基于MIT规则的自适应扩展集员估计方法

用于非线性椭球估计的自适应扩展集员(Adaptive extended set-membership filter, AESMF)算法在实际应用中存在着过程噪声设定椭球与真实噪声椭球失配的问题, 导致滤波器的估计出现偏差甚至发散. 本文提出了一种基于MIT规则过程噪声椭球最优化的自适应扩展集员估计算法(MIT-AESMF), 用于解决非线性系统时变状态和参数的联合估计和定界中过程噪声无法精确建模问题的新算法. 本算法通过MIT优化规则,在线计算使一步预测偏差包络椭球最小化的过程噪声包络椭球, 以此保证滤波器健康指标满足有效条件; 最后, 采用地面移动机器人状态和动力学参数联合估计验证了所提出方法的有效性.     

一种新的基于保证定界椭球算法的非线性集员滤波器

基于未知但有界噪声假设的集员滤波器为传统的概率化滤波方法提供了一种可行的替代选择, 然而其潜在的计算负担和保守性考虑制约了该方法的实际应用. 本文提出一种新的基于保证定界椭球近似的改进集员滤波方法, 用于解决针对非线性系统的状态估计问题,在保证实时性的前提下降低了算法的保守性. 首先,对非线性模型进行线性化处理,采用DC (Difference of convex)规划方法对线性化误差进行外包定界, 并通过椭球近似将其融合到系统噪声中; 在此基础上提出了一种结合了椭球直和计算和基于迭代外定界椭球算法的椭球--带交集计算 所构成的经典预测--更新步骤来估计得到状态的可行椭球集. 与常规的非线性扩展集员滤波方法的仿真比较表明了本文所提出算法的有效性和改进性能.     

非线性系统中心差分集员估计方法

用于非线性椭球估计的扩展集员算法在实际应用中存在着实现性差、边界估计相对保守等缺陷.本文提出了一种用于非线性系统状态估计的中心差分集员估计方法,以改善传统非线性集员滤波算法的估计性能.为克服泰勒展开的固有缺陷,采用低阶多维Stirling内插多项式代替泰勒展开实现非线性模型的线性化处理;利用半定规划方法对线性化误差进行外包定界并将其融入过程噪声和量测噪声中,以降低误差定界的保守性;量测更新中,为提高算法的实时性,将量测椭球松弛为多个带的交,依次参与状态椭球的更新,从而实现状态定界椭球的次优估计;同时,对椭球—带交集迭代过程中椭球中心到超平面的归一化距离的计算方法进行了改进,使当前时刻每次迭代的椭球均参与计算并选取最优值,以减小累计误差.仿真结果表明了本文所提出算法的有效性和改进性能.     

基于改进集员滤波的港口自动跨运车状态估计方法

针对自动跨运车状态估计问题,设计改进的集员滤波算法,在未知有界噪声环境下,获取自动跨运车实时运动状态的估计信息.首先,将自动跨运车运动学模型进行线性化处理,同时考虑其转向因素和侧倾因素,得到车辆的动力学线性模型;其次,将可能存在的内外部扰动建模为未知有界噪声,进而设计改进的集员滤波器,通过获取状态椭球域实现对自动跨运车运动参数的状态估计,同时给出改进的集员滤波算法;最后,通过仿真实验验证所提出算法的可行性和有效性.实验结果表明,所提出的改进集员滤波算法具有良好的状态估计性能.     

基于超平行空间集员滤波的非线性系统状态估计方法

针对噪声有界但未知条件下的非线性系统状态估计问题,提出基于超平行空间集员滤波算法.利用Stirling矩阵将模型进行一阶展开,基于凸差规划完成线性化误差定界,采用超平行空间表示误差边界和状态可行集,求解下一时刻预测状态可行集超平行体.在更新步将观测值分解为多个带,融入观测值的线性化误差并将带依次与超平行体相交,得到该时刻超平行空间描述下的状态可行集更新情况.所提出算法能够避免在求解线性化误差过程中外包误差集合带来的体积扩充,降低非线性集员滤波算法的保守性,仿真示例验证了所提出算法的可行性和有效性.     

基于UD分解的自适应扩展集员估计方法

用于非线性椭球估计的扩展集员算法在实际应用中存在着数值稳定性差、计算复杂度高以及滤波器参数难以选择等问题. 本文提出了一种基于 UD 分解的自适应扩展集员估计算法, 用于解决非线性系统时变状态和参数的联合估计和定界问题. 新算法将 UD 分解与序列更新和选择更新策略结合起来, 改进了传统扩展集员算法的数值稳定性和实时性能; 同时, 对滤波器参数进行自适应选择以进一步降低计算复杂度并达到次优估计结果. 仿真实验表明了该算法的有效性和鲁棒性.     

基于OBE算法的自适应集员状态估计

研究了具有椭球集合描述的离散时间动态线性系统的状态估计问题.从提高计算的有 效性和可实现性的角度出发,通过在不同的更新阶段采用优化定界椭球(OBE)算法,提出了一 种新颖的解决状态估计的方法.通过与ROBP(recursive state bounding by parallelotopes)算法 和Kalman滤波的仿真比较,验证了本方法的性能.     

运用区间算法的约束非线性系统鲁棒模型预测控制

针对一类具有输入和状态约束的干扰有界非线性系统,提出了基于区间分析的约束非线性鲁棒模型预测控制,以降低计算量并扩大系统吸引域.首先,在集合运算的基础上,利用区间运算和函数区间扩展,给出了一种计算效能更好、保守性更低的非线性系统鲁棒一步集计算方法;其次,构造重叠的多面体控制不变集序列并以此计算约束非线性系统的鲁棒多步集,并通过设计基于集合的在线优化策略,提出了基于鲁棒一步集的单步优化非线性模型预测控制,有效降低了非线性优化的在线计算量;最后,仿真实例验证了算法的有效性.     

基于最优定界椭球的扩展集员滤波算法研究

针对噪声未知但有界的非线性系统,提出了一种基于最优定界椭球的扩展集员滤波算法.首先,对非线性状态方程和量测方程进行泰勒级数展开,采用区间分析方法对线性化误差进行外包定界,并通过椭球近似将其整合到系统噪声中;在此基础上通过预测步和滤波步两步过程来计算与量测和噪声边界近似相一致的待估计状态的可行集.以Duffing方程为例,与扩展卡尔曼滤波方法的仿真比较表明了该算法的精确性和鲁棒性.     

一种强跟踪有限差分滤波二元估计算法

针对非线性工业过程测量的滞后性和模型不确定性给系统状态估计和模型参数估计造成的困难,在扩展Kalman滤波器（EKF）的基础上,引入有限差分滤波器（FDEKF）和次优渐消因子,提出了一种强跟踪有限差分滤波状态和参数二元估计算法。该二元估计算法将滤波器分解为参数滤波和状态滤波两个过程,分别估计模型参数和系统状态。最后,将该算法应用于一化学反应过程的仿真,结果表明,这种强跟踪有限差分滤波的二元估计算法在原模型或参数存在偏差的情况下,仍能较准确地估计系统状态和模型参数,并具有较强的数值鲁棒性。     

Set-membership filtering for polytopic uncertain discrete-time systems

In this paper, a set-membership filtering problem is considered for systems with polytopic uncertainty. A recursive algorithm for calculating an ellipsoid which always contains the state is developed. In the prediction step, a predicted state ellipsoid is determined; in the update step, a state estimation ellipsoid is computed by combining the predicted state ellipsoid and the set of states compatible with the measurement equation. A smallest possible estimate set is calculated recursively by solving the semi-definite programming problems. Hence, the proposed set-membership filter relies on a two-step prediction–correction structure, which is similar to the Kalman filter. Simulation results are provided to demonstrate the effectiveness of the proposed method.     

Parameter set estimation for non-linear systems

Models of dynamical systems are instrumental for many purposes: prediction, control, simulation, tracking and so on. In this paper, we will show how parameter set estimation (PSE) can be applied to non-linear systems. Parameter set estimation identifies a set of estimates which are feasible with respect to the measured data and a priori information. This set of parameters, feasible for the given model structure, can then be used for system tracking or robust control designs. For application to robust control, it is important that the size of this set be as small as possible. In order to apply parameter set estimation techniques to a non-linear system, the system function is expressed in a tensor parameterization which is linear in the parameters (LP). Then it is shown how an optimum volume ellipsoid strategy for linear time invariant systems can be extended to this tensor parameterization of a non-linear system. The methodology is illustrated on two examples, the second of which uses data obtained from an operating glass furnace.     

不确定噪声下基于轴对称盒空间滤波的非线性系统状态估计

针对不确定噪声下的非线性系统状态估计问题, 本文提出了一种基于轴对称盒空间滤波的状态估计方法. 首先, 利用轴对称盒空间包裹线性化过程带来的误差项, 将状态函数线性化误差轴对称盒空间与噪声轴对称盒空间求取闵可夫斯基和, 得到干扰误差轴对称盒空间; 随后, 利用状态量、线性误差和测量噪声的轴对称盒空间的闵可夫斯基和, 得到系统状态预测集; 进而, 利用轴对称盒空间边界正交的性质, 将盒空间拆分为多组超平面, 构造测量更新的约束条件并得到集员包裹. 本文所提方法相比传统的椭球滤波方法而言, 降低了算法的复杂度, 减少了包裹状态可行集和线性化过程带来的余, 获得了更加紧致精确的系统状态集. 最后, 采用非线性弹簧–质量–阻尼器系统验证了本文所提算法的有效性.     

Adaptive model predictive control for a class of constrained linear systems based on the comparison model

This paper proposes an adaptive model predictive control (MPC) algorithm for a class of constrained linear systems, which estimates system parameters on-line and produces the control input satisfying input/state constraints for possible parameter estimation errors. The key idea is to combine the robust MPC method based on the comparison model with an adaptive parameter estimation method suitable for MPC. To this end, first, a new parameter update method based on the moving horizon estimation is proposed, which allows to predict an estimation error bound over the prediction horizon. Second, an adaptive MPC algorithm is developed by combining the on-line parameter estimation with an MPC method based on the comparison model, suitably modified to cope with the time-varying case. This method guarantees feasibility and stability of the closed-loop system in the presence of state/input constraints. A numerical example is given to demonstrate its effectiveness.     

Set membership state and parameter estimation for systems described by nonlinear differential equations

This paper investigates the use of guaranteed methods to perform state and parameter estimation for nonlinear continuous-time systems, in a bounded-error context. A state estimator based on a prediction-correction approach is given, where the prediction step consists in a validated integration of an initial value problem for an ordinary differential equation (IVP for ODE) using interval analysis and high-order Taylor models, while the correction step uses a set inversion technique. The state estimator is extended to solve the parameter estimation problem. An illustrative example is presented for each part.     

Set-based adaptive estimation for a class of nonlinear systems with time-varying parameters

In this paper, an adaptive estimation technique is proposed for the estimation of time-varying parameters for a class of continuous-time nonlinear system. A set-based adaptive estimation is used to estimate the time-varying parameters along with an uncertainty set. The proposed method is such that the uncertainty set update is guaranteed to contain the true value of the parameters. Unlike existing techniques that rely on the use of polynomial approximations of the time-varying behaviour of the parameters, the proposed technique does require a functional representation of the time-varying behaviour of the parameter estimates. A simulation example and a building systems estimation example are considered to illustrate the developed procedure and ascertain the theoretical results.     

Fault detection and estimation for a class of PIDE systems based on boundary observers

In this paper, we propose a simultaneous state estimation and fault estimation approach for a class of first‐order hyperbolic partial integral differential equation systems. Specifically, we consider the multiplicative boundary actuator and sensor faults, ie, unknown fault parameters multiplying by the boundary input or boundary state (ie, output). As a consequence, two difficulties arise immediately: (1) simultaneous estimation of both plant state and faults is a nonlinear problem due to the multiplication between fault parameters and plant signals; (2) no prior information is available to determine the type (actuator or sensor) of faults. To overcome these difficulties, this paper develops adaptive fault parameter update laws and embeds the resulting laws into the plant state observer design. First, we propose new approaches to estimate actuator fault and sensor fault, respectively. Next, we develop a novel method to simultaneously estimate actuator and sensor faults. The proposed observer and update laws, designed using only one boundary measurement, ensure both state estimation and fault parameter estimation. By choosing appropriate Lyapunov functions, we prove that the estimates of state and fault parameters converge to an arbitrarily small neighborhood of their true values. Numerical simulations are used to demonstrate the effectiveness of the proposed estimation approaches.     

Guaranteed robust nonlinear minimax estimation

Minimax parameter estimation aims at characterizing the set of all values of the parameter vector that minimize the largest absolute deviation between the experimental data and the corresponding model outputs. It is well known, however, to be extremely sensitive to outliers in the data resulting, e.g., of sensor failures. In this paper, a new method is proposed to robustify minimax estimation by allowing a prespecified number of absolute deviations to become arbitrarily large without modifying the estimates. By combining tools of interval analysis and constraint propagation, it becomes possible to compute the corresponding minimax estimates in an approximate but guaranteed way, even when the model output is nonlinear in its parameters. The method is illustrated on a problem where the parameters are not globally identifiable, which demonstrates its ability to deal with the case where the minimax solution is not unique.     

Composite adaptive control for Euler-Lagrange systems with additive disturbances

In a typical adaptive update law, the rate of adaptation is generally a function of the state feedback error. Ideally, the adaptive update law would also include some feedback of the parameter estimation error. The desire to include some measurable form of the parameter estimation error in the adaptation law resulted in the development of composite adaptive update laws that are functions of a prediction error and the state feedback. In all previous composite adaptive controllers, the formulation of the prediction error is predicated on the critical assumption that the system uncertainty is linear in the uncertain parameters (LP uncertainty). The presence of additive disturbances that are not LP would destroy the prediction error formulation and stability analysis arguments in previous results. In this paper, a new prediction error formulation is constructed through the use of a recently developed Robust Integral of the Sign of the Error (RISE) technique. The contribution of this design and associated stability analysis is that the prediction error can be developed even with disturbances that do not satisfy the LP assumption (e.g., additive bounded disturbances). A composite adaptive controller is developed for a general MIMO Euler-Lagrange system with mixed structured (i.e., LP) and unstructured uncertainties. A Lyapunov-based stability analysis is used to derive sufficient gain conditions under which the proposed controller yields semi-global asymptotic tracking. Experimental results are presented to illustrate the approach.     

Hybrid intelligent parameter estimation based on grey case-based reasoning for laminar cooling process

In this paper, a hybrid intelligent parameter estimation algorithm is proposed for predicting the strip temperature during laminar cooling process. The algorithm combines a hybrid genetic algorithm (HGA) with grey case-based reasoning (GCBR) in order to improve the precision of the strip temperature prediction. In this context, the hybrid genetic algorithm is formed by combining the genetic algorithm with an annealing and a local multidimensional search algorithm based on deterministic inverse parabolic interpolation. Firstly, the weight vectors of retrieval features in case-based reasoning are optimised using hybrid genetic algorithm in offline mode, and then they are used in grey case-based reasoning to accurately estimate the model parameters online. The hybrid intelligent parameter estimation algorithm is validated using a set of operational data gathered from a hot-rolled strip laminar cooling process in a steel plant. Experiment results show the effectiveness of the proposed method in improving the precision of the strip temperature prediction. The proposed method can be used in real-time temperature control of hot-rolled strip and has potential for parameter estimation of different types of cooling process.