Variational Analysis of Controlled Sweeping Processes

被引：0
作者：
B. S. Mordukhovich [1 ]
机构：
[1] Department of Mathematics, Wayne State University, Detroit, MI
来源：
Siberian Mathematical Journal | 2025年 / 66卷 / 2期
基金：
美国国家科学基金会; 澳大利亚研究理事会;
关键词：
517.988; discontinuous and dissipative differential inclusions; discrete approximations; existence and uniqueness of solutions; necessary optimality conditions; optimal control; sweeping processes;
D O I：
10.1134/S0037446625020211
中图分类号：
学科分类号：
摘要：
This paper is mainly a survey of some recent developments and applications of advanced variational analysis to a class of controlled dynamical systems governed by discontinuous dissipative differential inclusions that are known as sweeping processes. Our first topic here concerns the well-posedness of sweeping processes in Hilbert spaces with controlled polyhedral moving sets. Then we formulate novel classes of optimal control problems for constrained sweeping dynamics with free time and provide necessary optimality conditions for local minimizers in the case of finite-dimensional state spaces. Our approach is based on new versions of the method of discrete approximations of their own interest with employing appropriate tools of first-order and second-order variational analysis and generalized differentiation. © Pleiades Publishing, Ltd. 2025.
引用
收藏
页码：560 / 575
页数：15
相关论文
共 69 条
[1]  
Moreau J.J., Rafle par un convexe variable. I,, Travaux du Séminaire d’Analyse Convexe. Vol. I. Exp. no. 15, Univ. Sci. Tech. Languedoc, Montpellier (1971), 1–43
[2]  
Moreau J.J., Rafle par un convexe variable. II,, Travaux du Séminaire d’Analyse Convexe. Vol. II. Exp. no. 3, Univ. Sci. Tech. Languedoc, Montpellier (1972), 1–36
[3]  
Moreau J.J., Evolution problem associated with a moving convex set in a Hilbert space, J. Differential Equations, 26, 3, pp. 347-374, (1977)
[4]  
Adly S., A Variational Approach to Nonsmooth Dynamics. Applications in Unilateral Mechanics and Electronics, (2018)
[5]  
Adly S., Haddad T., Thibault L., Convex sweeping process in the framework of measure differential inclusions and evolution variational inequalities, Math. Program. Ser. B, 148, 1, pp. 5-47, (2014)
[6]  
Bounkhel M., Mathematical modeling and numerical simulations of the motion of nanoparticles in straight tube, Adv. Mech. Eng, 8, pp. 1-6, (2016)
[7]  
Brogliato B., Nonsmooth Mechanics, (2016)
[8]  
Brogliato B., Tanwani A., Dynamical systems coupled with monotone set-valued operators: formalisms, applications, well-posedness, and stability, SIAM Rev, 62, 1, pp. 3-129, (2020)
[9]  
Brokate M., Krejci P., Optimal control of ODE systems involving a rate independent variational inequality, Discrete Contin. Dyn. Syst. Ser. B, 18, 2, pp. 331-348, (2013)
[10]  
Colombo G., Thibault L., Prox-regular sets and applications, Handbook of Nonconvex Analysis, pp. 99-182, (2010)
1234567