Efficient moving horizon state and parameter estimation for SMB processes

In this paper, a moving horizon state and parameter estimation scheme for chromatographic simulated moving bed SMB processes is proposed. The simultaneous state and parameter estimation is based on a high-order nonlinear SMB model which incorporates rigorous models of the chromatographic columns and the discrete shiftings of the inlet and outlet ports. The estimation is performed using sparse measurement information: the concentrations of the components are only measured at the two outlet ports (which are periodically switched from one column to the next) and at one fixed location between two columns. The goal is to reconstruct the full state of the system, i.e. the concentration profiles along all columns, and to identify critical model parameters reliably such that the estimated model can be used in the context of online optimizing control. The state estimation scheme is based upon a deterministic model within the prediction horizon, state noise is only present in the state and the parameters prior to and at the beginning of the horizon. By solving the optimization problem with a multiple-shooting method and applying a real-time iteration scheme, the computation times are such that the scheme can be applied online. Numerical simulations of a validated model for a separation problem with nonlinear isotherms of the Langmuir type demonstrate the efficiency of the algorithm.     

Lagrangian duality between constrained estimation and control

We show that the Lagrangian dual of a constrained linear estimation problem is a particular nonlinear optimal control problem. The result has an elegant symmetry, which is revealed when the constrained estimation problem is expressed as an equivalent nonlinear optimisation problem. The results extend and enhance known connections between the linear quadratic regulator and linear quadratic state estimation problems.     

An integrated optimal control algorithm for discrete-time nonlinear stochastic system

Consider a discrete-time nonlinear system with random disturbances appearing in the real plant and the output channel where the randomly perturbed output is measurable. An iterative procedure based on the linear quadratic Gaussian optimal control model is developed for solving the optimal control of this stochastic system. The optimal state estimate provided by Kalman filtering theory and the optimal control law obtained from the linear quadratic regulator problem are then integrated into the dynamic integrated system optimisation and parameter estimation algorithm. The iterative solutions of the optimal control problem for the model obtained converge to the solution of the original optimal control problem of the discrete-time nonlinear system, despite model-reality differences, when the convergence is achieved. An illustrative example is solved using the method proposed. The results obtained show the effectiveness of the algorithm proposed.     

基于交互容积卡尔曼的随机切换系统故障诊断

针对一类随机切换非线性系统的故障检测和故障估计问题,提出了一种基于交互式多模型和容积卡尔曼滤波（IMM CKF）的系统状态估计算法。该算法利用容积卡尔曼滤波（CKF）在不同时刻对每个子系统进行状态估计,把不同子系统状态估计结果融合得到最终的状态估计,实现对系统真实状态的估计。针对一类随机切换非线性系统发生执行器故障,采用IMM CKF估计系统状态;然后分析了IMM CKF算法的稳定性;根据状态估计结果,构造残差信号,设计残差评价函数,检测故障发生。当检测到故障发生时,设计增广系统,对故障幅值进行估计。通过仿真实验验证提出算法的有效性,结果表明该算法可以较为准确地诊断系统故障。     

基于双线性模型的连续时间非线性最优控制的DISOPE 算法

对连续时间非线性最优控制问题出了基于双线性二次型问题的ＤＩＳＯＰＥ算法,在模型与实际存在差异的情况下,通过求解修正的基于双线性模型的优化总理２和参数估计问题,给出了实际问题的最优解,提出了求解非齐次双线性二次型问题的迭代算法,分析了该算法的收敛性,仿真结果表明该算法比现有算法有更好的收敛特性。     

一类不确定非线性MIMO系统的神经网络输出反馈跟踪控制

针对一类具有外部干扰的不确定仿射非线性MIMO系统提出了一种神经网络输出反馈跟踪控制方法. 在仅输出可测的情况下, 控制律和神经网络权值更新律中仅用到输出误差, 无需设计状态观测器或加入低通滤波器使得估计误差动态满足严格正实条件. 为抑制外部干扰和子系统间的交叉耦合及神经网络逼近误差, 在控制律中加入鲁棒控制项. 基于Lyapunov稳定性定理证明了系统的稳定性及信号的有界性. 仿真例子证实了所提方法的可行性.     

Simultaneous state and input estimation of hybrid systems with unknown inputs

This paper addresses the problem of the simultaneous state and input estimation for hybrid systems when subject to input disturbances. The proposed algorithm is based on the moving horizon estimation (MHE) method and uses mixed logical dynamical (MLD) systems as equivalent representations of piecewise affine (PWA) systems. So far the MHE method has been successfully applied for the state estimation of linear, hybrid, and nonlinear systems. The proposed extension of the MHE algorithm enables the estimation of unknown inputs, or disturbances, acting on the hybrid system. The new algorithm is shown to improve the convergence characteristics of the MHE method by reducing the delay of convergent estimates, while assuring convergence for every possible sequence of input disturbances. To ensure convergence the system is required to be incrementally input observable, which is an extension to the classical incremental observability property.     

基于支持向量机的可分离非线性动态系统辨识

针对状态变量和控制变量可分离的非线性动态系统模型,通过引入两个非线性核函数重新设计了标准支持向量机的回归估计模型,使之适用于非线性动态系统的辨识. 它包含两个分别关于状态变量和控制变量的非线性函数,用于辨识可分离变量非线性动态系统中的两个非线性函数.文中的仿真实验验证了我们算法用于非线性动态系统辨识的有效性.     

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.     

不确定系统的变结构鲁棒自适应控制及其在机械手控制中的应用

本文针对一类不确定非线性系统,通过状态微分同坯变换和反馈控制建立了系统的变结构鲁棒控制设计过程,并在此基础上提出了一种新型的变结构鲁棒自适应控制算法。该算法优点是:1)不需要确切知道系统不确定性,也不需要知道不确定性的界,而是利用自适应规律对系统不确定性范围进行在线估计;2)能够保证系统获得较为满意的动态性能;3)控制规律是连续性的,因而避免了一般变结构系统中的不连续控制所导致的颤振现象。为了说明本文所提算法的正确性,本文还以二连杆机械手为例讨论了其终端夹持不定载荷时的轨迹跟踪问题。     

基于极大似然准则和最大期望算法的自适应UKF 算法

针对噪声先验统计特性未知情况下的非线性系统状态估计问题,提出了基于极大似然准则和 最大期望算法的自适应无迹卡尔曼滤波(Unscented Kalman filter, UKF) 算法.利用极大似然准则构造含有噪声统计特性的对数似然函数,通 过最大期望算法将噪声估计问题转化为对数似然函数数学期望极大化问题,最终得到带次优递 推噪声统计估计器的自适应UKF算法.仿真分析表明,与传统UKF算法相比,提出的自适应UKF算法 有效克服了传统UKF算法在系统噪声统计特性未知情况下滤波精度下降的问题,并实现了系统噪 声统计特性的在线估计.     

Constrained state estimation for nonlinear discrete-time systems: stability and moving horizon approximations

State estimator design for a nonlinear discrete-time system is a challenging problem, further complicated when additional physical insight is available in the form of inequality constraints on the state variables and disturbances. One strategy for constrained state estimation is to employ online optimization using a moving horizon approximation. We propose a general theory for constrained moving horizon estimation. Sufficient conditions for asymptotic and bounded stability are established. We apply these results to develop a practical algorithm for constrained linear and nonlinear state estimation. Examples are used to illustrate the benefits of constrained state estimation. Our framework is deterministic.     

Observer forms for perspective systems

The estimation of three-dimensional position information from two-dimensional images in computer vision systems can be formulated as a state estimation problem for a nonlinear perspective dynamic system. The multi-output state estimation problem has been treated by several authors using methods for nonlinear observer design. This paper shows that a perspective system can be transformed to two observer forms, and provides constructive methods for arriving at the transformations. These observer forms lead to straightforward observer designs. First, it is shown that, using an output transformation, the system admits an observer form which leads to an observer with linear error dynamics. A second observer design is based on a time-scaled block triangular form. Both designs assume a commonly used observability condition. The designs are demonstrated in simulation.     

A hybrid learning scheme combining EM and MASMOD algorithms forfuzzy local linearization modeling

Fuzzy local linearization (FLL) is a useful divide-and-conquer method for coping with complex problems such as modeling unknown nonlinear systems from data for state estimation and control. Based on a probabilistic interpretation of FLL, the paper proposes a hybrid learning scheme for FLL modeling, which uses a modified adaptive spline modeling (MASMOD) algorithm to construct the antecedent parts (membership functions) in the FLL model, and an expectation-maximization (EM) algorithm to parameterize the consequent parts (local linear models). The hybrid method not only has an approximation ability as good as most neuro-fuzzy network models, but also produces a parsimonious network structure (gain from MASMOD) and provides covariance information about the model error (gain from EM) which is valuable in applications such as state estimation and control. Numerical examples on nonlinear time-series analysis and nonlinear trajectory estimation using FLL models are presented to validate the derived algorithm.     

Output feedback adaptive DSC for nonlinear systems with guaranteed L-infinity tracking performance

In this paper, the problem of output tracking for a class of uncertain nonlinear systems is considered. First, neural networks are employed to cope with uncertain nonlinear functions, based on which state estimation is constructed. Then, an output feedback control system is designed by using dynamic surface control (DSC). To guarantee the L-infinity tracking performance, an initialization technique is presented. The main feature of the scheme is that explosion of complex- ity problem in backstepping control is avoided, and there is no need to update the unknown parameters including control gains as well as neural networks weights, the adaptive law with one update parameter is necessary only at the first design step. It is proved that all signals of the closed-loop system are semiglobally uniformly ultimately bounded and the L-infinity performance of system tracking error can be guaranteed. Simulation results demonstrate the effectiveness of the proposed scheme.     

Output mini-max control for polynomial systems: analysis and applications

This paper presents a solution to a robust optimal regulation problem for a nonlinear polynomial system affected by parametric and matched uncertainties, which is based only on partial state information. The parameters describing the dynamics of the nonlinear polynomial plant depend on a vector of unknown parameters, which belongs to a finite parametric set, and the application of a certain control input is associated with the worst or least favourable value of the unknown parameter. A high-order sliding mode state reconstructor is designed for the nonlinear plant in such a way that the previously designed control can be applied for a system with incomplete information. Additionally, the matched uncertainty is also compensated by means of the same output-based regulator. The obtained algorithm is applied to control an uncertain nonlinear inductor circuit of the third order and a mechanical pendulum of the third order, successfully verifying the effectiveness of the developed approach.     

基于粒子滤波的机动目标跟踪算法仿真研究

针对非线性多目标模型,应用粒子滤波算法,这种方法不受模型线性和Gauss假设的约束,是一种处理非线性非高斯动态系统状态递推估计的有效算法。在粒子滤波的基础上融合扩展卡尔曼滤波算法和无迹卡尔曼滤波算法。融合后的新算法在计算提议概率密度分布时,粒子的产生充分考虑当前时刻的量测,使得粒子的分布更加接近状态的后验概率分布,再用平滑算法处理滤波的结果。仿真结果表明,算法有较好的跟踪效果。     

Unscented卡尔曼滤波在状态估计中的应用

针对非线形系统的滤波问题,无法使用卡尔曼滤波器（KF）,扩展卡尔曼滤波（EKF）方法虽能应用于非线形系统,但给出的是状态的有偏估计,并且对模型误差的鲁棒性较差。为了给出更好的状态估计值,该文介绍了Unscented卡尔曼滤波（UKF）的基本原理。其思想是：基于unscented变换,UKF滤波算法能够给出更精确的均值和协方差的估计,从而带来更高的精度。最后通过Mackey—Glass模型时间序列的状态估计仿真实侧说明：同EKF相比,UKF的滤波精度和稳定性都显著提高了,还可避免计算烦琐的Jacobi矩阵,是一种良好的非线性滤波方法。     

Optimal state estimation for stochastic systems: an informationtheoretic approach

In this paper, we examine the problem of optimal state estimation or filtering in stochastic systems using an approach based on information theoretic measures. In this setting, the traditional minimum mean-square measure is compared with information theoretic measures, Kalman filtering theory is reexamined, and some new interpretations are offered. We show that for a linear Gaussian system, the Kalman filter is the optimal filter not only for the mean-square error measure, but for several information theoretic measures which are introduced in this work. For nonlinear systems, these same measures generally are in conflict with each other, and the feedback control policy has a dual role with regard to regulation and estimation. For linear stochastic systems with general noise processes, a lower bound on the achievable mutual information between the estimation error and the observation are derived. The properties of an optimal (probing) control law and the associated optimal filter, which achieve this lower bound, and their relationships are investigated. It is shown that for a linear stochastic system with an affine linear filter for the homogeneous system, under some reachability and observability conditions, zero mutual information between estimation error and observations can be achieved only when the system is Gaussian     

Cooperative Localization of AUVs Using Moving Horizon Estimation

This paper studies the localization problem of autonomous underwater vehicles (AUVs) constrained by limited size, power and payload. Such AUVs cannot be equipped with heavy sensors which makes their underwater localization problem difficult. The proposed cooperative localization algorithm is performed by using a single surface mobile beacon which provides range measurement to bound the localization error. The main contribution of this paper is twofold: 1) The observability of single beacon based localization is first analyzed in the context of nonlinear discrete time system, deriving a sufficient condition on observability. It is further compared with observability of linearized system to verify that a nonlinear state estimation is necessary. 2) Moving horizon estimation is integrated with extended Kalman filter (EKF) for three dimensional localization using single beacon, which can alleviate the computational complexity, impose various constraints and make use of several previous range measurements for each estimation. The observability and improved localization accuracy of the localization algorithm are verified by extensive numerical simulation compared with EKF.