间歇过程的批内自优化控制

针对间歇过程的实时优化问题,提出了一种基于自优化控制的批内优化方法.以测量变量的线性组合为被控变量,在单批次内跟踪控制被控变量实现间歇过程的实时优化.根据是否在间歇过程的不同阶段切换被控变量,给出了两种自优化控制策略,对每种策略又分别提出两种设定轨线选取方案.为求解这些情形下的最优被控变量(组合矩阵),以最小化平均经济损失为目标,推导了组合矩阵和经济损失之间的函数关系,分别将其描述为相应的非线性规划问题.在此基础上,进一步引入了扩张组合矩阵,将这些非线性规划问题归纳为求解扩张组合矩阵的一致形式(扩张组合矩阵具有不同的结构约束),并推导得到了其中一种方案的解析解计算方法.以一个间歇反应器为研究对象,验证了方法的有效性.     

金氰化浸出过程的自优化控制

针对湿法冶金金氰化浸出过程的实时优化问题,提出一个自优化控制方案.基于系统的参数不确定模型,选择并求解输出变量的线性组合为被控变量,在反馈控制器作用下跟踪其恒定设定值,实现浸出过程在不确定性扰动下的自优化控制.仿真结果验证了该控制方案的有效性:扰动产生时,系统的经济指标在常规控制作用下得到改善,并最终运行于真实的最优点附近,提高了浸出过程的生产效益.     

基于RVM的非线性预测控制及在聚丙烯牌号切换中的应用

针对由被控对象非线性和优化目标函数非凸性带来的建模与实时优化问题求解的困难,提出一种基于相关向量机(RVM)的非线性多步模型预测控制算法.采用RVM建立非线性预测模型,并将差分进化算法引入非线性预测控制中发挥其伞局最优、鲁棒、快速收敛等优点,在线求解多变量、多约束的非线性规划问题.利用实际生产数据进行聚丙烯牌号切换仿真,结果表明,该算法可大幅度减少切换时间,降低过渡料产量,提高经济效益.     

加速分支定界算法在化工过程合成中的应用

在化工过程合成中,人们在确定研究系统的最大超结构后,通常采用混合整数非线性规划模型将其表达,而后通过计算机对该模型求解,从而找到最佳的流程结构.然而,近年来出现了1种新的求解过程,称为加速分支定界法(ABB),是在最大结构已知的基础上,采用分支定界法进行求解的思路.该算法克服了传统方法在处理整型变量时出现的麻烦,不需要建立复杂的混合整数非线性规划模型,就可以实现计算机自动寻找最优的过程流程,为快速有效地求解化工过程综合优化问题提供了1种新的途径.本文对分支定界法与加速分支定界法进行了详细比较,证实了ABB算法在实现自动寻找最优流程结构的合理性与可靠性.最后,以生化法制备丁醇、乙醇和丙酮的下游分离提纯为实例,研究了ABB算法在过程优化中的应用.结果表明,该算法克服了传统方法在处理整型变量时出现的麻烦,是1种快速有效地求解化工过程综合优化问题的新途径.     

求解动态优化问题的自组织进化算法

为在环境发生变化后跟踪最优解的变化,提出一种自组织单变量边缘分布算法(SOUMDA)来求解动态优化问题.自组织策略包含扩散和惯性速度模型,扩散模型利用当前环境的局部信息使群体向外扩散,惯性速度模型利用最优解的历史信息进行预测.将自组织策略与单变量边缘分布算法(UMDA)结合,使得算法在环境变化后自适应地增加种群多样性,提高算法适应能力,快速跟踪最优解.利用动态sphere函数对所提出的算法进行测试,并与UMDA和MUMDA算法进行比较,结果表明所设计的算法能快速适应环境的变化,跟踪最优解.     

双层结构预测控制研究进展

现代工业大系统的优化控制采用递阶结构,其中以预测控制为代表的先进过程控制已经成为重要的一级.目前,主流的工业预测控制技术均采用双层结构,即包含稳态优化层和动态控制层.双层结构预测控制技术可以有效解决复杂工业过程常见的多目标优化、多变量控制的难点问题.本文简要总结了双层结构预测控制的算法,并从控制输入与被控输出稳态关系入手分析了多变量预测控制稳态解的相容性和唯一性,说明了稳态优化的重要性.针对双层结构预测控制与区间预测控制的性能比较、稳态模型的奇异性以及闭环系统动态特性等提出了一些见解,并指出了需要重点研究的主题.     

解方程组的单神经元自适应控制微粒群算法

基于微粒群算法解决函数优化问题的优点,提出了使用微粒群算法求解方程组,并给出了求解方程组的通用模型.应用标准微粒群算法求解方程组容易陷入局部极值,导致方程组的解精度不高,并且算法具有较复杂的非线性特性.因此,将微粒群算法作为控制对象,引入单神经元控制器控制算法的惯性权重,将控制器具有的自学习、自适应能力和算法的全局优化特性相结合,用于方程组的求解.实验结果表明,该方法是有效可行的,适合于求解实际工程问题中的高非线性度方程组.     

含扩散项不可靠生产系统最优生产控制的数值求解

针对含扩散项不可靠随机生产系统最优生产控制的优化命题, 采用数值解方法来求解该优化命题最优控制所满足的模态耦合的非线性偏微分HJB方程. 首先构造Markov链来近似生产系统状态演化, 并基于局部一致性原理, 把求解连续时间随机控制问题转化为求解离散时间的Markov决策过程问题, 然后采用数值迭代和策略迭代算法来实现最优控制数值求解过程. 文末仿真结果验证了该方法的正确性和有效性.     

烟花算法求解非线性方程组

烟花算法是最近提出的一种效率较高的优化算法,已被用于求解众多的优化问题.给出利用烟花算法求解非线性方程组的方法.实验表明,所提出的算法对于求解变量耦合的非线性方程组比其他算法占有优势,进一步分析存在优势的原因.     

求解非线性方程组的蚁群算法

研究非线性方程组的求解问题,提高有效性。针对非线性方程数与变量数一致的非线性方程组问题,当方程组是一些强非线性方程组时,传统方法易导致失败,有效率低。为了提高求解强非线性方程组的求解效率,提出一种蚁群算法的求解方法。首先将方程组问题转化为函数优化问题,然后用全局搜索速度快的蚁群算法对函数进行求解,找到最优解,最后通过具体实例进行仿真研究,结果表明蚁群算法的有效性。     

一种基于Wiener模型的非线性预测控制算法

针对一类Wiener模型描述的非线性系统,提出了一种改进的非线性预测控制算法.该算法利用Laguerre函数描述Wiener模型动态线性部分的控制信号，将预测控制中在预测时域内优化求解未来控制输入序列转化为优化求解一组无记忆的Laguerre系数,以减少优化所需的计算量.利用静态模糊模型来逼近Wiener模型的非线性部分,将非线性预测控制优化问题转化为线性预测控制优化问题,克服了求控制输入时解非线性方程的困难,进而推导出了预测控制输入的解析式.CSTR过程的仿真结果表明了本文算法的有效性和可行性.     

用于间歇化工过程最优设计的遗传算法

间歇化工过程的最优设计问题是一类复杂且难以求解的组合优化问题。通过把这类问题分解为只包含离散变量的主导问题和只含连续变量的子问题,把遗传算法和线性规划法结合起来对其进行求解。并在算法中引入了一类新的算子,显著地提高了收敛概率、算例表明,该方法可以避免直接求解过程的复杂性和困难,并且具有很好的全局收敛性。     

A Computational Method for Stochastic Optimal Control Problems in Financial Mathematics

Principle of optimality or dynamic programming leads to derivation of a partial differential equation (PDE) for solving optimal control problems, namely the Hamilton‐Jacobi‐Bellman (HJB) equation. In general, this equation cannot be solved analytically; thus many computing strategies have been developed for optimal control problems. Many problems in financial mathematics involve the solution of stochastic optimal control (SOC) problems. In this work, the variational iteration method (VIM) is applied for solving SOC problems. In fact, solutions for the value function and the corresponding optimal strategies are obtained numerically. We solve a stochastic linear regulator problem to investigate the applicability and simplicity of the presented method and prove its convergence. In particular, for Merton's portfolio selection model as a problem of portfolio optimization, the proposed numerical method is applied for the first time and its usefulness is demonstrated. For the nonlinear case, we investigate its convergence using Banach's fixed point theorem. The numerical results confirm the simplicity and efficiency of our method.     

Discrete-time optimal control for stochastic nonlinear polynomial systems

This paper presents a solution to the discrete-time optimal control problem for stochastic nonlinear polynomial systems over linear observations and a quadratic criterion. The solution is obtained in two steps: the optimal control algorithm is developed for nonlinear polynomial systems by considering complete information when generating a control law. Then, the state estimate equations for discrete-time stochastic nonlinear polynomial system over linear observations are employed. The closed-form solution is finally obtained substituting the state estimates into the obtained control law. The designed optimal control algorithm can be applied to both distributed and lumped systems. To show effectiveness of the proposed controller, an illustrative example is presented for a second degree polynomial system. The obtained results are compared to the optimal control for the linearized system.     

A genetic algorithm using priority-based encoding with new operators for fixed charge transportation problems

In this paper, we propose a genetic algorithm using priority-based encoding (pb-GA) for linear and nonlinear fixed charge transportation problems (fcTP) in which new operators for more exploration are proposed. We modify a priority-based decoding procedure proposed by Gen et al. [1] to adapt with the fcTP structure. After comparing well-known representation methods for a transportation problem, we explain our proposed pb-GA. We compare the performance of the pb-GA with the recently used spanning tree-based genetic algorithm (st-GA) using numerous examples of linear and nonlinear fcTPs. Finally, computational results show that the proposed pb-GA gives better results than the st-GA both in terms of the solution quality and computation time, especially for medium- and large-sized problems. Numerical experiments show that the proposed pb-GA better absorbs the characteristics of the nonlinear fcTPs.     

On the solution of mixed-integer nonlinear programming models for computer aided molecular design

This paper addresses the efficient solution of computer aided molecular design (CAMD) problems, which have been posed as mixed-integer nonlinear programming models. The models of interest are those in which the number of linear constraints far exceeds the number of nonlinear constraints, and with most variables participating in the nonconvex terms. As a result global optimization methods are needed. A branch-and-bound algorithm (BB) is proposed that is specifically tailored to solving such problems. In a conventional BB algorithm, branching is performed on all the search variables that appear in the nonlinear terms. This translates to a large number of node traversals. To overcome this problem, we have proposed a new strategy for branching on a set of linear branchingfunctions, which depend linearly on the search variables. This leads to a significant reduction in the dimensionality of the search space. The construction of linear underestimators for a class of functions is also presented. The CAMD problem that is considered is the design of optimal solvents to be used as cleaning agents in lithographic printing.     

Newton-conjugate gradient （CG） augmented Lagrangian method for path constrained dynamic process optimization

In this paper, a Newton-conjugate gradient (CG) augmented Lagrangian method is proposed for solving the path constrained dynamic process optimization problems. The path constraints are simplified as a single final time constraint by using a novel constraint aggregation function. Then, a control vector parameterization (CVP) approach is applied to convert the constraints simplified dynamic optimization problem into a nonlinear programming (NLP) problem with inequality constraints. By constructing an augmented Lagrangian function, the inequality constraints are introduced into the augmented objective function, and a box constrained NLP problem is generated. Then, a linear search Newton-CG approach, also known as truncated Newton (TN) approach, is applied to solve the problem. By constructing the Hamiltonian functions of objective and constraint functions, two adjoint systems are generated to calculate the gradients which are needed in the process of NLP solution. Simulation examples demonstrate the effectiveness of the algorithm.     

求解含非线性参数的QoS路由的启发式算法

具有非线性参数的QoS路由分为含有非线性约束条件的QoS路由和含有非线性优化目标的QoS路由两类，它们都是NP问题．提出了两种启发式算法求解这两类QOS路由优化问题问题．对第一类问题，求解去掉非线性约束条件后的优化问题．如果找到的解满足非线性约束条件，则该解是最优解；否则在优化问题中添加一个新的线性约束，将已得到的解去掉，反复下去就可得到最终解．对第二类问题，将非线性优化目标换为约束条件中的线性参数，求解此优化模型，如果有解，则记录此时对应的非线性目标值．而后增加一个新的线性约束，去掉刚才得到的解，比较两次得到的非线性目标值，保留最小值．如果得到的解不满足该线性参数的约束条件，则算法结束；否则继续迭代．证明了两种算法的收敛性，并且时间复杂性为近似多项式时间．计算实例表明了算法的有效性．     

基于强化学习的部分线性离散时间系统的最优输出调节

针对同时具有线性外部干扰与非线性不确定性下的离散时间部分线性系统的最优输出调节问题, 提出了仅利用在线数据的基于强化学习的数据驱动控制方法. 首先, 该问题可拆分为一个受约束的静态优化问题和一个动态规划问题, 第一个问题可以解出调节器方程的解. 第二个问题可以确定出控制器的最优反馈增益. 然后, 运用小增益定理证明了存在非线性不确定性离散时间部分线性系统的最优输出调节问题的稳定性. 针对传统的控制方法需要准确的系统模型参数用来解决这两个优化问题, 提出了一种数据驱动离线策略更新算法, 该算法仅使用在线数据找到动态规划问题的解. 然后, 基于动态规划问题的解, 利用在线数据为静态优化问题提供了最优解. 最后, 仿真结果验证了该方法的有效性.     

Two aggregate-function-based algorithms for analysis of 3D frictional contact by linear complementarity problem formulation

Three dimensional frictional contact is formulated as linear complementarity problem (LCP) by using the parametric variational principle and quadratic programming method. Two aggregate-function-based algorithms, called respectively as self-adjusting interior point algorithm and aggregate function smoothing algorithm, are proposed for the solution of the LCP derived from the contact problems. A nonlinear finite element code is developed for numerical analysis of 3D multi-body contact problems. Four numerical examples are computed to demonstrate the applicability and computational efficiency of the methods proposed.