In this paper, we discuss virtual element method (VEM) approximation of optimal control problem governed by Brinkman equations with control constraints. Based on the polynomial projections and variational discretizati...In this paper, we discuss virtual element method (VEM) approximation of optimal control problem governed by Brinkman equations with control constraints. Based on the polynomial projections and variational discretization of the control variable, we build up the virtual element discrete scheme of the optimal control problem and derive the discrete first order optimality system. A priori error estimates for the state, adjoint state and control variables in L<sup>2</sup> and H<sup>1</sup> norm are derived. The theoretical findings are illustrated by the numerical experiments.展开更多
In this paper, we propose the nonconforming virtual element method (NCVEM) discretization for the pointwise control constraint optimal control problem governed by elliptic equations. Based on the NCVEM approximation o...In this paper, we propose the nonconforming virtual element method (NCVEM) discretization for the pointwise control constraint optimal control problem governed by elliptic equations. Based on the NCVEM approximation of state equation and the variational discretization of control variables, we construct a virtual element discrete scheme. For the state, adjoint state and control variable, we obtain the corresponding prior estimate in H<sup>1</sup> and L<sup>2</sup> norms. Finally, some numerical experiments are carried out to support the theoretical results.展开更多
随着化工行业朝着智能化方向发展,化工反应系统频繁遭受网络攻击,产生了严重的后果。现有工控安全仿真研究大多单独在网络领域进行,缺少针对化工反应系统的工控安全仿真技术。因此,针对该问题,以化工反应系统中常见的连续搅拌式反应釜(c...随着化工行业朝着智能化方向发展,化工反应系统频繁遭受网络攻击,产生了严重的后果。现有工控安全仿真研究大多单独在网络领域进行,缺少针对化工反应系统的工控安全仿真技术。因此,针对该问题,以化工反应系统中常见的连续搅拌式反应釜(continuous stirred tank reactor,CSTR)为研究对象,提出一种针对CSTR的工控安全虚实融合仿真技术。首先建立CSTR控制系统模型,提出了基于攻击类型分析、攻击仿真方法、响应分析方法与攻击监测和控制方法的工控安全虚实融合仿真技术框架,利用CSTR工控安全仿真平台,实现了针对CSTR系统的攻击模拟和响应分析,并验证了提出的针对网络攻击的监测和控制方法,为推动网络安全在化工领域内的研究提供了借鉴。展开更多
文摘In this paper, we discuss virtual element method (VEM) approximation of optimal control problem governed by Brinkman equations with control constraints. Based on the polynomial projections and variational discretization of the control variable, we build up the virtual element discrete scheme of the optimal control problem and derive the discrete first order optimality system. A priori error estimates for the state, adjoint state and control variables in L<sup>2</sup> and H<sup>1</sup> norm are derived. The theoretical findings are illustrated by the numerical experiments.
文摘In this paper, we propose the nonconforming virtual element method (NCVEM) discretization for the pointwise control constraint optimal control problem governed by elliptic equations. Based on the NCVEM approximation of state equation and the variational discretization of control variables, we construct a virtual element discrete scheme. For the state, adjoint state and control variable, we obtain the corresponding prior estimate in H<sup>1</sup> and L<sup>2</sup> norms. Finally, some numerical experiments are carried out to support the theoretical results.
文摘随着化工行业朝着智能化方向发展,化工反应系统频繁遭受网络攻击,产生了严重的后果。现有工控安全仿真研究大多单独在网络领域进行,缺少针对化工反应系统的工控安全仿真技术。因此,针对该问题,以化工反应系统中常见的连续搅拌式反应釜(continuous stirred tank reactor,CSTR)为研究对象,提出一种针对CSTR的工控安全虚实融合仿真技术。首先建立CSTR控制系统模型,提出了基于攻击类型分析、攻击仿真方法、响应分析方法与攻击监测和控制方法的工控安全虚实融合仿真技术框架,利用CSTR工控安全仿真平台,实现了针对CSTR系统的攻击模拟和响应分析,并验证了提出的针对网络攻击的监测和控制方法,为推动网络安全在化工领域内的研究提供了借鉴。
