Linear Fuzzy Clustering With Selection of Variables Using Graded Possibilistic Approach

Linear fuzzy clustering is a useful tool for knowledge discovery in databases (KDD), and several modifications have been proposed in order to analyze real world data. This paper proposes a new approach for estimating local linear models, in which linear fuzzy clustering is performed by selecting variables that are useful for extracting correlation structure in each cluster. The new clustering model uses two types of memberships. One is the conventional membership that represents the degree of membership of each sample in each cluster. The other is the additional parameter that represents the relative responsibility of each variable for estimation of local linear models. The additional membership takes large values when the variable has close relationship with local principal components, and is calculated by using the graded possibilistic approach. Numerical experiments demonstrate that the proposed method is useful for identifying local linear model taking typicality of each variable into account.     

Fuzzy modeling and control of an engine air inlet with exhaust gas recirculation

The purpose of this paper is to present an original fuzzy modeling method applied to a highly non- linear physical system, an engine air inlet with exhaust gas recirculation. This system is modeled with fuzzy logic rules of the Takagi–Sugeno type. The rule base switches between local linear models defined in the whole state space. The control objective is to preserve the linear behavior of the closed-loop system in all operating conditions. To reach this objective, the linear control tools are applied to each local linear model. The fuzzy model rule-base structure is then used to switch between local controllers.     

Recurrent neuro-fuzzy networks for nonlinear process modeling

A type of recurrent neuro-fuzzy network is proposed in this paper to build long-term prediction models for nonlinear processes. The process operation is partitioned into several fuzzy operating regions. Within each region, a local linear model is used to model the process. The global model output is obtained through the centre of gravity defuzzification which is essentially the interpolation of local model outputs. This modeling strategy utilizes both process knowledge and process input/output data. Process knowledge is used to initially divide the process operation into several fuzzy operating regions and to set up the initial fuzzification layer weights. Process I/O data are used to train the network. Network weights are such trained so that the long-term prediction errors are minimized. Through training, membership functions of fuzzy operating regions are refined and local models are learnt. Based on the recurrent neuro-fuzzy network model, a novel type of nonlinear model-based long range predictive controller can be developed and it consists of several local linear model-based predictive controllers. Local controllers are constructed based on the corresponding local linear models and their outputs are combined to form a global control action by using their membership functions. This control strategy has the advantage that control actions can be calculated analytically avoiding the time consuming nonlinear programming procedures required in conventional nonlinear model-based predictive control. The techniques have been successfully applied to the modeling and control of a neutralization process.     

基于神经网络非线性模型的多级工作点阶跃响应扩展DMC预测控制

利用前馈神经网络建立对象的非线性预测模型,在不同工作点做阶跃响应,建立其局部线性模型,用隶属函数将局部线性模型加权得到全局线性模型,全局线性模型用于滚动优化,非线性模型用于预测系统输出和校正线性模型,实现非线性预测控制,仿真结果表明该方法控制效果良好,可满足实时要求。     

基于一种新模糊模型的非线性系统模糊辨识

提出一种基于新的模糊模型和加权递推最小二乘算法 (WRLSA)的非线性系统模糊辨识方法.新型的具有插值能力的模糊系统可以通过学习从输入输出采样数据中提取MISO系统模糊规则,它继承了Sugeno模型及其变化形式的许多优点.采用相应的模糊隶属函数,使得被辨识的模型可用若干局部线性模型来表示,然后利用WRLSA拟合这些线性模型.给出了详细的模糊辨识算法,为了验证该辨识方法的有效性,还给出了对熟知的Box-Jenkins数据的辨识结果.     

Multiple model bank selection based on nonlinearity measure and H-gap metric

This paper provides a systematic method for model bank selection in multi-linear model analysis for nonlinear systems by presenting a new algorithm which incorporates a nonlinearity measure and a modified gap based metric. This algorithm is developed for off-line use, but can be implemented for on-line usage. Initially, the nonlinearity measure analysis based on the higher order statistic (HOS) and the linear cross correlation methods are used for decomposing the total operating space into several regions with linear models. The resulting linear models are then used to construct the primary model bank. In order to avoid unnecessary linear local models in the primary model bank, a gap based metric is introduced and applied in order to merge similar linear local models. In order to illustrate the usefulness of the proposed algorithm, two simulation examples are presented: a pH neutralization plant and a continuous stirred tank reactor (CSTR).     

A neurofuzzy scheme to on-line identification in an adaptive–predictive control

A neurofuzzy scheme has been designed to carry out on-line identification, with the aim of being used in an adaptive–predictive dynamic matrix control (DMC) of unconstrained nonlinear systems represented by a transfer function with varying parameters. This scheme supplies to the DMC controller the linear model and the nonlinear output predictions at each sample instant, and is composed of two blocks. The first one makes use of a fuzzy partition of the external variable universe of discourse, which smoothly commutes between several linear models. In the second block, a recurrent linear neuron with interpretable weights performs the identification of the models by means of supervised learning. The resulting identifier has several main advantages: interpretability, learning speed, and robustness against catastrophic forgetting. The proposed controller has been tested both on simulation and on a real laboratory plant, showing a good performance.     

Identification of Friction and Rigid-Body Dynamics of Parallel Kinematic Structures for Model-Based Control

Until now, the experimental identification of the dynamics of parallelrobots is restricted to simple models in combination with adaptivecontrol algorithms. This gap is closed by a new approach presented inthis paper, which is suited for even complex parallel kinematicstructures. The approach consists of two steps and utilizes simplepoint-to-point (PTP) motions that lead to a separation of friction andrigid-body dynamics. In the first step, local models are determined fora lot of different configurations, i.e. end-effector positions. In thesecond step, the overall friction model and the overall rigid-bodymodel are calculated from the local models by linear Least-Squaresestimators. The use of linear estimators is based on a formulation ofthe dynamic equations, which is linear with respect to a dynamicparameter vector of minimal dimension. This formulation is automaticallyobtained by an algorithm, which utilizes Jourdain's principle of virtualpower. The experimental application of the identified model tomodel-based feedforward control of the innovative hexapod PaLiDA, whichhas been developed by the Institute of Production Engineering andMachine Tools of the University of Hannover, proves the capability andefficiency of the presented algorithms.     

Dynamics identification and control of nonlinear MIMO coupled plant using supervised neural gas and comparison with recurrent neural controller

The dynamics identification and subsequent control of a nonlinear system is not a trivial issue. The application of a neural gas network that is trained with a supervised batch version of the algorithm can produce identification models in a robust way. In this paper, the neural model identifies each local transfer function, demonstrating that the local linear approximation can be done. Moreover, other parameters are analyzed in order to obtain a correct modeling. Furthermore, the algorithm is applied to control a nonlinear multi-input multi-output system composed of tanks. In addition, this plant is a coupled system where the manipulated input variables are influencing all the output variables. The aim of the work is to demonstrate that the supervised neural gas algorithm is able to obtain linear models to be used in a state space design scenario to control nonlinear coupled systems and guarantee a robust control method. The results are compared with the common approach of using a recurrent neural controller trained with a dynamic backpropagation algorithm. Regarding the steady-state errors in disturbance rejection, reference tracking and sensitivity to simple process changes, the proposed approach shows an interesting application to control nonlinear plants.

     

Predictive control based on local linear fuzzy models

This paper deals with predictive control based on fuzzy models. A novel algorithm (LOLIMOT) is proposed for the construction of Takagi-Sugeno fuzzy models. The rule consequents are optimized by a local orthogonal least-squares method that selects the significant regressors. The rule premises are optimized by a tree construction algorithm which partitions the input space in hyper-rectangles. A generalized predictive controller (GPC) and a dynamic matrix controller (DMC) are designed. Both controllers require the extraction of a linear model from the Takagi-Sugeno fuzzy model. For the GPC a new technique called local dynamic linearization is proposed that exploits the special structure of the local linear models. The DMC is based on the evaluation of a step response. The effectiveness of both the identification algorithm and the predictive controllers is shown by application to temperature control of an industrial-scale cross-flow heat exchanger.     

Fixed-structure Gaussian process model

This article describes a method for modelling non-linear dynamic systems from measurement data. The method merges the linear local model blending approach in the velocity-based linearisation form with Bayesian Gaussian process (GP) modelling. The new Fixed-Structure GP (FSGP) model has a predetermined linear model structure with varying and probabilistic parameters represented by GP models. These models have several advantages for the modelling of local model parameters as they give us adequate results, even with small data sets. Furthermore, they provide a measure of the confidence in the prediction of the varying parameters and information about the dependence of the parameters on individual inputs. The FSGP model can be applied for the extended local linear equivalence class of non-linear systems. The obtained non-linear system model can be, for example, used for control-system design. The proposed modelling method is illustrated with a simple example of non-linear system modelling for control design.     

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     

Sample sizes required to detect interactions between two binary fixed-effects in a mixed-effects linear regression model

Mixed-effects linear regression models have become more widely used for analysis of repeatedly measured outcomes in clinical trials over the past decade. There are formulae and tables for estimating sample sizes required to detect the main effects of treatment and the treatment by time interactions for those models. A formula is proposed to estimate the sample size required to detect an interaction between two binary variables in a factorial design with repeated measures of a continuous outcome. The formula is based, in part, on the fact that the variance of an interaction is fourfold that of the main effect. A simulation study examines the statistical power associated with the resulting sample sizes in a mixed-effects linear regression model with a random intercept. The simulation varies the magnitude (Δ) of the standardized main effects and interactions, the intraclass correlation coefficient (ρ), and the number (k) of repeated measures within-subject. The results of the simulation study verify that the sample size required to detect a 2×2 interaction in a mixed-effects linear regression model is fourfold that to detect a main effect of the same magnitude.     

基于多模型的非线性系统自适应最小方差控制

对于一类典型的离散时间非线性系统, 提出了一种基于多模型的自适应最小方差控制方法. 通过在平衡点附近建立线性模型, 用径向基函数神经元网络来补偿建模误差和未建模动态, 形成了非线性系统的多模型表示. 采用了具有积分性质的切换指标函数作为切换法则和最小方差的控制方法构成了多模型自适应控制器. 仿真实验的结果表明了这种方法的有效性.     

Novel direct and self-regulating approaches to determine optimum growing multi-experts network structure

This work presents two novel approaches to determine optimum growing multi-experts network (GMN) structure. The first method called direct method deals with expertise domain and levels in connection with local experts. The growing neural gas (GNG) algorithm is used to cluster the local experts. The concept of error distribution is used to apportion error among the local experts. After reaching the specified size of the network, redundant experts removal algorithm is invoked to prune the size of the network based on the ranking of the experts. However, GMN is not ergonomic due to too many network control parameters. Therefore, a self-regulating GMN (SGMN) algorithm is proposed. SGMN adopts self-adaptive learning rates for gradient-descent learning rules. In addition, SGMN adopts a more rigorous clustering method called fully self-organized simplified adaptive resonance theory in a modified form. Experimental results show SGMN obtains comparative or even better performance than GMN in four benchmark examples, with reduced sensitivity to learning parameters setting. Moreover, both GMN and SGMN outperform the other neural networks and statistical models. The efficacy of SGMN is further justified in three industrial applications and a control problem. It provides consistent results besides holding out a profound potential and promise for building a novel type of nonlinear model consisting of several local linear models.     

Modelling and multi-objective optimal control of batch processes using recurrent neuro-fuzzy networks

In this paper, the modelling and multi-objective optimal control of batch processes, using a recurrent neuro-fuzzy network, are presented. The recurrent neuro-fuzzy network, forms a "global" nonlinear long-range prediction model through the fuzzy conjunction of a number of "local" linear dynamic models. Network output is fed back to network input through one or more time delay units, which ensure that predictions from the recurrent neuro-fuzzy network are long-range. In building a recurrent neural network model, process knowledge is used initially to partition the processes non-linear characteristics into several local operating regions, and to aid in the initialisation of corresponding network weights. Process operational data is then used to train the network. Membership functions of the local regimes are identified, and local models are discovered via network training. Based on a recurrent neuro-fuzzy network model, a multi-objective optimal control policy can be obtained. The proposed technique is applied to a fed-batch reactor.     

Stable Adaptive Fuzzy Control with TSK Fuzzy Friction Estimation for Linear Drive Systems

This paper considers the control of a linear drive system with friction and disturbance compensation. A stable adaptive controller integrated with fuzzy model-based friction estimation and switching-based disturbance compensation is proposed via Lyapunov stability theory. A TSK fuzzy model with local linear friction models is suggested for real-time estimation of its consequent local parameters. The parameters update law is derived based on linear parameterization. In order to compensate for the effects resulting from estimation error and disturbance, a robust switching law is incorporated in the overall stable adaptive control system. Extensive computer simulation results show that the proposed stable adaptive fuzzy control system has very good performances, and is potential for precision positioning and trajectory tracking control of linear drive systems.     

Parameterization and Stabilization of the Equilibrium Points of Affine Non-linear Control Systems

The paper investigates the equilibrium points of affine non-linear control systems and constructs a scheduled control law composed of a feedforward control and a family of state feedbacks. When the design of a non-linear system is decomposed into the design of a family of linear time-invariant systems, it is required to generate parameterized linear models for the plant and to develop a scheduling scheme guaranteeing stability. To solve these difficulties, we parameterized the equilibrium points of the system by constructing a coordinate transformation into a new coordinate system with the parameter coordinates. Then, the system is represented by a parameterized family of linear models along its equilibrium manifold. With these parameterized linear families, we designed a scheduled control law with a feedforward control and local linear robust controllers so that the overall feedback stabilizes the plant about the equilibrium points. The approach is illustrated by applying it to the control of an arm-driven inverted pendulum.     

Interpolating optimizing process control

A new model-based optimizing controller for a set of nonlinear systems is proposed. The nonlinear model set is based on a convex combination of two bounding linear models. An optimal control sequence is computed for each of the two bounding models. The proposed control algorithm is based on a convex combination of the two control sequences. A novel feature in these two optimizations is an added constraint related to the feasibility of the ‘other’ bounding model. The control algorithm can for example be used in model predictive control. We provide robust feasibility guarantees and an upper bound on the optimal criterion if the bounding models are linear FIR models. Further, simulation examples demonstrate significant feasibility improvements in the case where the bounding models are general linear state-space models. The proposed method guarantees robust feasibility for a 1-step ahead prediction in the general case. This can be of interest in MPC applications.     

Long Range Predictive Control of Nonlinear Processes Based on Recurrent Neuro-Fuzzy Network Models

A recurrent neuro-fuzzy network-based nonlinear long range model predictive control strategy is proposed in this paper. The process operation is partitioned into several fuzzy operating regions. Within each region, a local linear model is used to model the process. The global model output is obtained through the centre of gravity defuzzification. Based upon a neuro-fuzzy network model, a nonlinear model-based predictive controller can be developed by combining several local linear model-based predictive controllers which usually have analytical solutions. This strategy avoids the time consuming numerical optimisation procedure, and the uncertainty in convergence to the global optimum which are typically seen in conventional nonlinear model-based predictive control strategies. Furthermore, control actions obtained based on local incremental models contain integration actions which can nat-urally eliminate static control offsets. The technique is demonstrated by an application to the modelling and control of liquid level in a water tank.