An optimal control problem with a relaxed state constraint.

被引：0
|
作者：
Aseev, S. M. [1 ]
机构：
[1] Russian Acad Sci, Steklov Math Inst, RAS, Moscow 119991, Russia
来源：
TRUDY INSTITUTA MATEMATIKI I MEKHANIKI URO RAN | 2024年 / 30卷 / 03期
关键词：
optimal control; differential inclusion; Pontryagin's maximum principle; refined Euler-Lagrange inclusion; state constraint; discontinuous integrand; risk zone; MINIMAL TIME;
D O I：
10.21538/0134-4889-2024-30-3-14-29
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We explore an optimal control problem in the context of a specified open set representing "undesirable" system states. This problem statement is closely linked to the standard optimal control problem with a state constraint and can be viewed as a relaxation of the latter. The interrelation between these problems is examined. The recently derived necessary first-order optimality conditions for the discussed problem are presented. Additionally, an illustrative example is given.
引用
收藏
页码：14 / 29
页数：16
相关论文
共 50 条
  • [1] An Optimal Control Problem with a Relaxed State Constraint
    S. M. Aseev
    Proceedings of the Steklov Institute of Mathematics, 2024, 327 (Suppl 1) : S28 - S43
  • [2] An optimal synthesis for a triple integrator with a state constraint.
    Voronina, E. Yu.
    Dmitruk, A. V.
    TRUDY INSTITUTA MATEMATIKI I MEKHANIKI URO RAN, 2024, 30 (03): : 68 - 85
  • [3] Analysis of the Optimal Relaxed Control to an Optimal Control Problem
    Lou, Hongwei
    APPLIED MATHEMATICS AND OPTIMIZATION, 2009, 59 (01): : 75 - 97
  • [4] Analysis of the Optimal Relaxed Control to an Optimal Control Problem
    Hongwei Lou
    Applied Mathematics and Optimization, 2009, 59
  • [5] OPTIMAL MULTIPLEXING OF HETEROGENEOUS TRAFFIC WITH HARD CONSTRAINT.
    Nain, Philippe
    Ross, Keith W.
    Performance Evaluation Review, 1986, 14 (01): : 100 - 108
  • [6] Optimal Control Problem for Cahn–Hilliard Equations with State Constraint
    Jiashan Zheng
    Yifu Wang
    Journal of Dynamical and Control Systems, 2015, 21 : 257 - 272
  • [7] OPTIMAL CONTROL PROBLEM WITH TERMINAL STATE CONSTRAINT ON TIME SCALES
    Zhan, Z. D.
    Wei, W.
    Li, Y. F.
    PACIFIC JOURNAL OF OPTIMIZATION, 2012, 8 (02): : 387 - 404
  • [8] Integral constraint regularization method for fractional optimal control problem with pointwise state constraint
    Wang, Fangyuan
    Chen, Chuanjun
    Zhou, Zhaojie
    CHAOS SOLITONS & FRACTALS, 2024, 180
  • [9] Optimal Control Problem for Cahn-Hilliard Equations with State Constraint
    Zheng, Jiashan
    Wang, Yifu
    JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS, 2015, 21 (02) : 257 - 272
  • [10] FINITE ELEMENT APPROXIMATIONS OF AN OPTIMAL CONTROL PROBLEM WITH INTEGRAL STATE CONSTRAINT
    Liu, Wenbin
    Yang, Danping
    Yuan, Lei
    Ma, Chaoqun
    SIAM JOURNAL ON NUMERICAL ANALYSIS, 2010, 48 (03) : 1163 - 1185
12345