman R E. Dynamic Programming. Princeton: Princeton University Press, 1957.
-
3Boltyanski V G, Gamkrelidze R V, Pontryagin L S. On the theory of optimal processes. Dokl Akad Nauk SSSR, 1956, 110:7-10.
-
4Boltyanskii V G. Sufficient conditions for optimality and the justification of the dynamic programmiilg method. SIAM J Control, 1966, 4:326-361.
-
5Cannarsa P, Carja O. on the Bellman equation for the minimum time problem in infinite dimensions. SIAM J Contr Opt, 20041 43:532-548.
-
6Carja O. The minimal time function in infinite dimension. SIAM J Contr Opt, 1993, 31:1103-1114.
-
7Carja O. On the minimum time function and the minimum energy problem; a nonlinear case. Syst Contr Lett, 2006, 55:543-548.
-
8Carja O, Lazu A. On the minimal time null controllability of the heat equation. Discrete Contin Dyn Syst, Proc 7th AIMS Conference on Dynamical Systems, Differential Equations and Applications, 2009: 143-150.
-
9Fattorini H O. Time-optimal control of solutions of operational differential equations. SIAM J Contr, 1964, 2:54-59.
-
10Fattorini H O. The maximum principle in infinite dimension. Discrete Contin Dyn Syst, 2000, 6:557-574.
-
1邓子辰,钟万勰.奇异控制本征值问题的研究[J].西北工业大学学报,1998,16(1):75-78. 被引量：1
-
2龙冬阳.关于一个Open问题的一些结果[J].中山大学学报（自然科学版）,1990,29(2):123-124.
-
3朱浸华,吴文权.向序半群同时添加单位元和最大元[J].四川师范大学学报（自然科学版）,2003,26(1):17-19. 被引量：2
-
4徐大川.BFGS算法对非凸函数优化问题的收敛性(英文)[J].运筹学学报,2000,4(2):71-74. 被引量：2
-
5Alberto CAVICCHIOLI(Department Of Mathematics,University of Modena,Via Campi 213/B, 41100 Modena, Italy,)Dusan REPOVS(Institute for Mathematics, Physics and Mechanics,University of Ljubljana,P. O. Box 64, Ljubljana 61111,Slovenia.Some Open Problems in Geometric Topologyof Low Dimensions[J].Chinese Quarterly Journal of Mathematics,1995,10(4):8-14.
-
6唐恒永,赵琨.资源有限的加权总完工时间单机排序问题[J].运筹与管理,2004,13(3):48-51. 被引量：2
-
7钟万勰,程耿东.奇异控制正则化及刚度移置法[J].信息与控制,1991,20(4):21-26. 被引量：4
-
8沈传龙,黄允宝.关于C~∞─字的幂[J].高校应用数学学报（A辑）,1994,9(4):449-452. 被引量：6
-
9游兆永,徐洪坤.On a Problem of Van Dulst[J].Chinese Quarterly Journal of Mathematics,1990,5(1):11-13.
-
10王帮海.量子逻辑的发展及其理论基础[J].现代计算机,2009,15(8):11-13.
