非线性大系统的跟踪具有不同幅值轨线的分散型迭代学习控制器

在大型工业过程递阶稳态优化中, 可行的方法是利用系统的实际信息以修正基于模型的最优解. 在这种情形下, 得出一幅值不等的阶跃型控制值序列, 而且该控制值序列依次激励实际系统. 本文将一组迭代学习控制器分散地嵌入到一类非线性工业过程的递阶稳态优化进程中, 每一子系统的迭代学习控制器将产生一强化的控制信号序列以替代相应的具有不同幅值的阶跃型控制值序列, 目的是不断改进系统的暂态品质. 通过卷积的 Hausdorff-Young 不等式, 本文分析了学习控制律在 Lebesgue-P 范数意义下的收敛性, 讨论了系统的非线性性和关联性对控制律收敛性的影响. 最后, 数字仿真验证了所研究的学习控制机理的正确性和有效性.     

Iterative learning controllers with time-varying gains for large-scale industrial processes to track trajectories with different magnitudes

In this article, a set of decentralised open-loop and closed-loop iterative learning controllers are embedded into the procedure of steady-state hierarchical optimisation utilising feedback information for large-scale industrial processes. The task of the learning controllers is to generate a sequence of upgraded control inputs iteratively to take responsibility for sequential step function-type control decisions, each of which is determined by the steady-state optimisation layer and then imposed on the real system for feedback information. In the learning control scheme, the learning gains are designated to be time-varying which are adjusted by virtue of expertise experiences-based IF-THEN rules, and the magnitudes of the learning control inputs are amplified by the sequential step function-type control decisions. The aim of learning schemes is to further effectively improve the transient performance. The convergence of the updating laws is deduced in the sense of Lebesgue 1-norm by taking advantage of the Hausdorff–Young inequality of convolution integral and the Hoelder inequality of Lebesgue norm. Numerical simulations manifest that both the open-loop and the closed-loop time-varying learning gain-based schemes can effectively decrease the overshoot, accelerate the rising speed and shorten the settling time, etc.     

Filter-based iterative learning control for linear large-scale industrial processes

In the procedure of the steady-state hierarchical optimization with feedback for large-scale industrial processes, a sequence of set-point changes with different magnitudes is carried out on the optimization layer. To improve the dynamic performance of transient response driven by the set-point changes, a filter-based iterative leaning control strategy is proposed. In the proposed updating law, a local-symmetric-integral operator is adopted for eliminating the measurement noise of output information, a set of desired trajectories are specified according to the set-point changes sequence, the current control input is iteratively achieved by utilizing smoothed output error to modify its control input at previous iteration, to which the amplified coefficients related to the different magnitudes of set-point changes are introduced. The convergence of the algorithm is conducted by incorporating frequency-domain technique into time-domain analysis. Numerical simulation demonstrates the effectiveness of the proposed strategy.     

动态博弈框架下的分布式动态优化

为了实时在线求解复杂的大规模动态优化问题,本文基于动态博弈理论提出了一种分布式动态优化方案,滚动合作博弈优化(RCGO).首先基于滚动时域优化框架,该方案将原本复杂的大规模动态优化问题分解为若干简单的小规模局部优化子问题,使得计算复杂度降低从而保证优化求解的实时性.之后本文基于动态博弈提出了分解迭代法求解各局部动态优化子问题,并对RCGO优化方案下系统稳定性进行分析.最后本文选择一个化工过程网络作为仿真案例,基于RCGO方案得到了极大化经济效益下该网络的最优操作.优化结果表明在求解复杂大规模动态优化问题时, RCGO方案较传统的集中式优化方案在由系统经济效益、闭环控制性能及优化求解实时性等组成的综合指标上有较大优势.     

Decentralized Iterative Learning Control to Large-Scale Industrial Processes for Nonrepetitive Trajectory Tracking

In the procedure of steady-state hierarchical optimization with feedback for a large-scale industrial process, it is usual that a sequence of step set-point changes is carried out and used by the decision-making units while searching the eventual optimum. In this case, the real process experiences a form of disturbances around its operating set-point. In order to improve the dynamic performance of transient responses for such a large-scale system driven by the set-point changes, an open-loop proportional integral derivative-type iterative learning control (ILC) strategy is explored in this paper by considering the different magnitudes of the controller's step set-point change sequence. Utilizing the Hausdorff-Young inequality of convolution integral, the convergence of the algorithm is derived in the sense of Lebesgue-P norm. Furthermore, the extended higher order ILC rule is developed, and the convergence is analyzed. Simulation results illustrate that the proposed ILC strategies can remarkably improve the dynamic performance such as decreasing the overshoot, accelerating the transient response, shortening the settling time, etc.     

具有滞后的饱和非线性工业控制系统的迭代学习控制

基于稳态优化中递阶控制结构,对具有滞后的非平滑饱和非线性工业控制系统施行迭 代学习控制,提出了期望目标轨线δ-可达以及迭代学习算法的ε-收敛的慨念,给出了加权超前 PD-型开环迭代学习算法,对算法的收敛性进行论证.数字仿真证明了算法的有效性,并表明对 工业控制系统的动态品质有显著改进.     

Two-stage scheme for global identification of interconnected steady-state systems

A two-stage scheme is introduced to find the large-scale globally optimal model of an interconnected steady-state system having a structure described by an interconnection matrix. Numerical realization of the scheme by using the standard optimization techniques is discussed, and an analysis of the identification accuracy is conducted.     

迭代学习控制技术回顾与长期学习控制展望

本文首先回顾了迭代学习控制中初始状态漂移问题和单调收敛性分析的研究技术.其次,综述了高阶迭代学习控制机制及其收敛速度比较和有效性.再次,评述了重复运行大系统和变幅值大工业过程的迭代学习控制机理.最后,展望了长期学习控制的研究趋势等.     

An interative learning control scheme using the weighted least-squares method

An iterative learning control scheme is described for linear discrete-time systems. A weighted least-squares criterion of learning error is optimized to obtain a unique control gain for a case when the number of sampling is relatively small. It is then shown that algorithmic convergence can be readily guaranteed, because the present learning rule consists of a steady-state Kalman filter. By paying attention to the sparse system structure for the system's impulse response model, we further derive a suboptimal iterative learning control for a practical case when the number of sampling is large.     

Gradient‐based back‐propagation dynamical iterative learning scheme for the neuro‐fuzzy inference system

In this paper, a gradient‐based back propagation dynamical iterative learning algorithm is proposed for structure optimization and parameter tuning of the neuro‐fuzzy system. Premise and consequent parameters of the neuro‐fuzzy model are initialized randomly and then tuned by the proposed iterative algorithm. The learning algorithm is based on the first order partial derivative of the output with respect to the structure parameters. The first order derivative of the model output with respect to the structure parameters determines the sensitivity of the model to structure parameters. The sensitivity values are then used to set the tuning factors and parameters updating step sizes. Therefore, an adaptive dynamical iterative scheme is achieved which adapts the learning procedure to the current state of the performance during the optimization process. Larger tuning step sizes make the convergence speed higher and vice versa. In this regard, this parameter is treated according to the calculated sensitivity of the model to the parameter. The proposed learning algorithm is compared with the least square back propagation method, genetic algorithm and chaotic genetic algorithm in the neuro‐fuzzy model structure optimization. Smaller mean square error and shorter learning time are sought in this paper, and the performance of the proposed learning algorithm is versified regarding these criteria.     

约束不确定系统的误差有界无偏跟踪

为使精密制造设备中定位机构实现在容许的误差带内对时变轨迹的精准无偏跟踪,针对约束不确定系统提出一种基于鲁棒控制不变(RCI)集的误差有界且无偏模型预测控制(EOMPC)方法.首先,为了消除由扰动引起的稳态误差,构建包含可测输出、估计状态和估计扰动的增广系统作为EOMPC的预测模型以提高预测精度;其次,基于增广系统和轨迹模型,使用可以在有限步内终止的迭代方法求解RCI集,并将其作为最优控制问题(OCP)中的状态约束以实现误差有界的跟踪;然后,为保障OCP的实时性,给出一种可在线执行的数值优化方案;最后,在磁悬浮定位系统上验证了所提出方法的有效性.     

Chaos control of performance measure approach for evaluation of probabilistic constraints

Performance measure approach (PMA) is a recently proposed method for evaluation of probabilistic constraints in reliability-based design optimization of structure. The advanced mean-value (AMV) method is well suitable for PMA due to its simplicity and efficiency. However, when the AMV iterative scheme is applied to search for the minimum performance target point for some nonlinear performance functions, the iterative sequences could fall into the periodic oscillation and even chaos. In the present paper, the phenomena of numerical instabilities of AMV iterative solutions are illustrated firstly. And the chaotic dynamics analysis on the iterative procedure of AMV method is performed. Then, the stability transformation method of chaos feedback control is suggested for the convergence control of AMV procedure in the parameter interval in which the iterative scheme fails. Numerical results of several nonlinear performance functions demonstrate that the control of periodic oscillation, bifurcation and chaos for AMV iterative procedure is achieved, and the stable convergence solutions are obtained.     

Two-level solution method for Markov chain modelling transfer lines with unreliable servers and finite buffers

Transfer lines with inter-stage buffers and unreliable servers are often modelled by means of Markov chains. Because of the large number of states, solving the steady-state equations of the chain is not a trivial task. This paper proposes a two-level iterative scheme for computing the steady-state probability distribution. In the framework of non-negative matrix theory some general results are proved which guarantee the convergence of the proposed procedure. Moreover, numerous numerical experiments are given, which show that the two-level iterative scheme enjoys a very good rate of convergence. The method also works suitably for solving the steady-state probability equation of chains modelling systems with more than three stages.     

新型同步发电机励磁控制器的设计

针对传统的基于迭代学习控制算法的同步发电机励磁控制器存在初始控制信号由经验确定的问题,提出了一种基于即时学习型迭代学习控制算法的同步发电机励磁控制器的设计方案。该方案在迭代学习控制算法中引入即时学习算法,利用即时学习算法计算初始控制信号,有效减少了初始控制信号与理想控制信号之间的误差。仿真结果表明,该励磁控制器收敛速度快,具有更强的维持机端电压的能力。     

Iterative learning Kalman filter for repetitive processes

In this paper, a discrete-time iterative learning Kalman filter scheme is proposed for repetitive processes to reject repeatable disturbances as well as random noises. The proposed state estimator scheme integrates Kalman filter with iterative learning control. The estimation process contains two stages: a conventional Kalman filter is applied in the first stage; the second stage refines the estimates in an iterative learning fashion, leading to a gradual improvement on the estimation performance. According to the estimates that the first stage feeds to the second stage, the optimal design includes two types – posterior type and priori type. In order to reduce the memory and computation load of the optimal design, two suboptimal estimators are provided as well. The stability of the both suboptimal estimators is also studied. Furthermore, a lower bound is given to estimate the ultimate estimation performance before implementing any estimation. Finally, an illustrative example of injection molding is given to verify the performance of the four estimators developed.     

基于伪谱法的滑翔轨迹多级迭代优化策略

伪谱法可实时求解具有高度非线性动态特性的飞行器最优轨迹;以X-51A相似飞行器模型为研究对象,采用增量法与查表插值建立纵向气动力模型,伪谱法与序列二次规划算法求解滑翔轨迹最优控制问题;提出使用多级迭代优化策略,为序列二次规划算法求解伪谱法参数化得到的大规模非线性规划问题提供初值,弥补序列二次规划算法在求解大规模非线性规划问题过程中,出现的初值敏感、收敛速度减慢等问题。通过与传统方法求解出的状态量与控制量仿真飞行状态进行对比,证明了多级迭代优化策略的有效性和高效性,该策略在实际工程应用中取得了良好效果。     

Data‐based iterative learning mechanism for unknown input‐output coupling parameters/matrices

In this paper, we explore how to get the information of input‐output coupling parameters (IOCPs) for a class of uncertain discrete‐time systems by using iterative learning technique. Firstly, by taking advantage of repetitiveness of control system and informative input and output data, we design an iterative learning scheme for unknown IOCPs. It is shown that we can get the exact values of IOCPs one by one through running the repetitive system T+1 times if the control system is with identical initial state and noise free. Secondly, we give the iterative learning scheme for unknown IOCPs in the presence of measurement noise, system noise, or initial state drift and analyze the influence factors on the performance of developed iterative learning scheme. Meanwhile, we introduce the maximum allowable control deviation into the iterative learning mechanism to minimize the negative impact of noise on the performance of learning scheme and to enhance the robust of iterative learning scheme. Thirdly, for a class of multiple‐input–multiple‐output systems, we also develop iterative learning mechanism for unknown input‐output coupling matrices. Finally, an illustrative example is given to demonstrate the effectiveness of proposed iterative learning scheme.     

基于LMI方法的保性能迭代学习算法设计

研究基于性能的迭代学习算法设计与优化问题.首先定义了迭代域二次型性能函数,然后针对线性离散系统给出了迭代域最优迭代学习算法;基于线性矩阵不等式(LMI)方法,针对不确定线性离散系统给出了保性能迭代学习算法及其优化方法.对于这两类迭代学习算法,只要调整性能函数中的权系数矩阵,便可很好地调整迭代学习收敛速度.另外,保性能迭代学习算法设计及优化过程,可利用MATLAB工具箱很方便地求解.     

工业过程稳态优化进程中的噪声平滑型迭代学习控制

针对具有噪声的工业过程稳态优化进程，提出迭代学习控制以期改善控制系统的动态品质，建立了基本的加权噪声平滑型迭代学习控制算法结构。利用频域时域相结合的方法分析和论证了算法的收敛性，给出噪声平滑参数的确定策略，数字仿真表明，平滑型迭代学习控制算法能有效消除噪声对系统输出信号的影响，显著改善工业过程稳态优化进程中控制系统的动态品质。     

锑浮选过程加药量自适应迭代学习控制

针对现有的加药量控制方法需要浮选过程动态模型或是鲁棒性不足的问题, 提出一种基于自适应动态规划 (ADP) 的浮选过程加药量自适应迭代学习控制方法. 首先, 将药剂量控制问题转化为两级优化问题 (问题 1 和问题 2). 其中, 基于前馈控制原理求解问题 1 得出前馈补偿分量以抑制外界扰动. 然后, 采用基于值迭代的 ADP 算法, 求解问题 2 以得到最优反馈增益, 从而设计一个数据驱动的最优加药量控制策略使最终的生产指标 (精矿品位和尾矿品位) 跟踪给定值, 且药剂量消耗最少. 最后, 通过工业生产数据进行仿真验证, 证明所提方法的收敛性和稳定性.