基于泡沫图像特征的金锑浮选入矿品位估计

入矿品位是金锑浮选加药量控制的重要依据.针对入矿品位在线检测困难的问题,提出一种基于泡沫图像特征的入矿品位估计方法.该估计方法首先针对样本数据中存在的不确定性,提出一种基于核主元分析(KPCA)和模糊C均值聚类–概率支持向量回归(FCM--PSVR)的建模方法,然后利用泡沫图像特征与加药量等数据建立起金锑入矿品位和精矿品位的估计模型,最后采用基于专家规则的方法对入矿品位估计结果的可信度进行评价.该方法在金锑浮选工艺中进行了工业验证,为指导金锑浮选加药量的控制起到了重要作用.     

基于神经网络近似的自适应优化控制

为了解决初始和终端确定的一类离散时间非线性系统有限时间优化控制,利用动态规划原理求解过程中遇到维数灾的问题,提出了基于神经网络的自适应动态规划近似优化控制.在分析动态规划求解遇到维数灾的基础上,进而给出了迭代ADP算法,并采用神经网络近似代价函数和控制律来实现迭代ADP算法,设计近似优化控制器.通过mat lab实验仿真结果表明,采用迭代ADP算法能够避免求解中遇到的维数灾,从而有效地实现了一类离散时间非线性系统的有限时间近似优化控制.     

泡沫图像特征驱动的锑粗选加药控制策略

锑粗选工序的加药控制直接影响精选与扫选的性能.通常由人工观察泡沫手动调节药剂.这种方式,存在控制滞后、主观随意性大、易导致浮选性能不稳定甚至恶化的问题.对此,我们提出一种泡沫图像特征驱动的锑粗选加药控制策略.利用概率支持向量回归方法建立基于锑粗选关键泡沫图像特征与加药量的入矿品位估计模型;在此基础上,采用操作模式匹配方法实现加药量的预设定,快速满足入矿品位类型变化后新的控制要求;并采用基于区间II型模糊系统的加药反馈控制器减小泡沫状态与期望的偏差.工业验证结果表明,该方法能有效代替人工加药并改善了锑浮选性能.     

基于评价网络近似误差的自适应动态规划优化控制

为了求解有限时域最优控制问题,自适应动态规划(ADP)算法要求受控系统能一步控制到零。针对不能一步控制到零的非线性系统,提出一种改进的ADP算法,其初始代价函数由任意的有限时间容许序列构造。推导了算法的迭代过程并证明了算法的收敛性。当考虑评价网络的近似误差并满足假设条件时,迭代代价函数将收敛到最优代价函数的有界邻域。仿真例子验证了所提出方法的有效性。     

基于ADP的导引控制一体化全状态受限反演控制

针对导引控制一体化设计中状态受限及非线性最优问题，提出了一种结合反演控制与自适应动态规划（ADP）技术，考虑全状态受限的新型导引控制一体化设计方法.首先，将状态受限的严格反馈系统通过坐标变换转化为非状态受限系统.然后，采用前馈反演控制与反馈最优控制相结合的设计思路，利用ADP技术在线求解非线性HJB方程得到最优解.最后通过李亚普诺夫理论证明了系统的闭环稳定性与所有信号的一致有界性.与传统方法的对比仿真验证了该设计方法的可行性与优越性.     

数据驱动的浮选过程运行反馈解耦控制方法

浮选过程是利用矿物本身的亲水或疏气性质或经药剂处理得到的亲水或疏气性质进行矿物分离的物理过程.本文通过建立以矿浆液位和矿浆流量为输入，以浮选过程的精矿品位与尾矿品位为输出的多变量、强耦合、非线性、时变的运行过程模型，利用未建模动态前一拍可测的特点，提出了包括矿物品位运行过程控制器驱动模型、PID控制器、反馈解耦控制器、未建模动态补偿器的数据驱动的一步最优未建模动态补偿PID解耦控制方法，实现了消除稳态误差、静态解耦与未建模动态的补偿，通过浮选过程运行反馈控制仿真实验验证了本文所提方法的有效性.     

基于预测模型的浮选过程pH值控制

矿浆pH值是泡沫浮选过程中的一个非常重要的被控量.目前,多数选厂的矿浆pH值控制基本是依靠现场工人定期对矿浆样本进行pH值测量,凭主观经验对pH调整剂进行调整.由于操作工人的主观性和随意性的影响以及矿浆样本pH值测量与药剂调整间存在的较长的时间滞后,矿浆pH值波动频繁,很难使矿物浮选保持在一个稳定最优生产状态下运行.为了使矿浆pH值保持在一个期望的生产状态,基于浮选泡沫表面视觉信息提出了一种新的矿浆pH值控制方法,分别采用基于泡沫视觉信息的自适应遗传混合神经网络AG-HNN和自适应遗传PID(AG-PID)控制方法建立了矿浆pH值预测模型和pH值控制模型,基于所建立预测和控制模型对浮选药剂用量进行调整,解决了浮选矿浆pH值波动问题.工业浮选现场的实验结果表明该方法可以使矿浆pH值保持在一个期望的范围内,有效提高浮选性能.     

基于数据ADP算法的一类带有执行器饱和的未知离散时间系统最优跟踪控制

针对一类带有执行器饱和的未知动态离散时间非线性系统, 提出了一种新的最优跟踪控制方案. 该方案基于迭代自适应动态规划算法, 为了实现最优控制, 首先建立了未知系统动态的数据辨识器. 通过引入M网络, 获得了稳态控制的精确表达式. 为了消除执行器饱和的影响, 提出了一个非二次的性能指标函数. 然后提出了一种迭代自适应动态规划算法获得最优跟踪控制的解, 并给出了收敛性分析. 为了实现最优控制方案, 神经网络被用来构建数据辨识器、计算性能指标函数、近似最优控制策略和求解稳态控制. 仿真结果验证了本文所提出的最优跟踪控制方法的有效性.     

基于马氏决策过程模型的动态系统学习控制:研究前沿与展望

基于马氏决策过程(Markov decision process, MDP)的动态系统学习控制是近年来一个涉及机器学习、控制理论和运筹学等多个学科的交叉研究方向, 其主要目标是实现系统在模型复杂或者不确定等条件下基于数据驱动的多阶段优化控制. 本文对基于MDP的动态系统学习控制理论、算法与应用的发展前沿进行综述,重点讨论增强学习(Reinforcement learning, RL)与近似动态规划(Approximate dynamic programming, ADP)理论与方法的研究进展,其中包括时域差值学习理论、求解连续状态与行为空间MDP的值函数逼近方法、 直接策略搜索与近似策略迭代、自适应评价设计算法等,最后对相关研究领域的应用及发展趋势进行分析和探讨.     

基于泡沫大小动态分布的浮选生产过程加药量健康状态分析

针对矿物浮选过程泡沫大小分布随着药剂量的改变而动态变化的特点,提出一种基于泡沫大小动态分布特征的具有自学习功能的浮选生产过程加药量健康状态统计模式识别方法.首先,通过泡沫图像分割、气泡尺寸分布核密度估计获得浮选气泡大小的概率密度分布函数,采用无监督的最远邻聚类方法获得典型药剂量添加状态下的气泡尺寸统计分布特征集;然后,采用简单的贝叶斯推理方法获得测试时间段对应的药剂添加健康状态分析识别结果,并根据浮选生产工况状态的动态变化对各典型药剂状态下的气泡大小统计分布特征集进行在线学习修正.实验结果表明,所提出方法能实时获取泡沫尺寸分布的动态变化,实现浮选药剂操作健康状态的自动识别与评价,为进一步实现浮选生产过程的加药量优化控制奠定了基础.     

Finite horizon optimal control of discrete-time nonlinear systems with unfixed initial state using adaptive dynamic programming

In this paper, we aim to solve the finite horizon optimal control problem for a class of discrete-time nonlinear systems with unfixed initial state using adaptive dynamic programming (ADP) approach. A new ε-optimal control algorithm based on the iterative ADP approach is proposed which makes the performance index function converge iteratively to the greatest lower bound of all performance indices within an error according to ε within finite time. The optimal number of control steps can also be obtained by the proposed ε-optimal control algorithm for the situation where the initial state of the system is unfixed. Neural networks are used to approximate the performance index function and compute the optimal control policy, respectively, for facilitating the implementation of the ε-optimal control algorithm. Finally, a simulation example is given to show the results of the proposed method.     

Optimal prescribed performance tracking control of nonlinear motor driven systems via adaptive dynamic programming

Although optimal regulation problem has been well studied, resolving optimal tracking control via adaptive dynamic programming (ADP) has not been completely resolved, particularly for nonlinear uncertain systems. In this paper, an online adaptive learning method is developed to realize the optimal tracking control design for nonlinear motor driven systems (NMDSs), which adopts the concept of ADP, unknown system dynamic estimator (USDE), and prescribed performance function (PPF). To this end, the USDE in a simple form is first proposed to address the NMDSs with bounded disturbances. Then, based on the estimated unknown dynamics, we define an optimal cost function and derive the optimal tracking control. The derived optimal tracking control is divided into two parts, that is, steady-state control and optimal feedback control. The steady-state control can be obtained with the tracking commands directly. The optimal feedback control can be obtained via the concept of ADP based on the PPF; this contributes to improving the convergence of critic neural network (CNN) weights and tracking accuracy of NMDSs. Simulations are provided to display the feasibility of the designed control method.     

Adaptive composite suboptimal control for linear singularly perturbed systems with unknown slow dynamics

In this article, using singular perturbation theory and adaptive dynamic programming (ADP) approach, an adaptive composite suboptimal control method is proposed for linear singularly perturbed systems (SPSs) with unknown slow dynamics. First, the system is decomposed into fast‐ and slow‐subsystems and the original optimal control problem is reduced to two subproblems in different time‐scales. Afterward, the fast subproblem is solved based on the known model of the fast‐subsystem and a fast optimal control law is designed by solving the algebraic Riccati equation corresponding to the fast‐subsystem. Then, the slow subproblem is reformulated by introducing a system transformation for the slow‐subsystem. An online learning algorithm is proposed to design a slow optimal control law by using the information of the original system state in the framework of ADP. As a result, the obtained fast and slow optimal control laws constitute the adaptive composite suboptimal control law for the original SPSs. Furthermore, convergence of the learning algorithm, suboptimality of the adaptive composite suboptimal control law and stability of the whole closed‐loop system are analyzed by singular perturbation theory. Finally, a numerical example is given to show the feasibility and effectiveness of the proposed methods.     

Finite horizon optimal control of non-linear discrete-time switched systems using adaptive dynamic programming with ε-error bound

In this paper, we aim to solve the finite-horizon optimal control problem for a class of non-linear discrete-time switched systems using adaptive dynamic programming(ADP) algorithm. A new ε-optimal control scheme based on the iterative ADP algorithm is presented which makes the value function converge iteratively to the greatest lower bound of all value function indices within an error according to ε within finite time. Two neural networks are used as parametric structures to implement the iterative ADP algorithm with ε-error bound, which aim at approximating the value function and the control policy, respectively. And then, the optimal control policy is obtained. Finally, a simulation example is included to illustrate the applicability of the proposed method.     

Adaptive dynamic programming for linear impulse systems

We investigate the optimization of linear impulse systems with the reinforcement learning based adaptive dynamic programming （ADP） method. For linear impulse systems, the optimal objective function is shown to be a quadric form of the pre-impulse states. The ADP method provides solutions that iteratively converge to the optimal objective function. If an initial guess of the pre-impulse objective function is selected as a quadratic form of the pre-impulse states, the objective function iteratively converges to the optimal one through ADP. Though direct use of the quadratic objective function of the states within the ADP method is theoretically possible, the numerical singularity problem may occur due to the matrix inversion therein when the system dimensionality increases. A neural network based ADP method can circumvent this problem. A neural network with polynomial activation functions is selected to approximate the pr~impulse objective function and trained iteratively using the ADP method to achieve optimal control. After a successful training, optimal impulse control can be derived. Simulations are presented for illustrative purposes.     

基于自适应动态规划的一类带有时滞的离散时间非线性系统的最优控制策略

针对一类状态和控制变量均带有时滞的非线性系统的带有二次性能指标函数最优控制问题, 本文提出了一种基于新的迭代自适应动态规划算法的最优控制方案. 通过引进时滞矩阵函数, 应用动态规划理论, 本文获得了最优控制的显式表达式, 然后通过自适应评判技术获得最优控制量. 本文给出了收敛性证明以保证性能指标函数收敛到最优. 为了实现所提出的算法, 本文采用神经网络近似性能指标函数、计算最优控制策略、求解时滞矩阵函数、以及给非线性系统建模. 最后本文给出了两个仿真例子说明所提出的最优策略的有效性.     

Adaptive Decoupling Control of Pulp Levels in Flotation Cells

Control of the pulp levels in flotation cells directly affects the grade of the concentrate and the tailings in a concentration plant. Nevertheless, with strong coupling among cell levels and nonlinearities in the flotation process, conventional control strategies cannot achieve satisfactory control performance. In this paper, a nonlinear multi‐model adaptive decoupling control strategy based on adaptive‐network‐based fuzzy inference systems (ANFIS) is proposed for the flotation process, which includes a linear adaptive decoupling controller, an ANFIS‐based nonlinear adaptive decoupling controller, and a switching mechanism. The proposed method not only improves the transient performance and mitigates effects of the nonlinearities on the system, but also guarantees the input‐output stability of the closed‐loop system. Successful application to the flotation process has been made in a concentration plant in China, and the feasibility and efficiency of the proposed method have been validated.     

Digital twin modeling for loaded contact pattern-based grinding of spiral bevel gears

To distinguish with the conventional tooth flank grinding only considering geometric accuracy, an innovative digital twin modeling is proposed for loaded contact pattern based grinding of spiral bevel gears. Where, data-driven grinding simulation, sensitivity analysis strategy, adaptive decision and control are developed. Focusing on loaded contact pattern optimization, numerical loaded tooth contact analysis (NLTCA) considering noncentrosymmetric problem and tooth flank roughness is developed for data-driven relationship establishment. Then, an adaptive data-driven tooth flank grinding decision and control model is established. Where, the universal motion concept (UMC) machine settings is selected as the optimal design variable. It is actually an infinite approximation to the target tooth flank in form of an adaptive control system. Moreover, with point-to-point material removal distribution, the different optimization strategies are proposed for accurate tooth flank grinding. In particular, the overcutting problem on the tooth flank grinding programming is investigated. Finally, Levenberg-Marquardt method is applied to solve the established nonlinear lease square model for the accurate machine tool settings having modification variations. Thus, this accurate data-driven digital twin modeling can achieve loaded contact pattern-based grinding. The provided numerical and test instances can verify the proposed digital twin modeling.