一般双率随机系统状态空间模型及其辨识

对于双率采样数据系统,本文使用提升技术,推导了双率系统的提升状态空间模型.对 于系统状态可测量的双率系统,利用最小二乘原理辨识提升系统模型的参数矩阵;对于状态不 可测的未知参数双率系统,利用递阶辨识原理,提出了双率系统递阶状态空间模型辨识方法,来 辨识系统的状态和参数.具体做法:基于获得的状态估计和提升系统的输入输出数据递归估计 系统参数,然后基于获得的参数估计,计算系统的状态.     

基于协同PSO算法的非均匀采样系统辨识

对于非均匀采样数据的双率系统,运用提升技术,得到系统离散状态空间模型,变换得到相应的传递函数模型。讨论在有色噪声和白噪声的干扰下,提出了利用协同粒子群（Cooperative Particle Swarm Optimization,CPSO）的新颖算法,通过实验仿真对比传统的算法和协同PSO算法的精度和鲁棒性,证明新型算法的有效性和合理性。     

多采样率系统的辨识问题综述

在多率采样系统中, 采样间隔不均匀. 本文综述了文献中有关多率采样系统的数学模型, 如线性周期时变模型、频域模型和连续状态空间模型等. 同时对相应的辨识方法, 如提升、频域方法、子空间辨识方法等, 也进行了全面的综述. 对多率采样系统辨识中存在的一些问题, 包括辨识模型的选择、一致性问题、带约束条件的辨识方法和辨识收敛性等, 也作了深入的讨论.     

Two recursive least squares parameter estimation algorithms for multirate multiple-input systems by using the auxiliary model

This paper considers identification problems of multirate multiple-input output error systems, derives the input-output representations by using the state space models of the multirate systems, and presents two auxiliary model based recursive least squares algorithms for the corresponding output error models with each subsystem having different or same denominator polynomials. The simulation results show the effectiveness of the proposed algorithms.     

输出信号量化的双率采样系统参数辨识方法

针对双率采样和信号量化(signal quantization)[BFQB]的控制系统,采用随机重复性试验测量信息,提出基于辅助模型的双率采样量化控制系统辨识方法.分析了在随机重复试验和放松估计误差方差条件下,双率采样量化系统的模型特征并给出了分两步辨识的策略,推导了进行参数辨识所满足的持续激励条件,并给出了基于辅助模型的双率采样量化控制系统量化辨识递推算法;接着分析了所给出量化辨识递推算法的收敛性,得到了双率采样量化系统参数估计误差上界的计算式,最后数字仿真验证了该算法及结论的有效性.     

非均匀采样多率ARMAX系统RELS算法性能分析

针对一类有色噪声干扰的非均匀采样多率ARMAX系统的辩识问题,基于增广参数维数理论,将系统模型参数化,将信息向量中含有的不可测噪声项用其估计残差代替,推导了非均匀采样ARMAX系统的递推增广最小二乘(RELS)算法;利用鞅收敛定理对该算法的收敛性进行了理论分析,结果表明该算法在噪声方差有界和广义持续激励的条件下能够收敛到真参数.仿真例子验证了该算法具有良好的收敛速度与估计精度.     

Multirate sampled-data systems: computing fast-rate models

This paper studies identification of a general multirate sampled-data system. Using the lifting technique, we associate the multirate system with an equivalent linear time-invariant system, from which a fast-rate discrete-time system is extracted. Uniqueness of the fast-rate system, controllability and observability of the lifted system, and other related issues are discussed. The effectiveness is demonstrated through simulation and real-time implementation.     

Generalized Yule-walker and two-stage identification algorithms for dual-rate systems

1 Introduction Presenting new identification methods and performance analysis of identification algorithms under weak conditions are everlasting themes and melodies of identification studies and are also my everlasting pursuits in life [1～4]. Multirate systems with different input and output sampling periods are very active in process industries [5～7], e.g. fermenta- tion processes [8], and petroleum production [9]. The stud- ies of multirate systems involve various areas of control, in- clu…     

Generalized Yule-walker and two-stage identification algorithms for dual-rate systems

In this paper, two approaches are developed for directly identifying single-rate models of dual-rate stochas- tic systems in which the input updating frequency is an integer multiple of the output sampling frequency. The first is the generalized Yule-Walker algorithm and the second is a two-stage algorithm based on the correlation technique. The basic idea is to directly identify the parameters of underlying single-rate models instead of the lifted models of dual-rate systems from the dual-rate input-output data, assuming that the measurement data are stationary and ergodic. An example is given.     

多变量系统状态空间模型的递阶辨识

研究多变量系统状态空间模型的递阶辨识问题,推广了作者提出的标量系统状态和参数联合辨识算法.当状态可量测时,利用最小二乘原理直接辨识状态空间模型的参数矩阵;当状态不可测时,利用递阶辨识原理提出了状态空间模型递阶辨识方法,使用系统输入输出数据来估计系统的未知状态和参数.状态空间模型递阶辨识方法分为两步:首先假设系统状态是已知的(即参数估计算法中的未知系统状态用其估计代替),基于状态估计和系统输入输出数据递归计算系统参数估计;然后基于系统输入输出数据和获得的参数估计,递归计算系统的状态估计.     

A modified stochastic gradient based parameter estimation algorithm for dual-rate sampled-data systems

In this paper, we propose a novel identification algorithm for a class of dual-rate sampled-data systems whose input–output data are measured by two different sampling rates. A polynomial transformation technique is employed to derive a mathematical model for such dual-rate systems. The proposed modified stochastic gradient algorithm has faster convergence rate than stochastic gradient algorithms for parameter identification using the dual-rate input–output data. Convergence properties of the algorithm are analyzed. Finally, illustrative and comparison examples are provided to verify the effectiveness and performance improvement of the proposed method.     

Combined parameter and output estimation of dual-rate systems using an auxiliary model

For a dual-rate sampled-data system, an auxiliary model based identification algorithm for combined parameter and output estimation is proposed. The basic idea is to use an auxiliary model to estimate the unknown noise-free output (true output) of the system, and directly to identify the parameters of the underlying fast single-rate model from the dual-rate input-output data. It is shown that the parameter estimation error consistently converges to zero under generalized or weak persistent excitation conditions and unbounded noise variance, and that the output estimates uniformly converge to the true outputs. An example is included.     

非均匀采样系统的一种递推辨识方法

在非均匀采样系统辨识方法中, 通常利用重采样、数值积分等方法来处理非均匀采样数据, 所用模型多为连续有理分式传递函数, 在递推形式下非均匀采样对象又常局限于``数据缺失'的情况. 本文研究更为一般的异步非均匀采样的多变量系统, 采用连续时间状态空间模型描述, 推导了模型参数、参数梯度和系统状态之间的相互递推关系, 构成一种可变迭代间隔的递推辨识算法, 在每次输出采样点上仅更新模型中受当前采样数据影响的参数. 这种辨识方法可以适用于任意非均匀采样系统, 多采样率系统也可作为一种特例适用于本算法. 仿真结果表明, 所提的方法是可行有效的.     

Least squares based iterative identification for a class of multirate systems

This paper studies modeling and identification problems for multi-input multirate systems with colored noises. The state-space models are derived for the systems with different input updating periods and furthermore the corresponding transfer functions are obtained. To solve the difficulty of identification models with unmeasurable noises terms, the least squares based iterative algorithm is presented by replacing the unmeasurable variables with their iterative estimates. Finally, the simulation results indicate that the proposed iterative algorithm has advantages over the recursive algorithms.     

State estimation and parameter identification method for dual-rate system based on improved Kalman prediction

For the dual-rate system, such as the process of space teleoperation whose control signals is partly determined by delayed feedback states, the state values and system parameters are coupled and influenced each other, which are hard to be estimated simultaneously. In this paper, we propose a novel method for this problem. Firstly, considering the asynchronism of the input and output sampling signals, an auxiliary model is modeled as a medium to the state and output functions. Secondly, the Kalman prediction algorithm is improved to estimate the state values at output signals of the dual-rate system. The general step is using the output estimated errors in original and auxiliary systems to modify the estimated state values of the auxiliary model, and then the unknown state values in original system is defined by the ones in auxiliary model. Based on improved Kalman algorithm and hierarchical identification algorithm, we present the detailed procedures of state estimation and parameter identification method for the dual-rate system. The processes of state estimation and parameter identification are calculated and modified alternately. Finally, the simulation results reveal that the state and parameters both approach to the real values and the state values converge faster than the parameters.     

Input-state model matching and ripple-free response for dual-rate systems

In this paper, we address the model matching problem for dual-rate systems where the controller output is generated at a faster rate than the measurement update rate. The model matching problem that has been studied in the literature requires the input-output properties of the closed-loop multirate system to match those of a desired single-rate linear time-invariant (LTI) system. In this paper, we consider the model matching problem from the input-state viewpoint: given a desired LTI system, find conditions and provide a controller design procedure to achieve matching between the closed-loop system and the desired system state variables at the measurement update rate. We provide a solution to this problem using a particular time-varying controller structure. In addition, we give conditions to avoid ripples in the steady-state output of the continuous-time plant; in particular, we show that some constraints on the input matrix of the desired system have to be posed. Numerical examples are given to illustrate the proposed method.     

一种基于小波多分辨分析的多率采样系统辨识方法

基于小波多分辨分析理论并结合面向控制的辨识思想, 提出一种多率采样系统分频段加权辨识方法. 首先研究了采样信息的一致性重构问题, 然后给出一种新颖的分频段加权辨识方法. 此方法的最大特点是对噪声不敏感, 易实现对感兴趣频段的精确建模, 便于和控制系统设计相配合. 仿真结果验证了这种方法的可行性.     

State-dependent parameter modelling and identification of stochastic non-linear sampled-data systems

State-dependent parameter representations of stochastic non-linear sampled-data systems are studied. Velocity-based linearization is used to construct state-dependent parameter models which have a nominally linear structure but whose parameters can be characterized as functions of past outputs and inputs. For stochastic systems state-dependent parameter ARMAX (quasi-ARMAX) representations are obtained. The models are identified from input–output data using feedforward neural networks to represent the model parameters as functions of past inputs and outputs. Simulated examples are presented to illustrate the usefulness of the proposed approach for the modelling and identification of non-linear stochastic sampled-data systems.     

非均匀周期采样系统的递阶最小二乘辨识方法

针对非均匀周期采样系统,通过状态空间模型离散化方法得到其输入输出表达形式.鉴于参数化后得到的辨识模型同时包含1个参数向量和1个参数矩阵,利用递阶辨识原理,将辨识模型分解为分别含有参数向量和参数矩阵的2个虚拟子系统;考虑到系统的因果约束问题,将包含参数矩阵的子系统分解为子子系统进行辨识,从而提出这类非均匀采样系统的递阶最小二乘辨识方法.仿真例子表明该算法是有效的.     

Nonlinear predictive control of irregularly sampled multirate systems using blackbox observers

This work aims the development of an inferential nonlinear model predictive control (NMPC) scheme based on a nonlinear fast rate model that is identified from irregularly sampled multirate data, which is corrupted with unmeasured disturbances and measurement noise. The model identification is carried out in two steps. In the first step, a MISO fast rate nonlinear output error (NOE) model is identified from the irregularly sampled output data. In the second step, a time varying nonlinear auto-regressive (NAR) type model is developed using the residuals generated in the first step. The deterministic and stochastic components of the observer are parameterized using generalized ortho-normal basis filters (GOBF). The identified NOE and NAR models are combined to form MISO state observers. We then proceed to use these identified observers to formulate a nonlinear MPC strategy for controlling irregularly sampled multirate systems. The identified observers are used to generate inter-sample estimates of the irregularly sampled outputs and for performing future trajectory predictions. The efficacy of the proposed modeling and control scheme is demonstrated using simulations on a benchmark continuous fermentation process. This process exhibits input multiplicity and change in the sign of steady state gain in the operating region. The validity of the proposed modeling and control scheme is also established by conducting identification and control experiments on a laboratory scale heater-mixer setup. The proposed NMPC gives satisfactory regulatory as well as servo performance over a wide operating range in the irregularly sampled multirate scenario.