Support vector method for identification of Wiener models

Support vector regression is applied to identify nonlinear systems represented by Wiener models, consisting of a linear dynamic system in series with a static nonlinear block. The linear block is expanded in terms of basis functions, such as Laguerre or Kautz filters, and the static nonlinear block is determined using support vector machine regression.     

Robust H ∞ fuzzy control of nonlinear systems with multiple time delays

A robustness design of fuzzy control via model-based approach is proposed in this article to overcome the effect of approximation error between multiple time-delay nonlinear systems and Takagi--Sugeno (T-S) fuzzy models. A stability criterion is derived based on Lyapunov's direct method to ensure the stability of nonlinear multiple time-delay systems especially for the resonant and chaotic systems. Positive definite matrices P and R_k of the criterion are obtained by using linear matrix inequality (LMI) optimization algorithms to solve the robust fuzzy control problem. In terms of the control scheme and this criterion, a fuzzy controller is then designed via the technique of parallel distributed compensation (PDC) to stabilize the nonlinear multiple time-delay system and the H ^∞ control performance is achieved at the same time. Finally, two numerical examples of the chaotic and resonant systems are demonstrated to show the concepts of the proposed approach.     

对一类不确定系统的推广波波关判据

本文将对一类不确定系统提出推广的波波夫判据,这类系统的线性部分乃诸顶点模型的凸组合,而非线性函数是处于某扇区内。判据说:不确定系统是某扇区绝对稳定的如果存在一条公共的波波夫直线使所有顶点系统的修正奈氏曲线位于这直线右侧。     

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.     

On robustness and stabilization of linear systems with delayednonlinear perturbations

In this paper, by employing a Razumikhin-type theorem, a robust stability criterion for a class of linear systems subject to delayed time-varying nonlinear perturbations is given. Then, stabilization of a class of linear systems subject to mismatched delayed time-varying nonlinear perturbations by linear controller is considered. For such systems, conditions which ensure closed-loop asymptotic stability are given. Numerical examples are given to illustrate the results     

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.     

Robust fuzzy tracking control for nonlinear networked control systems with integral quadratic constraints

This paper investigates the robust tracking control problem for a class of nonlinear networked control systems (NCSs) using the Takagi-Sugeno (T-S) fuzzy model approach. Based on a time-varying delay system transformed from the NCSs, an augmented Lyapunov function containing more useful information is constructed. A less conservative sufficient condition is established such that the closed-loop systems stability and time-domain integral quadratic constraints (IQCs) are satisfied while both time-varying network-induced delays and packet losses are taken into account. The fuzzy tracking controllers design scheme is derived in terms of linear matrix inequalities (LMIs) and parallel distributed compensation (PDC). Furthermore, robust stabilization criterion for nonlinear NCSs is given as an extension of the tracking control result. Finally, numerical simulations are provided to illustrate the effectiveness and merits of the proposed method.     

Identification of Objects by the Maximal Information Criterion

The design of predictive input-output models for linear and nonlinear systems with random signals is studied. Definitions are formulated and conditions for identifiability by information criteria are derived. A consistent method of identification of systems by the maximal information criterion is designed. The values of parameters of an object are used for identifying and designing unbiased models.     

Strong consistency of recursive identification for Hammerstein systems with discontinuous piecewise-linear memoryless block

This note deals with identification of Hammerstein systems with discontinuous piecewise-linear memoryless block followed by a linear subsystem. Recursive algorithms are proposed for estimating coefficients of the linear subsystem and six unknown parameters contained in the nonlinear static block. By taking a sequence of iid random variables with uniform distribution to serve as the system input, strong consistency is proved for all estimates given in the note. The theoretical results are verified by computer simulation.     

A gap metric based multiple model approach for nonlinear switched systems

Many applications in chemical engineering often exhibit a switching character due to the presence of discrete modes in the course of their operation. First principles models of such systems constructed using process simulators are far too complex for use in online applications, especially in model-based control. For such systems, numerous control-relevant modeling approaches have been reported in the literature such as mixed logic dynamical (MLD) models [1] and piece wise affine (PWA) [2] models among others. These models describe the evolution of states in each discrete mode using linear equations. Fewer control-relevant models have been reported that address the nonlinear behavior of switched systems. To model nonlinear hybrid systems, Nandola and Bhartiya [3] proposed a multiple linear model approach wherein multiple linear models are used to describe the dynamic behavior in each mode of the hybrid system. However, no guidelines were provided to select the number of models necessary in each mode and their region of validity. In this work, we address these lacunae by presenting a systematic multiple model approach to describe nonlinear switched systems. The method involves a trajectory based linearization and employs a model bank with a set of local linear models for each discrete operational mode. The model bank is generated by linearizing the first principles model across a carefully designed trajectory based on accuracy of multi-step ahead predictions. The numerous models thus obtained are clustered using the gap metric as the distance measure and representative models are selected. The selected linear models are aggregated using Bayesian or Fuzzy approaches to obtain the global model for the nonlinear switched system. A simulation case study of spherical two-tank system and an experimental case study of a benchmark problem consisting of three tanks are used to validate the proposed modeling strategy.     

A robust adaptive control method for Wiener nonlinear systems

This paper proposes a new robust adaptive control method for Wiener nonlinear systems with uncertain parameters. The considered Wiener systems are different from the previous ones in the sense that we consider nonlinear block approximation error, process noise, and measurement noise. The parameterization model is obtained based on the inverse of the nonlinear function block. The adaptive control method is derived from a modified criterion function that can overcome non‐minimum phase property of the linear subsystem. The parameter adaptation is performed by using a robust recursive least squares algorithm with a deadzone weighted factor. The control law compensates the model error by incorporating the unmodeled dynamics estimation. Theoretical analysis indicates that the closed‐loop system stability can be guaranteed under mild conditions. Numerical examples including an industrial problem are studied to validate the results. Copyright © 2016 John Wiley & Sons, Ltd.     

Developing a robust model predictive control architecture through regional knowledge analysis of artificial neural networks

Chemical processes are nonlinear. Model based control schemes such as model predictive control are highly related to the accuracy of the process model. For a highly nonlinear chemical system, it is clear to implement a nonlinear empirical model, such as artificial neural network model, should be superior to a linear model such as dynamic matrix model. However, unlike linear systems, the accuracy of a nonlinear empirical model strongly depends on its original data or training data based on how the model is built up. A regional-knowledge index is proposed in this study and applied in the analysis of dynamic artificial neural network models in process control. New input patterns that imply extrapolations and thus unreliable prediction by an artificial neural network model can be recognized from a significant decrease in the regional-knowledge index. To tackle the extrapolation problem and assure stability of the control system, we propose to run a neural adaptive controller in parallel with a model predictive control. A coordinator weights the outputs of these two controllers to make the final control decision. The present state of the controlled process and the model fitness to the present input pattern determine the weightings of the controller's output. The proposed analysis method and the modified model predictive control architecture have been applied to a neutralization process and excellent control performance is observed in this highly nonlinear system.     

A novel criterion for nonlinear time-delay systems using LMI fuzzy Lyapunov method

This study presents a kind of fuzzy robustness design for nonlinear time-delay systems based on the fuzzy Lyapunov method, which is defined in terms of fuzzy blending quadratic Lyapunov functions. The basic idea of the proposed approach is to construct a fuzzy controller for nonlinear dynamic systems with disturbances in which the delay-independent robust stability criterion is derived in terms of the fuzzy Lyapunov method. Based on the robustness design and parallel distributed compensation (PDC) scheme, the problems of modeling errors between nonlinear dynamic systems and Takagi–Sugeno (T–S) fuzzy models are solved. Furthermore, the presented delay-independent condition is transformed into linear matrix inequalities (LMIs) so that the fuzzy state feedback gain and common solutions are numerically feasible with swarm intelligence algorithms. The proposed method is illustrated on a nonlinear inverted pendulum system and the simulation results show that the robustness controller cannot only stabilize the nonlinear inverted pendulum system, but has the robustness against external disturbance.     

一类非线性离散系统模糊控制器的分析和设计

针对一类非线性离散不确定系统,在系统状态不可测的情况下,以T-S模型描述不同状态空间的局部动态区域,并通过中心平均反模糊化、乘积推理、单点模糊化方法得到全局模糊系统模型.基于李亚普诺夫理论和线性矩阵不等式,设计了一种基于观测器的鲁棒控制器,并对离散状态下的此类系统进行了稳定分析.最后通过M ATLAB仿真,证明了该方法的有效性.     

The complexity of model classes, and smoothing noisy data

We consider the problem of smoothing a sequence of noisy observations using a fixed class of models. Via a deterministic analysis, we obtain necessary and sufficient conditions on the noise sequence and model class that ensure that a class of natural estimators gives near-optimal smoothing. In the case of i.i.d. random noise, we show that the accuracy of these estimators depends on a measure of complexity of the model class involving covering numbers. Our formulation and results are quite general and are related to a number of problems in learning, prediction, and estimation. As a special case, we consider an application to output smoothing for certain classes of linear and nonlinear systems. The performance of output smoothing is given in terms of natural complexity parameters of the model class, such as bounds on the order of linear systems, the -norm of the impulse response of stable linear systems, or the memory of a Lipschitz nonlinear system satisfying a fading memory condition.     

DECENTRALIZED STABILIZATION OF H FUZZY CONTROL FOR NONLINEAR MULTIPLE TIME‐DELAY INTERCONNECTED SYSTEMS

A robustness design of fuzzy control is proposed in this paper to overcome the effect of modeling errors between nonlinear multiple time‐delay systems and fuzzy models. In terms of Lyapunov's direct method, a stability criterion is derived to guarantee the UUB (uniformly ultimately bounded) stability of nonlinear multiple time‐delay interconnected systems with disturbances. Based on this criterion and the decentralized control scheme, a set of fuzzy controllers is then synthesized via the technique of parallel distributed compensation (PDC) to stabilize the nonlinear multiple time‐delay interconnected systems and the Hcontrol performance is achieved in the mean time.     

Robust model predictive control of Wiener systems

Block-oriented models (BOMs) have shown to be appealing and efficient as nonlinear representations for many applications. They are at the same time valid and simple models in a more extensive region than time-invariant linear models. In this work, Wiener models are considered. They are one of the most diffused BOMs, and their structure consists in a linear dynamics in cascade with a nonlinear static block. Particularly, the problem of control of these systems in the presence of uncertainty is treated. The proposed methodology makes use of a robust identification procedure in order to obtain a robust model to represent the uncertain system. This model is then employed to design a model predictive controller. The mathematical problem involved in the controller design is formulated in the context of the existing linear matrix inequalities (LMI) theory. The main feature of this approach is that it takes advantage of the static nature of the nonlinearity, which allows to solve the control problem by focusing only in the linear dynamics. This formulation results in a simplified design procedure, because the original nonlinear model predictive control (MPC) problem turns into a linear one.     

Synchronization of ball and beam systems with neural compensation

Ball and beam system is one of the most popular and important laboratory models for teaching control system. It is a big challenge to synchronize ball and beam systems. There are two problems for ball and beam synchronized control: 1) many laboratories use simple controllers such as PD control, and theory analysis is based on linear models, 2) nonlinear controllers for ball and beam system have good theory results, but they are seldom used in real applications. In this paper we first use PD control with nonlinear exact compensation for the cross-coupling synchronization. Then a RBF neural network is applied to approximate the nonlinear compensator. The synchronization control can be in parallel and serial forms. The stability of the synchronization is discussed. Real experiments are applied to test our theory results.     

分组密码的并行工作模式

以AES为例，探讨分组密码的并行工作模式。在分组密码的四种标准工作模式中，除ECB模式外，其余工作模式均存在着反馈形式的迭代，这对数据的并行操作是一大障碍，给出了相应的三种并行密码模式，在不改变原分组密码算法的密码学特征的前提下，可以达到线性的加速比。