有色冶金过程不确定优化方法探讨

有色冶金过程受原料来源多样、工况条件波动、生产成分变化等因素的影响,存在大量的不确定性,严重影响了冶炼生产的稳定性与可靠性.鉴于此,综述不同类型不确定性优化问题的描述方法,具体包括概率不确定优化问题、模糊不确定优化问题和区间不确定优化问题.通过分析有色冶金生产过程的特点与需求,以3种典型的有色冶金过程不确定优化问题为例,探讨不同类型的有色冶金过程不确定优化方法.针对氧化铝生料浆配料过程的概率不确定优化问题,采用基于Hammersley sequence sampling(HSS)的方法实现不确定模型的确定性转换;针对湿法炼锌除铜过程的模糊不确定优化问题,采用基于模糊规则的方法进行确定性评估;针对锌电解分时供电过程的区间不确定优化问题,采用基于min-max的方法求解鲁棒解.工业运行数据均验证了上述方法的有效性.     

基于观测器的不确定动态时滞系统鲁棒镇定的Riccati方程方法

本文给出了一类不确定动态时滞系统基于观测器的鲁棒镇定方法，该类系统的状态、输人和输出矩阵均含有不确定性，且不确定性需满足给定的匹配条件，系统不仅有状态时滞，还有控制时滞，该方法通过求解两个代数Riccati方程实现，本文比较全面地解决了满足匹配条件的不确定动态时滞系统的鲁棒镇定问题．     

一类不确定系统基于滑模干扰补偿的广义预测控制

广义预测控制(GPC)是基于非线性机理模型的一种优化控制策略, 但当系统存在内部不确定性、建模动态误差和外部干扰的情况下, 采用基于标称系统模型的GPC方法的系统性能将显著下降. 为此, 针对一类不确定非线性系统, 首先分析设计了一种基于不确定模型的理想GPC控制律; 同时设计了一种滑模干扰补偿器(SMDC)对系统的复合干扰进行估计, 将其输出作为补偿控制与标称GPC控制律结合以消除不确定性和外干扰的影响, 并利用Lyapunov理论分析了闭环复合系统的性能; 最后将其应用于一种高超声速飞行器(HSV)姿态控制系统, 仿真结果表明该方法具有很好的鲁棒特性和干扰衰减特性.     

一类具有非三角结构的不确定非线性系统的自适应扰动抑制

研究一类不确定非线性系统的自适应扰动抑制问题.借助自适应技术与连续占优方法,所提出的控制策略能够处理多种不确定性的严重耦合,这些不确定性包括未知非线性参数、外部扰动和具有未知下界的时变控制系数.自适应状态反馈控制器是一维的,且其性能可以借助于$L_2-L_{2p     

使用鲁棒控制器稳定模糊系统模型

将非线性系统用T-S模糊动态模型描述,并将全局模糊系统模型表示成不确定系统形式采用新的鲁棒控制器设计方法,设计出使全局模糊系统模型渐近稳定的线性控制器避免了并行分配补偿法中求解公共矩阵P的困难.一级倒立摆的模糊控制器设计实例,证明了方案的简洁有效.     

一类不确定非线性系统的自适应鲁棒控制

针对一类由非线性微分方程描述的不确定单输入单输出(SISO)系统,提出了一种自适应鲁棒控制算法.设计了一动态滤波器并将其与原系统组成扩展系统,由滤波器求得控制律稳定扩展系统.算法绕开辨识模型参数而是直接估计函数值,加快了控制律的求解.设计了状态误差观测器,用观测器的值构造控制律逼近状态反馈时的控制效果.基于Lyapunov 稳定理论分析了扩展系统的渐近稳定性并给出了闭环稳定的充分条件.最后仿真结果验证了算法的有效性和鲁棒性.     

一类非线性不确定系统的最小方差神经控制

针对一类非线性不确定系统,提出一种新的基于神经网络动态补偿的最小方差控制方法（ＭＶＮＮＣ）。这种控制系统将传统的最小方差控制技术与神经网络优良的非线性逼近能力相结合,从而能有效地消除不确定性引起的控制误差,仿真实验表明,这种最小方差神经控制系统具有较强的鲁棒性和良好的动态性能。     

含约束的非线性不确定系统的鲁棒控制

讨论一类含约束的非线性不确定系统的鲁棒控制问题（这里的不确定性并不要求满足匹配条件）。在一定的假设条件下给出了使该类问题可解的充分条件，构造出相应的鲁棒控制器，该控制器避免了利用微分几何方法所得控制器易产生过度控制的缺点。     

保证瞬态性能的迭代学习控制

讨论一类不确定非线性系统的可保证瞬态性能的迭代学习控制问题.引入限定跟踪误差瞬态特性的界函数,通过误差转换方法,定义一个转换误差变量,将跟踪误差的保证瞬态特性问题转化为该误差变量的有界性问题.采用Lyapunov方法,设计迭代学习控制器处理系统中参数和非参数不确定性.并且,采用完全限幅学习机制,保证转换误差变量的有界性和一致收敛性.从而既能得出系统输出在整个作业区间的完全跟踪性能,同时又能够保证跟踪误差在每次迭代的过程中具有保证的瞬态特性.仿真结果验证了所提控制方法的有效性.     

一类非线性随机不确定系统有限时间H∞无穷滤波

研究一类具有时变、有界干扰的非线性随机不确定系统有限时间H∞滤波问题.首先,给出了非线性随机不确定系统有限时间H∞滤波问题的定义;其次,通过构造Lyapunov-Krasoviskii函数,并结合线性矩阵不等式（LMI）方法,给出了非线性随机不确定系统有限时间∞滤波器存在的充分条件;再次,将该问题简化为具有LMI约束的优化问题,并给出了相应的求解算法;最后,通过数值算例表明了所提出设计方法的有效性.     

Robustness of non-linear stochastic optimal control for quasi-Hamiltonian systems with parametric uncertainty

The robustness of non-linear stochastic optimal control for quasi-Hamiltonian systems with uncertain parameters is studied. Based on the independence of uncertain parameters and stochastic excitations, the non-linear stochastic optimal control for the nominal quasi-Hamiltonian system with average-value parameters is first obtained by using the stochastic averaging method and stochastic dynamical programming principle. Then, the means and standard deviations of root-mean-square responses, control effectiveness and control efficiency for the uncertain quasi-Hamiltonian system are calculated by using the stochastic averaging method and the probabilistic analysis. By introducing the sensitivity of the variation coefficients of controlled root-mean-square responses, control effectiveness and control efficiency to those of uncertain parameters, the robustness of the non-linear stochastic optimal control is evaluated. Two examples are given to illustrate the proposed control procedure and its robustness.     

Robust exponential stability of uncertain stochastic systems with probabilistic time‐varying delays

This paper is concerned with the problem of delay‐distribution–dependent robust exponential stability for uncertain stochastic systems with probabilistic time‐varying delays. Firstly, inspired by a class of networked systems with quantization and packet losses, we study the stabilization problem for a class of network‐based uncertain stochastic systems with probabilistic time‐varying delays. Secondly, an equivalent model of the resulting closed‐loop network‐based uncertain stochastic system is constructed. Different from the previous works, the proposed equivalent system model enables the controller design of the network‐based uncertain stochastic systems to enjoy the advantage of probability distribution characteristic of packet losses. Thirdly, by applying the Lyapunov‐Krasovskii functional approach and the stochastic stability theory, delay‐distribution–dependent robust exponential mean‐square stability criteria are derived, and the sufficient conditions for the design of the delay‐distribution–dependent controller are then proposed to guarantee the stability of the resulting system. Finally, a case study is given to show the effectiveness of the results derived. Moreover, the allowable upper bound of consecutive packet losses will be larger in the case that the probability distribution characteristic of packet losses is taken into consideration.     

Real-time optimization under parametric uncertainty: a probability constrained approach

Uncertainty is an inherent characteristic in most industrial processes, and a variety of approaches including sensitivity analysis, robust optimization and stochastic programming have been proposed to deal with such uncertainty. Uncertainty in a steady state nonlinear real-time optimization (RTO) system and particularly making robust decisions under uncertainty in real-time has received little attention. This paper discusses various sources of uncertainty within such closed loop RTO systems and a method, based on stochastic programming, that explicitly incorporates uncertainty into the RTO problem is presented. The proposed method is limited to situations where uncertain parameters enter the constraints nonlinearly and uncertain economics enter the objective function linearly. Our approach is shown to significantly improve the probability of a feasible solution in comparison to more conventional RTO techniques. A gasoline blending example is used to demonstrate the proposed robust RTO approach.     

Fault detection for uncertain LPV systems using probabilistic set-membership parity relation

This paper considers fault detection of uncertain linear parameter varying systems that have polynomial dependence on parametric uncertainties. A conventional set-membership (SM) approach is able to ensure zero false alarm rate (FAR) by using conservative threshold sets, but usually results in a high missed detection rate (MDR) due to equally treating all uncertainty realizations without distinguishing between high and low probability of occurrence. To address this limitation, a probabilistic SM parity relation approach is proposed to exploit probabilistic information on the parametric uncertainties, which results in a reduced MDR by admitting an acceptable FAR. The parity relation is first polynomially parameterized with respect to uncertain parameters. Then, Gaussian mixtures are adopted to efficiently compute uncertainty propagation from stochastic uncertainties to the residual distribution. To achieve an acceptable FAR, a non-convex confidence set of residuals – represented by a union of ellipsoids – is determined for the consistency test. The effectiveness of the proposed approach is illustrated using a continuous stirred tank reactor example including performance comparisons with a deterministic zonotope-based method.     

Distributed stochastic MPC for systems with parameter uncertainty and disturbances

A distributed stochastic model predictive control algorithm is proposed for multiple linear subsystems with both parameter uncertainty and stochastic disturbances, which are coupled via probabilistic constraints. To handle the probabilistic constraints, the system dynamics is first decomposed into a nominal part and an uncertain part. The uncertain part is further divided into 2 parts: the first one is constrained to lie in probabilistic tubes that are calculated offline through the use of the probabilistic information on disturbances, whereas the second one is constrained to lie in polytopic tubes whose volumes are optimized online and whose facets' orientations are determined offline. By permitting a single subsystem to optimize at each time step, the probabilistic constraints are then reduced into a set of linear deterministic constraints, and the online optimization problem is transformed into a convex optimization problem that can be performed efficiently. Furthermore, compared to a centralized control scheme, the distributed stochastic model predictive control algorithm only requires message transmissions when a subsystem is optimized, thereby offering greater flexibility in communication. By designing a tailored invariant terminal set for each subsystem, the proposed algorithm can achieve recursive feasibility, which, in turn, ensures closed‐loop stability of the entire system. A numerical example is given to illustrate the efficacy of the algorithm.     

Probabilistic dual heuristic programming-based adaptive critic

Adaptive critic (AC) methods have common roots as generalisations of dynamic programming for neural reinforcement learning approaches. Since they approximate the dynamic programming solutions, they are potentially suitable for learning in noisy, non-linear and non-stationary environments. In this study, a novel probabilistic dual heuristic programming (DHP)-based AC controller is proposed. Distinct to current approaches, the proposed probabilistic (DHP) AC method takes uncertainties of forward model and inverse controller into consideration. Therefore, it is suitable for deterministic and stochastic control problems characterised by functional uncertainty. Theoretical development of the proposed method is validated by analytically evaluating the correct value of the cost function which satisfies the Bellman equation in a linear quadratic control problem. The target value of the probabilistic critic network is then calculated and shown to be equal to the analytically derived correct value. Full derivation of the Riccati solution for this non-standard stochastic linear quadratic control problem is also provided. Moreover, the performance of the proposed probabilistic controller is demonstrated on linear and non-linear control examples.     

基于零级N/T泛数完整簇的概率逻辑算子的研究

在人工智能中不确定性理论、主观Bayes方法、证据理论等都是基于概率论的.但是,这些不确定性推理方法仅仅是基于概率,而不能真正实现逻辑框架内的概率逻辑不确定推理,产生这种现象的主要原因是概率逻辑自身存在着缺陷.按照泛逻辑学的生成规则,基于零级N/T/S范数完整簇从泛逻辑学的角度来构造概率逻辑算子.结果表明概率逻辑是能够在泛逻辑学的框架内进行柔性化的,是命题泛逻辑在h=0.75时的一种特例.     

概率逻辑、不确定逻辑和模糊逻辑之比较

通过一个实例分析比较了概率逻辑、主观概率逻辑、不确定逻辑和模糊逻辑的思想方法。提出了自己的观点：基于数据统计的概率逻辑是最科学的。不确定逻辑比主观概率逻辑更科学。当具有不确定性的原子命题具有独立性时,不确定逻辑和模糊逻辑的观点是一致的。而对于处理带有不确定性的相关性命题,不确定逻辑比模糊逻辑更科学。但是模糊逻辑在建立推理理论方面见长。     

概率不确定语言熵及其多属性群决策

针对概率不确定语言集的多个不确定语言术语和其概率各不相同的特点,提出基于概率不确定语言熵的多属性决策方法。定义四种新的概率不确定语言熵：模糊熵、犹豫熵、不完全信息熵和总熵,以分别测量概率不确定语言集的模糊性、犹豫性、信息不完全性和整体不确定性。给出了四种熵测度的公理化定义和表达式,根据概率不确定语言集的四种熵,构建能够解决属性权重未知的多属性决策模型,并通过案例和对比分析验证了该模型的有效性和合理性。     

Active disturbance rejection control approach to output‐feedback stabilization of lower triangular nonlinear systems with stochastic uncertainty

In this paper, we apply the active disturbance rejection control approach to output‐feedback stabilization for uncertain lower triangular nonlinear systems with stochastic inverse dynamics and stochastic disturbance. We first design an extended state observer (ESO) to estimate both unmeasured states and stochastic total disturbance that includes unknown system dynamics, unknown stochastic inverse dynamics, external stochastic disturbance, and uncertainty caused by the deviation of control parameter from its nominal value. The stochastic total disturbance is then compensated in the feedback loop. The constant gain and the time‐varying gain are used in ESO design separately. The mean square practical stability for the closed‐loop system with constant gain ESO and the mean square asymptotic stability with time‐varying gain ESO are developed, respectively. Some numerical simulations are presented to demonstrate the effectiveness of the proposed output‐feedback control scheme. Copyright © 2016 John Wiley & Sons, Ltd.