Contingent derivatives and regularization for noncoercive inverse problems

Abstract

We study the inverse problem of parameter identification in noncoercive variational problems that commonly appear in applied models. We examine the differentiability of the set-valued parameter-to-solution map using the first-order and the second-order contingent derivatives. We explore the inverse problem using the output least-squares and the modified output least-squares objectives. By regularizing the noncoercive variational problem, we obtain a single-valued regularized parameter-to-solution map and investigate its smoothness and boundedness. We also consider optimization problems using the output least-squares and the modified output least-squares objectives for the regularized variational problem. We give a complete convergence analysis showing that for the output least-squares and the modified output least-squares, the regularized minimization problems approximate the original optimization problems suitably. We also provide the first-order and the second-order adjoint method for the computation of the first-order and the second-order derivatives of the output least-squares objective. We provide discrete formulas for the gradient and the Hessian calculation and present numerical results.     

考虑完全拆分的拣选分批与拣选路径集成优化模型

在电商海量订单背景下,在线订单拣选作业难度加大,因此设计了基于订单完全拆分的拣选分批与拣选路径综合优化模型解决此问题.模型共分两阶段.第一阶段,基于种子算法,设计考虑订单完成度、等待时间与拣选路径的拣选分批模型;第二阶段以拣选单流为单队列,设计多拣选员并行服务的拣选系统.行走策略为基于返回型和遍历型的综合策略,拣选路径优化模型采用模拟退火算法求解.算例分析表明,与传统的不拆分拣选分批模型相比,构建的综合优化模型能够显著提高拣选系统效率.拣选员为4人时,模型能够使总服务时间减少58.79%,订单完成率提高10.09%.     

面向装配节点平衡的产品生产物流协调优化研究

在由多个并行零件生产线和装配线组成的产品生产物流中, 各生产线的瓶颈工序制约了装配节点及其整个生产物流的平衡. 为此, 基于约束理论和JIT(Just In Time)思想, 提出主、次瓶颈的概念及其判别方法和主瓶颈拉动次瓶颈、瓶颈前后拉动生产与平行顺序移动生产相结合的生产策略, 研究了基于负荷率的瓶颈工序负荷控制方法和主瓶颈触发次瓶颈拉式生产的时间控制方法, 使瓶颈工序利用率最大化, 各个零件到达装配节点的同步性得到改善. 算例的SIMIO仿真结果表明, 装配节点的在制品存量大幅度减少, 利用率提高.     

Eu:Lu2O3透明闪烁陶瓷的制备与性能

采用湿化学法合成了Eu原子掺量5%的Lu₂O₃陶瓷前驱体,通过SEM、XRD研究了煅烧前后前驱体和1 100 ℃煅烧4 h后粉体的形貌、结构以及物相。结果表明煅烧后的粉体为纳米类球形、高分散且结晶性良好的颗粒。颗粒尺寸为68.5 nm。使用煅烧后的粉体为原料,在1 650 ℃真空烧结30 h制备了高透过率的Eu:Lu₂O₃陶瓷,晶粒尺寸为46 μm,在611 nm处的直线透过率可以达到66.3%。此外对陶瓷的吸收曲线、光致激发和发射光谱特性以及X射线激发发射光谱进行研究。可观察到,Eu:Lu₂O₃陶瓷存在基质和激活离子两类吸收,光致发光光谱和X射线激发发射光谱均可以看出Eu:Lu₂O₃陶瓷存在极强的⁵D₀→⁷F₂跃迁发光,位于611 nm处。对比商业的BGO单晶的X射线发射光谱,可得本实验中制备的陶瓷的光输出为85 000 ph/MeV。Eu:Lu₂O₃陶瓷本身有着高X射线以及高能粒子的阻止能力,结合高光输出特性,表明Eu:Lu₂O₃陶瓷在X射线成像等领域具有巨大的潜在应用价值。     

放射性废物微波处理装置有效输出功率的测定

以微波为热源处理放射性废物的相关技术和装备的研究,在国外已经达到较高水平,在我国的相关研究较少。微波加热即物料在微波场中吸收消耗微波能量,并转化为热能用于物料温度升高。对于物料的处理效果主要与微波的有效输出功率有关。参考Schillman法测定了包括放射性废物微波处理装置的微波炉的有效输出功率,且经验证测定结果准确。微波有效输出功率的确定将对放射性废物微波处理工艺的研究打下基础。     

Resilient dissipative dynamic output feedback control for uncertain Markov jump Lur’e systems with time-varying delays

The resilient dissipative dynamic output feedback control problem for a class of uncertain Markov jump Lur’e systems with piecewise homogeneous transition probabilities and time-varying delays in the discrete-time domain are examined in this study. The designed controller can tolerate additive uncertainties in the controller gain matrix, which result from controller implementations. The time-varying delays are also supposed to be mode-dependent with lower and upper bounds known a priori. By constructing a Lyapunov–Krasovskii functional candidate, the sufficient conditions regarding the existence of desired resilient dissipative controllers are obtained in terms of linear matrix inequalities, thereby ensuring that the resulting closed-loop system is stochastically stable and strictly dissipative. Two numerical examples were established to illustrate the effectiveness of the proposed theoretical results.     

Terminal constrained robust hybrid iterative learning model predictive control for complex time-delayed batch processes

This work mainly addresses terminal constrained robust hybrid iterative learning model predictive control against time delay and uncertainties in a class of complex batch processes with input and output constraints. In this work, an equivalently novel extended two-dimensional switched system is first constructed to represent the process model by introducing state difference, output error and new relaxation variable information. Then, a hybrid predictive updating controller is proposed and an optimal performance index function including terminal constraints is designed. Under the condition that the switching signal meets certain conditions, the solvable problem of model predictive control is realized by Lyapunov stability theory. Meanwhile, the design scheme of controller parameters is also given. In addition, the robust constraint set is adopted to overcome the disadvantage that the traditional asymptotic stability cannot converge to the origin when it involves disturbances, such that the system state converges to the constraint set and meets its expected value. Finally, the effectiveness of the proposed algorithm is verified by controlling the speed and pressure parameters of the injection molding process.