基于微分进化算法的模糊模型设计

提出一种基于微分进化算法的TS模糊模型设计方法。该方法利用“匹茨堡型”实数编码的微分进化算法,对初始模糊模型的结构和参数进行学习。微分进化算法的目标函数同时考虑模型的精确性和解释性。利用该方法进行一类合成非线性动态系统的辨识,仿真结果验证了该方法的有效性。     

基于LSFD算法的小波模糊神经网络的研究与应用

利用小波变换的多分辨率特性构造小波模糊神经网络模型,并应用在非线性系统的辨识上.在参数学习上,给出了模糊微分与李亚普诺夫稳定相结合的新算法—LSFD算法,并与梯度下降法进行了对比.通过仿真,结果表明小波模糊神经网络模型与模糊神经网络、模糊小波神经网络、小波神经网络和神经网络等模型相比,其性能指标最小,收敛速度更快,更加准确.     

基于小波调制的连续系统模型辨识

介绍了连续模型辨识的调制函数法，其于小波分析理论，提出构造多分辨小波调 制函数的新思路，设计了高斯小波调制函数.以二阶系统为例，研究了调制窗口参数与辨识 精度的关系,并以此得到调制函数参数的设计依据.典型算例表明本文算法的有效性.     

跟踪-微分器用于连续系统辨识

利用跟踪－ 微分器估计连续系统状态并用最小二乘法估计系统参数,直接对连续系统进行辨识。仿真结果表明,不论是线性系统,还是非线性系统,只要结构对参数是线性的,利用这种方法都能有效地将其参数辨识出来     

跟踪—微分器用于连续系统辨识

利用跟踪－微分器估计连续系统状态并用最小二乘法估计系统参数,直接对连续系统进行辨识。仿真结果表明,不论是线性系统,还是非线性系统,只要结构对参数是线性的,利用这种方法都能有效地将其参数辨识出来。     

基于蚁群聚类算法的非线性系统辨识

基于T-S模型提出一种非线性系统的模型辨识方法.利用蚁群聚类算法进行结构辨识,确定系统的模糊空间和模糊规则数.在聚类的基础上,利用遗传算法辨识模糊模型的后件加权参数,得到一个精确的模糊模型,从而实现了参数辨识.仿真结果验证了所提出方法的有效性,表明该方法能够实现非线性系统的辨识,而且辨识精度较高.     

基于模糊神经网络的非线性系统模型的辨识

该文提出一种非线性系统的模型辨识方法．利用关系聚类法来进行结构辨识，从而自动获得模糊规则库，并可以得到模糊系统的初始参数，在聚类的基础上，构造一个与之相匹配的模糊神经网络，用它的学习算法来训练网络，得到一个精确的模糊模型，从而实现参数辨识，通过对两个非线性系统辨识的仿真结果验证了该方法的有效性。     

具有分片非线性输入的Wiener系统的随机梯度迭代(英文)

研究了一类具有分片非线性输入(又称为死区非线性输入)的Wiener系统的参数辨识,分片非线性输入是一个强非线性输入,其数学模型不能写成参数乘以输入的形式,首先引入开关函数,接着利用开关函数将原系统的不可辨识模型转换为可辨识模型,然后通过随机梯度迭代方法辨识出系统的参数,利用辨识出的参数可以计算出系统所有待辨识参数。仿真结果证明了本文方法的有效性。     

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.     

基于模糊树模型的间接自适应模糊控制

提出了一种基于模糊树模型的间接自适应模糊控制器的设计方法. 采用模糊树辨识方法离线辨识系统中的未知非线性函数, 得到初始的控制器, 然后在线调节模糊树模型中的线性参数, 改善控制器的性能, 实现对有界参考信号的跟踪控制. 通过对倒立摆系统进行数值仿真, 验证了所提方法的有效性和优越性.     

A method for estimating renal functions based on the radioisotope renogram

A method has been developed to predict or estimate the results of commonly used routine renal function tests based on a renogram. The model is built on two differential equations derived in terms of seven parameters which can be measured from tracings of radioactivity recorded on the heart, the kidneys, and the bladder. The model successfully reconstructed every possible variation of the renogram pattern by computer simulation. Expected results of the four renal function tests were computed by multiple regression equations using five out of the seven parameters as criteria variables (p less than 0.05). The four renal function tests were (1) a concentration test, (2) a PSP test, (3) the glomerular filtration rate, and (4) blood urea nitrogen.     

Fuzzy differential equations and the extension principle

We study the Cauchy problem for differential equations, considering its parameters and/or initial conditions given by fuzzy sets. These fuzzy differential equations are approached in two different ways: (a) by using a family of differential inclusions; and (b) the Zadeh extension principle for the solution of the model. We conclude that the solutions of the Cauchy problem obtained by both are the same. We also provide some illustrative examples.     

一种基于T-S模糊模型的混沌控制方法

用T-S模糊系统来逼近非线性系统,它的IF-THEN规则后件由线性状态空间子系统构成,进而可以应用模糊系统的控制理论求得模糊控制器,用此非线性控制器来控制非线性系统,以求良好的控制效果;将模糊控制技术应用于混沌控制中,可以克服反馈线性化等传统方法对参数完全精确已知的限制;模糊规则后件部分以局部线性方程形式给出的T-S模糊模型可以通过调整相关参数很好地逼近混沌系统,基于该模型采用平行分散补偿技术设计出具有相同规则数目的模糊控制器,控制器所有参数可以通过求解一组线性矩阵不等式一次性得到。仿真结果验证了该方法的有效性。     

Regression-based weight generation algorithm in neural network for solution of initial and boundary value problems

This paper introduces a new algorithm for solving ordinary differential equations (ODEs) with initial or boundary conditions. In our proposed method, the trial solution of differential equation has been used in the regression-based neural network (RBNN) model for single input and single output system. The artificial neural network (ANN) trial solution of ODE is written as sum of two terms, first one satisfies initial/boundary conditions and contains no adjustable parameters. The second part involves a RBNN model containing adjustable parameters. Network has been trained using the initial weights generated by the coefficients of regression fitting. We have used feed-forward neural network and error back propagation algorithm for minimizing error function. Proposed model has been tested for first, second and fourth-order ODEs. We also compare the results of proposed algorithm with the traditional ANN algorithm. The idea may very well be extended to other complicated differential equations.     

BOOMER, a simulation and modeling program for pharmacokinetic and pharmacodynamic data analysis

BOOMER is an improved version of an earlier non-linear regression program, MULTI-FORTE. Rather than the user writing a FORTRAN subroutine, models are defined by means of the parameters which make up the model. Models based on differential equations are specified by means of zero-order, first-order, or Michaelis-Menten-type rate constants. Doses (in units of mass) are translated into the usually observed concentration units by a reciprocal volume parameter. Integrated equation models are specified in terms of baseline terms, exponential terms, or the emax function with slope term as described by the Hill equation. Time points can be specified as parameters to specify dose times, infusion start/stop times, or lag times. With careful selection of parameters quite complex models can be specified. The user has a choice of differential equation solvers and fitting algorithms.     

Optimal Control for Partially Observed Nonlinear Deterministic Systems with Fuzzy Parameters

In this paper we consider the control problem for a class of partially observed deterministic systems governed by nonlinear differential equations with fuzzy parameters. Using Takagi–Sugeno fuzzy model, we propose a linear (fuzzy) controller, driven by the output process, for controlling the system. Further, using calculus of variations, we have developed a set of necessary conditions on the basis of which optimal control can be determined. Based on these necessary conditions we have proposed a numerical algorithm for computing optimal control along with some numerical simulations to illustrate the effectiveness of the proposed (fuzzy) control scheme.     

Filtering of Linear Partially Observe Stochastic Systems: The Fuzzy Logic Approach

In this paper we consider the filtering problem for a class of partially observed systems governed by linear stochastic differential equations. Using Takagi–Sugeno linear fuzzy model and assuming membership functions of Gaussian type, we have proposed minimum unbiased linear fuzzy filter, driven by the observed process, with the help of which the system states can be estimated from the observed data. Further, using calculus of variation, we have developed a set of necessary conditions of optimality on the basis of which filter parameters can be determined. Finally, numerical simulations are presented to illustrate the effectiveness of the proposed filter.     

Adaptive observer for estimating the parameters of an HIV model with mutants

Human immunodeficiency virus (HIV) causes acquired immune deficiency syndrome (AIDS). The process of infection and mutation by HIV can be described by fifth-order ordinary differential equations. These equations can be reduced to third-order differential equations through the singular perturbation theory. The objective of this paper is to present a parameter estimation algorithm for this third-order HIV model, using two (out of three) state variables. We first show that the parameters of the HIV model are identifiable with these measurements. The structure of the proposed estimator parallels that of the full state feedback estimator with the unavailable state replaced with an estimated variable. We then prove that the resulting adaptive observer equipped with the so-called σ-modification can be tuned to be ultimately bounded under some conditions in terms of the concentration of uninfected CD4+ T cells. Furthermore, it is seen through computer simulations that an iterative application of the proposed algorithm is effective; the estimated parameters approach their true values, and the stability analysis of the ensuing HIV model leads to the results that are consistent with those obtained previously.     

Fuzzy Optimal Control for Bilinear Stochastic Systems with Fuzzy Parameters

In this paper we consider the control problem for a class of partially observed bilinear stochastic systems with fuzzy parameters. Using Takagi–Sugeno fuzzy model, the problem is described by three sets of fuzzy stochastic differential equations: one for the state process, one for the observed process and one for the controller which is assumed to be driven by the observed process. With this formulation, the original stochastic control problem can be treated as a deterministic identification problem in which the controller parameters and the corresponding membership functions are the unknowns. Using a suitable performance index, we have developed a set of necessary conditions for determining the parameters of the controller and the corresponding membership functions. Finally, some numerical simulations are presented to illustrate the effectiveness of the proposed fuzzy control scheme.     

Simulating continuous fuzzy systems

In previous studies we concentrated on utilizing crisp, numeric simulation to produce discrete event fuzzy systems simulations. Then we extended this research to the simulation of continuous fuzzy systems models. In this study, we continue our study of continuous fuzzy systems using crisp continuous simulation. Consider a crisp continuous system whose process of evolution depends on differential equations. Such a system contains a number of parameters that must be estimated. Usually point estimates are computed and used in the model. However, these point estimates typically have uncertainty associated with them. We propose to incorporate uncertainty by using fuzzy numbers as estimates of these unknown parameters. Fuzzy parameters convert the crisp system into a fuzzy system. Trajectories describing the behavior of the system become fuzzy curves. We will employ crisp continuous simulation to estimate these fuzzy trajectories. Three examples are discussed.