Identification of an additive nonlinear system and its applications in generalized Hammerstein models

An identification algorithm is developed for a class of nonlinear systems that are multi-input and multi-output in an additive form. The convergence results are achieved and its applications to identification of a generalized Hammerstein system is also discussed.     

拟线性对称超松弛形两步递推辨识算法

本文提出一种线性系统拟线性对称超松弛两步递推辨识新算法，并对其收敛性应用常微分方程的方法进行了分析。仿真结果表明算法和本文的收敛定理是一致的。     

A stochastic PID controller for a class of MIMO systems

This paper deals with the design of a controller possessing tracking capability of any realisable reference trajectory while rejecting measurement noise. We consider discrete-time-varying multi-input multi-output stable linear systems and a proportional-integral-derivative (PID) controller. A novel recursive algorithm estimating the time-varying PID gains is proposed. The development of the proposed algorithm is based on minimising a stochastic performance index. The implementation of the proposed algorithm is described and boundedness of trajectories and convergence characteristics are presented for a discretised continuous-time model. Simulation results are included to illustrate the performance capabilities of the proposed algorithm.     

状态空间模型下的Hammerstein系统的递推子空间辨识方法

一般来说, 单输入单输出情形下的Hammerstein系统可以由转移函数来表示, 而对于多输入多输出情形下的系统其输入与输出间的关系难以表示. 本文基于Hammerstein系统的状态空间模型, 研究了其子空间辨识方法. 在开环情形, 对Hammerstein系统给出了在其非线性函数可以由有限基函数线性表示的情形的子空间辨识方法, 及其递推实现. 并且初步分析了这些方法的渐近性质. 针对这一方法, 我们给出了一个数据模拟实例分析方法的优劣.     

Real-time design of an adaptive nonlinear predictive controller

Based on real-time identification and using the concept of NARX (Nonlinear AutoRegressive with exogenous inputs) models, a new adaptive nonlinear predictive controller (ANPC) design is proposed. NARX models represent a natural way to describe the input-output relationship of severely nonlinear systems. From an initial batch of input-output data, a parsimonious NARX model is obtained using the Modified Gram-Schmidt (MGS) orthogonalization algorithm. Following this initial off-line identification and model reduction procedure, the control loop is closed. The ANPC directly uses the obtained structure and initial parameter estimates, which are updated each time step using recursive identification. The controller is designed similar to a typical linear predictive controller based on solving a nonlinear programming (NLP) problem. This paper shows how to solve this NLP problem on-line without the knowledge of the NARX model structure. The design is given for the multi-input multi-output (MIMO) case.     

T-S模糊广义系统的逼近性

本文研究T-S模糊广义系统的逼近性,给出了T-S模糊广义系统的逼近性定理.证明其可以以任意的精度逼近一类广泛存在的非线性广义系统.还将MISO(多输入单输出)情况推广到MIMO(多输入多输出)的情况.在逼近性定理的基础上,利用神经网络的方法对非线性广义系统建模,给出了神经网络的结构及学习算法.本文共提出了两种神经网路的训练策略,对各自的优点与不足给出了分析,最后用数值例子验证了算法的有效性.     

Identification of nonlinear dynamical systems using multilayered neural networks

A novel multilayer discrete-time neural net paradigm is presented for the identification of multi-input multi-output (MIMO) nonlinear dynamical systems. The major novelty of this approach is a rigorous proof of identification error convergence that reveals a requirement for a new identifier structure and nonstandard weight tuning algorithms. The NN identifier includes modified delta rule weight tuning and exhibits a learning-while-functioning feature instead of learning-then-functioning, so that the identification is on-line with no explicit off-line learning phase needed. The structure of the neural net (NN) identifier is derived using a passivity aproach. Linearity in the parameters is not required and certainty equivalence is not used. The notion of persistency of excitation (PE) and passivity properties of the multilayer NN are defined and used in the convergence analysis of both the identification error and the weight estimates.     

A Recursive Orthogonal Least Squares Algorithm for Training RBF Networks

A recursive orthogonal least squares (ROLS) algorithm for multi-input, multi-output systems is developed in this paper and is applied to updating the weighting matrix of a radial basis function network. An illustrative example is given, to demonstrate the effectiveness of the algorithm for eliminating the effects of ill-conditioning in the training data, in an application of neural modelling of a multi-variable chemical process. Comparisons with results from using standard least squares algorithms, in batch and recursive form, show that the ROLS algorithm can significantly improve the neural modelling accuracy. The ROLS algorithm can also be applied to a large data set with much lower requirements on computer memory than the batch OLS algorithm.     

High-pain adaptive stabilization of multivariable linear systems — revisited

We consider the class of multi-input multi-output, finite dimensional, state space systems of the form , where the state dimension is unknown, the system is minumum phase, and it is known that det(CB) ≠ 0. For this class a universal adaptive high gain controller — not based on identification or estimation algorithms — is presented which ensures exponential decay of the motion of the closed-loop system. It is shown that the controller is robust with respect to certain nonlinear perturbations.     

Realisation of linear time-varying systems

In this paper, the realisation problem of linear multi-input multi-output, time-varying systems is studied. The approach, based on the theory of non-commutative polynomial rings, yields explicit and simple formulas for computation of the state coordinates as well as for state equations in observable canonical form. The formulas are based on (left) Euclidean polynomial division.     

Subspace identification for fractional order Hammerstein systems based on instrumental variables

This paper focuses on time-domain identification issues of multi-input multi-output (MIMO) fractional order Hammerstein systems which are the extension of traditional Hammerstein type models by allowing linear part to be fractional order systems. The principal component analysis (PCA) method in subspace family is extended to identify coefficient matrixes of fractional order systems. Singular value decomposition (SVD) is utilized to estimate the unknown parameters of nonlinear part of system directly. A proper instrumental variable is chosen to eliminate the bias of identification results. Numerical simulation validates the proposed method.     

A subspace algorithm for the identification of discrete time frequency domain power spectra

In this paper we present a new subspace algorithm for the identification of multi-input multi-output linear discrete time systems from measured power spectrum data. We show how the state space system matrices can be determined by taking the inverse discrete Fourier transform of the given data and applying the result to a new realization algorithm. Special attention is paid to ensure the positive realness of the identified power spectrum. The computational speed is improved by applying a Lanczos algorithm. The algorithm is illustrated with two practical examples.     

Convergence of stochastic gradient estimation algorithm for multivariable ARX-like systems

This paper studies the convergence of the stochastic gradient identification algorithm of multi-input multi-output ARX-like systems (i.e., multivariable ARX-like systems) by using the stochastic martingale theory. This ARX-like model contains a characteristic polynomial and differs from the conventional multivariable ARX system. The results indicate that the parameter estimation errors converge to zero under the persistent excitation conditions. The simulation results validate the proposed convergence theorem.     

Multi-output process identification

In model based control of multivariate processes, it has been common practice to identify a multi-input single-output (MISO) model for each output separately and then combine the individual models into a final MIMO model. If models for all outputs are independently parameterized then this approach is optimal. However, if there are common or correlated parameters among models for different output variables and/or correlated noise, then performing identification on all outputs simultaneously can lead to better and more robust models. In this paper, theoretical justifications for using multi-output identification for a multivariate process are presented and the potential benefits from using them are investigated via simulations on two process examples: a quality control example and an extractive distillation column. The identification of both the parsimonious transfer function models using multivariate prediction error methods, and of non-parsimonious finite impulse response (FIR) models using multivariate statistical regression methods such as partial least squares (PLS2), canonical correlation regression (CCR) and reduced rank regression (RRR) are considered. The multi-output identification results are compared to traditional single-output identification from several points of view: best predictions, closeness of the model to the true process, the precision of the identified models in frequency domain, stability robustness of the resulting model based control system, and multivariate control performance. The multi-output identification methods are shown to be superior to the single-output methods on the basis of almost all the criteria. Improvements in the prediction of individual outputs and in the closeness of the model to the true process are only marginal. The major benefits are in the stability and performance robustness of controllers based on the identified models. In this sense the multi-output identification methods are more ‘control relevant’.     

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.     

An optimal stochastic multivariable PID controller: a direct output tracking approach

This paper deals with the design of an optimal stochastic controller possessing tracking capability of any reference output trajectory in the presence of measurement noise. We consider multi-input multi-output linear time-invariant systems and a proportional-integral-derivative (PID) controller. The system under consideration needs not be stable. A recursive algorithm providing optimal time-varying PID gains is proposed for the case where the number of inputs is larger than or equal to the number of outputs. The development of the proposed algorithm aims for per-time-sample minimisation of the mean-square output error in the presence of erroneous initial conditions, measurement noise, and process noise. Necessary and sufficient conditions are provided for the convergence of the output error covariance. In addition, convergence results are presented for discretised continuous-time plants. Simulation results are included to illustrate the performance capabilities of the proposed algorithm. Performance comparison with an optimal stochastic iterative learning control scheme, an optimal PID controller, an adaptive PID controller, and a recent optimal stochastic PID controller are also included.     

基于输入输出线性化方法的一类多输入多输出非线性系统的观测器设计

研究一类多输入多输出仿射非线性系统的状态观测器设计问题. 基于输入输出线性化方法提出了一类多输入多输出仿射非线性系统的状态观测器设计的新方法, 并给出保证状态估计误差渐近趋于零的充分条件. 算例表明了所得结果的有效性.     

Event-triggered adaptive fuzzy tracking control of nonlinear MIMO systems

This paper addresses the problem of an adaptive fuzzy event-triggered control (ETC) for uncertain multi-input and multi-output nonlinear systems. To reduce the communication burden of the network control systems, a novel state-dependent event-triggering condition is designed to decide when to update the controllers. By combining the backstepping and event-trigged techniques, the adaptive fuzzy ETC strategies are developed and the resulting closed-loop system is semi-global bounded. Finally, the analytical results are substantiated using simulation studies.     

大变量多输出逻辑函数实质项识别算法

在对Espresso算法进行分析改进的基础上,提出了一种基于全域识别的多输入多输出逻辑函数实质本源项、完全冗余项和相对冗余项生成算法,该算法通过对基于积项表示的多输入多输出逻辑函数的余因子计算来进行全域判断,根据全域判断结果来识别实质本源项、完全冗余项和相对冗余项,从而构成实质本源项集合、完全冗余项集合和相对冗余项集合.对基于二级SOP型的多输入多输出逻辑函数设计了多输入多输出逻辑函数优化识别软件系统,允许的最大输入变量数为128、最大输出变量数为256、最大输入输出变量总和为300、最大输入积项数为20 000.软件系统在Pentium 1.8GHz、512MB内存的计算机上通过了Benchmark例题的测试.