Model identification using tie line power and frequency measurements

The identification of dynamic models which relate power and frequency deviations on a tie line of a power system is investigated. The identification problem is posed and three identification algorithms are presented which produce least squares models with different structural properties. Model order is determined by applying residual and system structure tests to a sequence of models of increasing order. These tests indicate the model order for both equivalent realizations and predictive models. Equivalent realizations are identified on one data set and then their performance as a dynamic equivalent is evaluated on a second data set. These equivalent realizations are also used to predict frequency in an iterative frequency prediction algorithm. Predictive models are also identified and their performance as frequency predictors is evaluated using a direct prediction algorithm. The identification of dynamic equivalents provides information about the structural properties of power systems. The use of dynamic equivalents and predictive models for frequency prediction indicates the tradeoff in accuracy vs the prediction interval which can be obtained using these least squares algorithms and the measurement device presently available.     

Variable projection algorithms with sparse constraint for separable nonlinear models

Separable nonlinear models are widely used in various fields such as time series analysis, system modeling, and machine learning, due to their flexible structures and ability to capture nonlinear behavior of data. However, identifying the parameters of these models is challenging, especially when sparse models with better interpretability are desired by practitioners. Previous theoretical and practical studies have shown that variable projection (VP) is an efficient method for identifying separable nonlinear models, but these are based on L2 penalty of model parameters, which cannot be directly extended to deal with sparse constraint. Based on the exploration of the structural characteristics of separable models, this paper proposes gradient-based and trust-region-based variable projection algorithms, which mainly solve two key problems: how to eliminate linear parameters under sparse constraint; and how to deal with the coupling relationship between linear and nonlinear parameters in the model. Finally, numerical experiments on synthetic data and real time series data are conducted to verify the effectiveness of the proposed algorithms.     

On the nonuniqueness of singular value functions and balanced nonlinear realizations

The notion of balanced realizations for nonlinear state space model reduction problems was first introduced by Scherpen in 1993. Analogous to the linear case, the so-called singular value functions of a system describe the relative importance of each state component from an input–output point of view. In this paper it is shown that the procedure for nonlinear balancing has some interesting ambiguities that do not occur in the linear case. Specifically, distinct sets of singular value functions and balanced realizations are possible.     

Control of discrete time nonlinear systems with a time-varying structure

In this paper, we present a control methodology for a class of discrete time nonlinear systems that depend on a possibly exogenous scheduling variable. This class of systems consists of an interpolation of nonlinear dynamic equations in strict feedback form, and it may represent systems with a time-varying nonlinear structure. Moreover, this class of systems is able to represent some cases of gain scheduling control, Takagi-Sugeno fuzzy systems, as well as input-output realizations of nonlinear systems which are approximated via localized linearizations. We present two control theorems, one using what we call a “global” approach (akin to traditional backstepping), and a “local” approach, our main result, where backstepping is again used but the control law is an interpolation of local control terms. An aircraft wing rock regulation problem with varying angle of attack is used to illustrate and compare the two approaches.     

On condition/event systems with discrete state realizations

This paper introduces condition/event (C/E) systems as a class of continuous-time discrete event dynamic systems (DEDS) with two types of discrete-valued input and output signals:condition signals andevent signals. In applications such as discrete control, C/E systems provide an intuitive continuous-time modeling framework amenable to block diagram representation. In this paper we consider C/E systems with discrete state realizations, and study the relationship between continuous-time C/E systems and untimed models of their sequential inputoutput behavior called C/E languages. We show that C/E systems with discrete state realizations are necessarilytime-change invariant (Theorem 3.1), which means the ensemble of admissible continuous-time input-output behaviors is completely characterized by the C/E language for the system (Theorem 4.1). It is also shown that deterministic C/E systems with discrete state realizations are necessarily discrete-time (clocked) systems (Corollary 3.1), and that finite discrete state realizations exist for a C/E system only if its related C/E language has a finite state generator (Theorem 4.2). Finally, we develop equivalent discrete-state realizations for C/E systems resulting from cascade and feedback interconnections. The paper concludes with a discussion of several directions for future research.Please direct correspondence concerning this paper to B.H. Krogh at the above address.     

A method to construct reduced‐order parameter‐varying models

This paper describes a method to construct reduced‐order models for high‐dimensional nonlinear systems. It is assumed that the nonlinear system has a collection of equilibrium operating points parameterized by a scheduling variable. First, a reduced‐order linear system is constructed at each equilibrium point using state, input, and output data. This step combines techniques from proper orthogonal decomposition, dynamic mode decomposition, and direct subspace identification. This yields discrete‐time models that are linear from input to output but whose state matrices are functions of the scheduling parameter. Second, a parameter‐varying linearization is used to connect these linear models across the various operating points. The key technical issue in this second step is to ensure the reduced‐order linear parameter‐varying system approximates the nonlinear system even when the operating point changes in time. Copyright © 2016 John Wiley & Sons, Ltd.     

Review of rational (total) nonlinear dynamic system modelling,identification, and control

This paper is a summary of the research development in the rational (total) nonlinear dynamic modelling over the last two decades. Total nonlinear dynamic systems are defined as those where the model parameters and input (controller outputs) are subject to nonlinear to the output. Previously, this class of models has been known as rational models, which is a model that can be considered to belong to the nonlinear autoregressive moving average with exogenous input (NARMAX) model subset and is an extension of the well-known polynomial NARMAX model. The justification for using the rational model is that it provides a very concise and parsimonious representation for highly complex nonlinear dynamic systems and has excellent interpolatory and extrapolatory properties. However, model identification and controller design are much more challenging compared to the polynomial models. This has been a new and fascinating research trend in the area of mathematical modelling, control, and applications, but still within a limited research community. This paper brings several representative algorithms together, developed by the authors and their colleagues, to form an easily referenced archive for promotion of the awareness, tutorial, applications, and even further research expansion.     

Fixed point iteration in identifying bilinear models

Inspired by fixed point theory, an iterative algorithm is proposed to identify bilinear models recursively in this paper. It is shown that the resulting iteration is a contraction mapping on a metric space when the number of input–output data points approaches infinity. This ensures the existence and uniqueness of a fixed point of the iterated function sequence and therefore the convergence of the iteration. As an application, one class of block-oriented systems represented by a cascade of a dynamic linear (L), a static nonlinear (N) and a dynamic linear (L) subsystems is illustrated. This gives a solution to the long-standing convergence problem of iteratively identifying LNL (Winer–Hammerstein) models. In addition, we extend the static nonlinear function (N) to a nonparametric model represented by using kernel machine.     

Input design for structured nonlinear system identification

This paper is concerned with the input design problem for a class of structured nonlinear models. This class contains models described by an interconnection of known linear dynamic systems and unknown static nonlinearities. Many widely used model structures are included in this class. The model class considered naturally accommodates a priori knowledge in terms of signal interconnections. Under certain structural conditions, the identification problem for this model class reduces to standard least squares. We treat the input design problem in this situation.An expression for the expected estimate variance is derived. A method for synthesizing an informative input sequence that minimizes an upper bound on this variance is developed. This reduces to a convex optimization problem. Features of the solution include parameterization of the expected estimate variance by the input distribution, and a graph-based method for input generation.     

Computation of thermodynamic mixing parameters for isostructural,binary crystalline solutions using solvus experimental data

FORTRAN IV subroutines are presented for calculating the mixing parameters of the two-parameter Margules, van Laar, and quasichemical solution models. For isostructural, binary crystalline solutions the mixing parameters of these models are calculated using experimental data on the compositions and equilibration temperatures (K) of the two phases in binary “solvus-pairs”. However, the equations used in the calculations are different for each model, and computational methods range from direct calculation (Margules and van Laar models), to solution of two simultaneous nonlinear equations (quasichemical model). Most of the subroutines have been written so that they can be incorporated easily into a user's linear least-squares regression program to compute equations relating a set of values for a parameter to temperature, or temperature and pressure.Crystal structure plays an important role in the calculation of mixing parameters for the three solution models. For solvi among phases of different structure, mixing-parameter values should be calculated using not only the compositions and equilibration temperatures of the two phases in solvus-pairs, but also the values for the differences in free energies of the crystal structures in the standard state. Some thermodynamic theory of mutual solubility among binary crystalline phases of like and unlike structure will be described in detail.     

基于Hammerstein模型描述的非线性系统辨识新方法

Hammerstein模型常用来描述pH值或具有幂函数、死区、开关等特性的过程,本文提出了一种辨识此类对象模型结构和参数的新方法,首先将非线性静态部分和线性动态部分分别用非线性基和Laguerre级数表示,然后通过最小二乘法、矩阵特征值分解和矩阵扩维,辨识出两部分参数．并证明了该方法在输出端存在白噪声情况下误差的收敛性．此方法仅需假设输入为持续激励,适用范围广,计算简单,辨识精度高．最后通过pH中和滴定实验验证了以上结论．     

Search strategies for shape regularized active contour

Nonlinear shape models have been shown to improve the robustness and flexibility of contour-based object segmentation when there are appearance ambiguities between the object and the background. In this paper, we focus on a new search strategy for the shape regularized active contour (ShRAC) model, which adopts existing nonlinear shape models to segment objects that are similar to a set of training shapes. The search for optimal contour is performed by a coarse-to-fine algorithm that iterates between combinatorial search and gradient-based local optimization. First, multi-solution dynamic programming (MSDP) is used to generate initial candidates by minimizing only the image energy. In the second step, a combination of image energy and shape energy is minimized starting from these initial candidates using a local optimization method and the best one is selected. To generate diverse initial candidates while reducing invalid shapes, we apply two pruning methods to the search space of MSDP. Our search strategy combines the advantages of global combinatorial search and local optimization, and has shown excellent robustness to local minima caused by distracting suboptimal solutions. Experimental results on segmentation of different anatomical structures using ShRAC, as well as preliminary results on human silhouette segmentation are provided.     

Dynamic neural networks with hybrid structures for nonlinear system identification

Dynamic neural networks (DNNs) have important properties that make them convenient to be used together with nonlinear control approaches based on state space models and differential geometry, such as feedback linearisation. However the mapping capability of DNNs are quite limited due to their fixed structure, that is, the number of layers and the number of hidden units. An example shown in this paper has demonstrated this limitation of DNNs. The development of novel DNN structures, which has good mapping capability, is a relevant challenge being addressed in this paper. Although the structure is changed minorly only, the mapping capability of the new designed DNN in this paper has been improved dramatically. Previous work [J. Deng et al., 2005. The dynamic neural network of a hybrid structure for nonlinear system identification. In: 16th IFAC World Congress, Prague.] presents a new dynamic neural network structure which is suitable for the identification of highly nonlinear systems, which needs the outputs from the real system for training and operation. This paper presents a hybrid dynamic neural network structure which presents a similar idea of serial–parallel hybrid structure, but it uses an output from another neural network for training and operation classified as a serial–parallel model. This type of DNNs does not require the output of the plant to be used as an input to the model. This neural network has the advantages of good mapping capabilities and flexibilities in training complicated systems, compared to the existed DNNs. A theoretical proof showing how this hybrid dynamic neural network can approximate finite trajectories of general nonlinear dynamic systems is given. To illustrate the capabilities of the new structure, neural networks are trained to identify a real nonlinear 3D crane system.     

Adaptive control of a class of nonlinear time-varying systems with multiple models

The adaptive control of nonlinear systems that are linear in the unknown but time-varying parameters are treated in this paper. Since satisfactory transient performance is an important factor, multiple models are required as these parameters change abruptly in the parameter space. In this paper we consider both the multiple models with switching and tuning methodology as well as multiple models with second level adaptation for this class of systems. We demonstrate that the latter approach is better than the former.     

Control design approaches for nonlinear systems using multiple models

It is difficult to realize control for some complex nonlinear systems operated in different operating regions. Based on developing local models for different operating regions of the process, a novel algorithm using multiple models is proposed. It utilizes dynamic model bank to establish multiple local models, and their membership functions are defined according to respective regions. Then the nonlinear system is approximated to a weighted combination of the local models. The stability of the nonlinear system is proven. Finally, simulations are given to demonstrate the validity of the proposed method.     

A sufficient condition to test identifiability of nonlinear delayed-differential models with constant delays and multi-inputs

In this paper, an original result in terms of a sufficient condition to test the identifiability of nonlinear delayed-differential models with constant delays and multi-inputs is given. The identifiability is studied for the linearized system and a criterion for linear systems with constant delays is provided, from which the identifiability of the original nonlinear system can be proved. This result is obtained by combining a classical identifiability result for nonlinear ordinary differential systems due to Grewal and Glover (1976) with the identifiability of linear delayed-differential models developed by Orlov, Belkoura, Richard, and Dambrine (2002). This paper is a generalization of Denis-Vidal, Jauberthie, and Joly-Blanchard (2006), which deals with the specific case of nonlinear delayed-differential models with two delays and a single input.     

双足机器人步态控制研究方法综述

概括地介绍了双足机器人步态控制领域内的主要研究思路．详细阐述了基于双足动力学特征的3种建模方法,包括倒立摆模型、被动步态模型、质量弹簧模型的特点．另外讨论了两种常用的约束条件(稳定判据与能量约束)和3种智能控制方法(神经元理论、模糊逻辑与遗传算法)在双足机器人步态控制中的研究情况．     

Fuzzy model based adaptive control for a class of nonlinear systems

A fuzzy model based adaptive control algorithm for a class of continuous-time nonlinear dynamic systems is presented. The fuzzy model consisting of a set of linear fuzzy local models that are combined using a fuzzy inference mechanism is used to model a class of nonlinear systems. Each fuzzy local model represents a linearized model corresponding to the operating point of the controlled nonlinear system. The proposed control algorithm employs the fuzzy controller that is designed by considering the linear state feedback controller corresponding to the fuzzy local model with the maximum weight and the switching-σ modification adaptive controller to adaptively compensate for the plant nonlinearities. Stability robustness of the closed-loop system is analyzed in Lyapunov sense. It is shown, that the proposed control algorithm guarantees global stability of the system with the output of the system approaching the origin if there are no disturbances and uncertainties, converging to the neighborhood of the origin for all realizations of uncertainties and disturbances. The simulation examples for controlling inverted pendulum system are given to illustrate the effectiveness of the proposed method