一种求解最优控制问题的变时间节点控制向量参数化方法

控制向量参数化方法是求解最优控制问题的一种常用数值方法。它通过离散化控制时域,将控制向量近似地表示成一组参数化的函数。离散化后的时间网格通常是固定的,其划分会影响到最优控制问题数值求解的精度和效率。为了同时优化控制参数和时间网格节点,提出了一种时间节点可变的控制向量参数化方法。推导出了最优控制性能指标对时间参数的导数与对时间分段长度导数之间的关系,得到了性能指标的梯度表达式。用两个经典最优控制实例对所提出的方法进行了测试,结果表明所提出方法能够更好地逼近最优控制轨迹。     

一种基于伪Wigner-Ville分析的动态优化问题网格重构策略

为了解决控制向量参数化方法逼近精度和计算时间之间的矛盾,提出了一种基于伪Wigner-Ville时频分析的控制向量参数化方法。该方法首先给定较少的网格进行第一次优化迭代,快速获得控制变量的大致轨迹。然后通过伪Wigner-Ville分析得出不同时间网格节点瞬时频率变化对性能指标的影响,籍此对原有网格节点进行重构,包括对时间节点的消除、细化。并且结合变时间节点控制向量参数化方法的思想,将瞬时频率为极大值时对应的时间节点作为待优化参数,与控制变量一同进行求解优化,从而找到准确的最优时间切换点。三个经典的化工反应实例用于验证所提方法,计算结果表明:与传统的控制向量参数化方法和文献结果相比,所提方法可以更有效地重构时间网格,找到准确的时间切换点,不仅计算成本低,而且计算精度更出色。     

一种基于伪Wigner-Ville分析的动态优化问题网格重构策略

为了解决控制向量参数化方法逼近精度和计算时间之间的矛盾，提出了一种基于伪Wigner-Ville时频分析的控制向量参数化方法。该方法首先给定较少的网格进行第一次优化迭代，快速获得控制变量的大致轨迹。然后通过伪Wigner-Ville分析得出不同时间网格节点瞬时频率变化对性能指标的影响，籍此对原有网格节点进行重构，包括对时间节点的消除、细化。并且结合变时间节点控制向量参数化方法的思想，将瞬时频率为极大值时对应的时间节点作为待优化参数，与控制变量一同进行求解优化，从而找到准确的最优时间切换点。三个经典的化工反应实例用于验证所提方法，计算结果表明：与传统的控制向量参数化方法和文献结果相比，所提方法可以更有效地重构时间网格，找到准确的时间切换点，不仅计算成本低，而且计算精度更出色。     

基于PSO-控制变量参数化混合策略的间歇化工过程优化控制

控制变量参数化方法作为一种化工过程动态优化的梯度搜索算法,其求解效率过于依赖初始给定轨迹。目前初始轨迹一般都是设定在边界值或中间值,缺乏科学依据,从而大大影响了算法的收敛速度。针对这一问题,提出了一种粒子群优化(PSO)与控制变量参数化方法混合的策略,首先利用粒子群优化对间歇化工过程最优控制量进行求解,结果作为控制变量参数化方法初始给定轨迹,进行二次优化。双层优化的混合策略提高了控制变量参数化方法的收敛速度和粒子群优化算法的求解精度。将混合策略应用于两个间歇化工过程优化控制实例,仿真结果表明了该算法对求解化工过程动态优化问题具有可行性和有效性。     

基于PSO-控制变量参数化混合策略的间歇化工过程优化控制

控制变量参数化方法作为一种化工过程动态优化的梯度搜索算法，其求解效率过于依赖初始给定轨迹。目前初始轨迹一般都是设定在边界值或中间值，缺乏科学依据，从而大大影响了算法的收敛速度。针对这一问题，提出了一种粒子群优化(PSO)与控制变量参数化方法混合的策略，首先利用粒子群优化对间歇化工过程最优控制量进行求解，结果作为控制变量参数化方法初始给定轨迹，进行二次优化。双层优化的混合策略提高了控制变量参数化方法的收敛速度和粒子群优化算法的求解精度。将混合策略应用于两个间歇化工过程优化控制实例，仿真结果表明了该算法对求解化工过程动态优化问题具有可行性和有效性。     

基于锚节点等边三角形分布的质心定位算法研究

针对正六边形网格定位算法定位误差不均匀和正方形网格定位算法冗余节点过多等问题,提出了一种新的基于锚节点等边三角形分布的质心定位算法.该算法运用网格划分理论,验证这种网格划分的合理性;通过实验,探索各项参数对于这种新算法的影响.仿真结果表明,该算法在结构简单、硬件投入和功耗相对较少的情况下,提高了节点定位的精确度.但该算法在锚节点数量和计算量上都有所增加,有待下一步改进.     

平行反应的近似最佳温度控制

本文讨论了Pontryagin极大(极小)值原理及控制向量参数化两种方法来求取近似最佳温度控制,提高平行反应主产品产率,控制向量参数化方法较简单,计算量少,对一般化学反应器的最佳控制均能适用。     

塑料制件最大流长比算法研究与应用

提出了计算塑料制件最大流长比(流动长度与厚度的比值)的算法。该算法利用三角形网格模型表示复杂制件的中面模型，通过对三角单元的带权边进行细分，由细分得到的点、边和原三角网格模型上的节点构成带权图G，采用快速最短路径法(FSPA)动态计算带权图上两点的最短路径，从而得到制件上由一点到任意点的最短路径值即流长比。该算法效率高，容易实现，可通过改善网格质量和调整细分参数γ控制近似精度。给出了该算法的两个应用实例。     

气体辅助注射成型气道网格算法

根据气体辅助注射成型的特点,在塑件表面三角形网格的基础上,提出了手工拟合气道路径和自动求解气道节点相结合的方法生成气道网格,并给出了求解多边形最大内切圆的气道网格算法和优化气道网格的算法,通过软件应用和实例分析,证明所提出的算法是行之有效的。该算法为气体辅助注射成型模拟分析的数值计算提供了依据。     

基于自适应粒子群优化算法的预测控制算法及其在加热炉支管平衡中的应用

多变量和输出受限系统的预测控制问题一般表现为一个不易直接求解的多变量且多约束的非线性动态规划问题.传统优化方法在解决此优化问题时,存在易收敛到非法解或局部极小、计算时间长以及对模型参数与初值依赖性强的缺点.提出了一种基于自适应粒子群优化的预测控制算法(APSO-DMC),采用自适应粒子群优化算法(APSO)作为模型预测控制的优化方法,在线实时求解最优控制律,从而有效地克服了传统优化方法的不足.将此算法应用于常减压装置加热炉支管温度平衡控制中,仿真试验结果显示了该方法的有效性.     

Optimization for ASP flooding based on adaptive rationalized Haar function approximation

This paper presents an adaptive rationalized Haar function approximation method to obtain the optimal injection strategy for alkali-surfactant-polymer (ASP) flooding. In this process, the non-uniform control vector parameterization is introduced to convert original problem into a multistage optimization problem, in which a new normalized time variable is adopted on the combination of the subinterval length. Then the rationalized Haar function approximation method, in which an auxiliary function is introduced to dispose path constraints, is used to transform the multistage problem into a nonlinear programming. Furthermore, an adaptive strategy proposed on the basis of errors is adopted to regulate the order of Haar function vectors. Finally, the nonlinear programming for ASP flooding is solved by sequential quadratic programming. To illustrate the performance of proposed method, the experimental comparison method and control vector parameterization (CVP) method are introduced to optimize the original problem directly. By contrastive analysis of results, the accuracy and efficiency of proposed method are confirmed.     

分批补料反应过程的非固定终端经济优化控制

针对批次生产周期不确定问题,提出一种非固定终端的经济优化控制方法。首先采用经济模型预测控制方法,用收益最大化的经济型目标函数代替终端约束,并将批次生产周期纳入被优化变量,建立动态经济优化问题,并通过对每个控制变量进行有差异的参数化,将动态优化问题转化为非线性规划（NLP）问题;然后使用内点罚函数法求解含非线性约束的优化问题,得到的最优控制序列和最佳批次生产周期,可将不确定扰动带来的损失降低到最小。其次采用非固定预测时域的滚动时域控制方法,不仅提高多变量系统的协同控制能力,而且根据实时预测终端产品产量不断优化更新关键操纵变量的控制分段函数的分割数及控制序列,从而可灵活优化操纵变量和操作时间的轨迹。最后在苯胺加氢过程上进行了批次优化控制性能测试,测试结果表明,非固定终端的经济优化控制从批次的总生产效益角度来优化每个批次生产的操作条件,实现批次反应过程生产时间与经济效益的最优化管理。     

Control Vector Parameterization‐Based Adaptive Invasive Weed Optimization for Dynamic Processes

A novel optimal approach named invasive weed optimization‐control vector parameterization (IWO‐CVP) for chemical dynamic optimization problems is proposed where CVP is used to transform the problem into a nonlinear programming (NLP) problem and an IWO algorithm is then applied to tackle the NLP problem. To improve efficiency, a new adaptive dispersion IWO‐based approach (ADIWO‐CVP) is further suggested to maintain the exploration ability of the algorithm throughout the entire searching procedure. Several classic chemical dynamic optimization problems are tested and detailed comparisons are carried out among ADIWO‐CVP, IWO‐CVP, and other methods. The research results demonstrate that ADIWO‐CVP not only is efficient, but also outperforms IWO‐CVP in terms of both accuracy and convergence speed.     

基于差分进化算法的控制变量参数化方法及其在化工过程动态优化中的应用(英文)

Two general approaches are adopted in solving dynamic optimization problems in chemical processes, namely, the analytical and numerical methods. The numerical method, which is based on heuristic algorithms, has been widely used. An approach that combines differential evolution (DE) algorithm and control vector parameterization (CVP) is proposed in this paper. In the proposed CVP, control variables are approximated with polynomials based on state variables and time in the entire time interval. Region reduction strategy is used in DE to reduce the width of the search region, which improves the computing efficiency. The results of the case studies demonstrate the feasibility and efficiency of the proposed methods.     

OPTIMAL CONTROL BY EVOLUTIONARY ALGORITHM TECHNIQUE COMBINED WITH SPLINE APPROXIMATION METHOD

Optimal control problems are notoriously difficult to solve analytically or numerically except for limited cases of simple dynamics. Evolutionary algorithms are a promising method of solving various optimal control problems arising in practice since they do not require the expression of Lagrange's adjoint system and can easily implement the inequality constraints on the control variable. In this article, the evolutionary algorithm method is combined with the spline method so that the smooth control profile and switching time of bang-bang control could be obtained simultaneously. The optimal profiles obtained by the proposed method are compared with exact solutions if available. The proposed method could solve the problems only if there are only model equations and performance index functions, and even then the solution profiles are complicated. It is demonstrated that the evolutionary algorithm with the spline method can solve a wide range of optimal control problems including those of the bang-bang type.     

OPTIMAL CONTROL BY EVOLUTIONARY ALGORITHM TECHNIQUE COMBINED WITH SPLINE APPROXIMATION METHOD

Optimal control problems are notoriously difficult to solve analytically or numerically except for limited cases of simple dynamics. Evolutionary algorithms are a promising method of solving various optimal control problems arising in practice since they do not require the expression of Lagrange's adjoint system and can easily implement the inequality constraints on the control variable. In this article, the evolutionary algorithm method is combined with the spline method so that the smooth control profile and switching time of bang-bang control could be obtained simultaneously. The optimal profiles obtained by the proposed method are compared with exact solutions if available. The proposed method could solve the problems only if there are only model equations and performance index functions, and even then the solution profiles are complicated. It is demonstrated that the evolutionary algorithm with the spline method can solve a wide range of optimal control problems including those of the bang-bang type.     

Using Dynamic Optimization Technique to Study the Operation of Batch Reactors

How to apply the global optimization technique, simulated annealing, and to explore the operation of batch reactors is addressed in this study. Based on the operating purposes and the imposed constraints, the batch reactor operations are first formulated as two optimal control problems: the maximal yield (or conversion) problem and the minimal operating time problem. The problems are then converted into non‐linear programming problems by the concept of control vector parameterization. The converted problems are solved by the algorithm derived from simulated annealing to determine the optimal operating policy and the performance index. These results are useful in assessing design and operation of batch reactors. In this article, the CSTR model is used to demonstrate the convenience and robustness of the proposed algorithm. Two typical reaction models are used to discuss the operations based on the optimal solutions.