Recursive identification of linear and non-linear systems

The paper develops recursive techniques for off-line identification of linear and nonlinear systems. It is shown that if the system is linear and time invariant, impulse response characterization of the system coupled with an orthogonal series approximation can be utilized for the purpose stated above. The techniques of adaptive Kalman filtering are shown to be applicable, which besides permitting recursive evaluation of the coefficients, lead to a number of important advantages. In the second part of the study, the proposed method is extended for recursive identification of a class of non-linear systems which can be represented as a cascade combination of a linear dynamical system and a non-linear zero memory system. The method of Volterra series representation of such systems is utilized. Results are illustrated through numerical examples in each case.     

Sugeno模糊模型的辨识与控制

提出了一种新的Sugeno模糊模型辨识算法和对非线性系统进行并行化设计的方 法.在Sugeno模糊模型辨识中,应用模糊聚类方法可将其前提结构和结论参数的辨识分开进 行,减少了计算量;对于非线性系统的控制,Sugeno模糊模型实际上是动态系统的局部线性 化,可采用并行设计的方法设计控制器,然后通过模糊推理得到全局控制量.最后通过倒立摆 系统的控制说明了本文算法的有效性.     

基于Retri网的市场需求预测模型研究

市场需求预测问题具有多因素、离散、动态和并发等特点，尤其是并发性始终影响预测结果的稳定性和精度。本文利用Ｐｅｔｒｉ网良好的离散事件动态表达和计算能力以及图形表示的直观性，建立市场需求预测问题的Ｐｅｔｒｉ网模型，并对模型的动态、并发问题进行分析     

快速扩散制造中的工作流管理技术

针对武器装备快速扩散制造的效率问题,以军工产品的扩散制造为实例背景,提出一种支持快速扩散制造的工作流管理技术,包括工作流建模技术、工作流运行控制技术和工作流系统实现方法,采用Petri网建模方法和基于Web的工作流引擎技术。阐明扩散制造中工作流管理系统的体系结构。结果证明其在提高军工产品制造效率方面效果良好。     

Hierarchical visualization of time-series data using switching linear dynamical systems

We propose a novel visualization algorithm for high-dimensional time-series data. In contrast to most visualization techniques, we do not assume consecutive data points to be independent. The basic model is a linear dynamical system which can be seen as a dynamic extension of a probabilistic principal component model. A further extension to a particular switching linear dynamical system allows a representation of complex data onto multiple and even a hierarchy of plots. Using sensible approximations based on expectation propagation, the projections can be performed in essentially the same order of complexity as their static counterpart. We apply our method on a real-world data set with sensor readings from a paper machine.     

Hinging hyperplane based regression tree identified by fuzzy clustering and its application

Hierarchical fuzzy modeling techniques have great advantage since model accuracy and complexity can be easily controlled thanks to the transparent model structures. A novel tool for regression tree identification is proposed based on the synergistic combination of fuzzy c-regression clustering and the concept of hierarchical modeling. In a special case (c = 2), fuzzy c-regression clustering can be used for identification of hinging hyperplane models. The proposed method recursively identifies a hinging hyperplane model that contains two linear submodels by partitioning operating region of one local linear model resulting a binary regression tree. Novel measures of model performance and complexity are developed to support the analysis and building of the proposed special model structure. Effectiveness of proposed model is demonstrated by benchmark regression datasets. Examples also demonstrate that the proposed model can effectively represent nonlinear dynamical systems. Thanks to the piecewise linear model structure the resulted regression tree can be easily utilized in model predictive control. A detailed application example related to the model predictive control of a water heater demonstrate that the proposed framework can be effectively used in modeling and control of dynamical systems.     

Lazy learning for local modelling and control design

This paper presents local methods for modelling and control of discrete-time unknown non-linear dynamical systems, when only input-output data are available. We propose the adoption of lazy learning, a memory-based technique for local modelling. The modelling procedure uses a query-based approach to select the best model configuration by assessing and comparing different alternatives. A new recursive technique for local model identification and validation is presented, together with an enhanced statistical method for model selection. A lso, three methods to design controllers based on the local linearization provided by the lazy learning algorithm are described. In the first method the lazy technique returns the forward and inverse models of the system which are used to compute the control action to take. The second is an indirect method inspired by self-tuning regulators where recursive least squares estimation is replaced by a local approximator. The third method combines the linearization provided by the local learning techniques with optimal linear control theory, to control non-linear systems about regimes which are far from the equilibrium points. Simulation examples of identification and control of non-linear systems starting from observed data are given.     

Model order selection of nonlinear input–output models––a clustering based approach

Selecting the order of an input–output model of a dynamical system is a key step toward the goal of system identification. The false nearest neighbors algorithm (FNN) is a useful tool for the estimation of the order of linear and nonlinear systems. While advanced FNN uses nonlinear input–output data-based models for the model-based selection of the threshold constant that is used to compute the percentage of false neighbors, the computational effort of the method increases along with the number of data and the dimension of the model. To increase the efficiency of this method, in this paper we propose a clustering-based algorithm. Clustering is applied to the product space of the input and output variables. The model structure is then estimated on the basis of the cluster covariance matrix eigenvalues. The main advantage of the proposed solution is that it is model-free. This means that no particular model needs to be constructed in order to select the order of the model, while most other techniques are ‘wrapped' around a particular model construction method. This saves the computational effort and avoids a possible bias due to the particular construction method used. Three simulation examples are given to illustrate the proposed technique: estimation of the model structure for a linear system, a polymerization reactor and the van der Vusse reactor.     

A recursive (on-line) identification of bilinear systems

A recursive identification of a discrete dynamical system is presented in this paper. Two methods of recursive identification, namely the recursive extended least-squares method and the recursive maximum likelihood method, are described and analysed. The techniques are illustrated numerically with simulations.     

Optimal Control of Nonlinear Inverted Pendulum System Using PID Controller and LQR: Performance Analysis Without and With Disturbance Input

Linear quadratic regulator(LQR) and proportional-integral-derivative(PID) control methods, which are generally used for control of linear dynamical systems, are used in this paper to control the nonlinear dynamical system. LQR is one of the optimal control techniques, which takes into account the states of the dynamical system and control input to make the optimal control decisions.The nonlinear system states are fed to LQR which is designed using a linear state-space model. This is simple as well as robust. The inverted pendulum, a highly nonlinear unstable system, is used as a benchmark for implementing the control methods. Here the control objective is to control the system such that the cart reaches a desired position and the inverted pendulum stabilizes in the upright position. In this paper, the modeling and simulation for optimal control design of nonlinear inverted pendulum-cart dynamic system using PID controller and LQR have been presented for both cases of without and with disturbance input. The Matlab-Simulink models have been developed for simulation and performance analysis of the control schemes. The simulation results justify the comparative advantage of LQR control method.     

Bayesian identification of stochastic linear systems with observations at multiple scales

A Bayesian system identification approach to modelling stochastic linear dynamical systems involving multiple scales is proposed, where multiscale means that the output of the system is observed at one (coarse) resolution whilst the input of the system can only be observed at another (fine) resolution. The proposed method identifies linear models at different levels of resolution, where the link between the two resolutions is realised via a non-overlapping averaging process. The averaged data at the coarse level of resolution is assumed to be a set of observations from an implied process so that the implied process and the output of the system result in an errors-in-variables model at the coarse level of resolution. By using a Bayesian inference and Markov chain Monte Carlo method, such a modelling framework results in different dynamical models at different levels of resolution at the same time. The new method is also shown to have the ability to combine information across different levels of resolution. Simulation examples are provided to show the efficiency of the new method. Furthermore, an application to the analysis of the relativistic electron intensity at the geosynchronous orbit is also included.     

Analysis of Hybrid Systems Based on Hybrid Net Condition/Event System Model

In thispaper, hybrid net condition /event systems are introducedas a model for hybrid systems. The model consists of a discretetimed Petri net and a continuous Petri net which interact eachother through condition and event signals. By introducing timeddiscrete places in the model, timing constraints in hybrid systemscan be easily described. For a class of hybrid systems that canbe described as linear hybrid net condition /eventsystems whose continuous part is a constant continuous Petrinet, two methods are developed for their state reachability analysis.One is the predicate-transformation method, which is an extensionof a state reachability analysis method for linear hybrid automata.The other is the path-based method, which enumerates all possiblefiring seqenences of discrete transitions and verifies if a givenset of states can be reached from another set by firing a sequenceof discrete transitions. The verification is performed by solvinga constraint satisfaction problem. A technique that adds additionalconstraints to the problem when a discrete state is revisitedalong the sequence is developed and used to prevent the methodfrom infinite enumeration. These methods provide a basis foralgorithmic analysis of this class of hybrid systems.     

基于LS-SVM飞机大迎角动态辨识方法研究

确定飞机在大迎角飞行状态时的动态系统参考模型,对于支持飞机控制系统的稳定性和控制增稳设计有着重要的影响。为了精确描述飞机大迎角机动非定常、非线性数学模型,提出利用最小二乘支持向量机(LS-SVM)对飞机大迎角状态飞行时的非线性动态系统进行辨识,利用网络搜索和交叉验证的方法选择支持向量机参数,并建立了飞机大迎角动力学参考模型,仿真验证显示方法具有较强的泛化能力和较高的辨识效果。     

基于Petri网模型的主动对象研究

本文分析了Ｐｅｔｒｉ网及其动态行为特性，扩充了事件、条件、动作等成份的内涵，引入了基于Ｐｅｔｒｉ网事件驱动的主动对象模型，并分析了该主动对象的性质，介绍了主动对象的实现     

Adaptive Control for the Systems Preceded by Hysteresis

Hysteresis hinders the effectiveness of smart materials in sensors and actuators. It is a challenging task to control the systems with hysteresis. This note discusses the adaptive control for discrete time linear dynamical systems preceded with hysteresis described by the Prandtl-Ishlinskii model. The time delay and the order of the linear dynamical system are assumed to be known. The contribution of the note is the fusion of the hysteresis model with adaptive control techniques without constructing the inverse hysteresis nonlinearity. Only the parameters (which are generated from the parameters of the linear system and the density function of the hysteresis) directly needed in the formulation of the controller are adaptively estimated online. The proposed control law ensures the global stability of the closed-loop system, and the output tracking error can be controlled to be as small as required by choosing the design parameters. Simulation results show the effectiveness of the proposed algorithm.     

Hardware-based neural identification: Linear dynamical systems

In this paper, a hardware-based neural identification method is proposed in order to learn the characteristics or structure of a discrete linear dynamical system. Quick or instant identification of unknown dynamical systems is particularly required for practical controls not only in intelligent mechatronics such as, for example, automatic selforganized running of mobile vehicles, but in intelligent self-controlled systems. We developed a new method of hardware-based identification for general dynamical systems using a digital neural network very large scale integration (VLSI) chip, RN-200, where sixteen neurons and a total of 256 synapses are integrated in a 13.73×13.73 mm² VLSI chip, fabricated using RICOH 0.8 μm complementary metal oxide semiconductor CMOS technology (RICOH, Yokohama, Japan). This paper describes how to implement neural ideitification in both learning and feedfoward processing (recognizing) using a RICOH RN-2000 neurocomputer which consists of seven RN-200 digital neural network VLSI chips.     

A graph-theoretic multiple logic fault analysis through petri-nets

In this paper a new and a graph theoretic approach based on Petrinet model for calculating any order Boolean Difference has been suggested. The concept of Boolean Difference has also been extended to generate a complete test set for all possible multiple faults on any number of lines of a logic circuit. The approach is based on the study of the system of open paths in an acyclic graph and on some basic theorems established in the paper. Unlike algebraic methods, this method is suitable for machine computation and is therefore, applicable to arbitrarily large circuits.     

Weighted Version of Extended Nearest Neighbors

This paper investigates the problem of stability analysis for switched complex dynamical networks with mixed time-varying delays and parameter uncertainties. The switched complex dynamical networks are composed of m modes that are switched from one to another based on time, state, etc. Although, the active subsystem is known in any instance, but the switching law such as transition probabilities are not known. The model for each mode is considered affine with matched and unmatched perturbations. The main purpose of the addressed problem is to design a filter error for the switched complex dynamical networks such that the dynamics of the error converges to the asymptotically irrespective of the admissible parameter variations with the gains. Then, by utilizing the Lyapunov functional method, the stochastic analysis combined with the matrix inequality techniques, a sufficient condition in terms of linear matrix inequalities is presented to ensure the $$H_\infty $$ performance of the complex dynamical system models. Finally, a numerical example is presented to illustrate the effectiveness of the proposed design method.     

Auxiliary model-based least-squares identification methods for Hammerstein output-error systems

The difficulty in identification of a Hammerstein (a linear dynamical block following a memoryless nonlinear block) nonlinear output-error model is that the information vector in the identification model contains unknown variables—the noise-free (true) outputs of the system. In this paper, an auxiliary model-based least-squares identification algorithm is developed. The basic idea is to replace the unknown variables by the output of an auxiliary model. Convergence analysis of the algorithm indicates that the parameter estimation error consistently converges to zero under a generalized persistent excitation condition. The simulation results show the effectiveness of the proposed algorithms.