Constructive approximation of non‐linear discrete‐time systems

It is known that large classes of approximately‐finite‐memory maps can be uniformly approximated arbitrarily well by the maps of certain non‐linear structures. As an application, it was proved that time‐delay networks can be used to uniformly approximate arbitrarily well the members of a large class of causal nonlinear dynamic discrete‐time input–output maps. However, the proof is non‐constructive and provides no information concerning the determination of a structure that corresponds to a prescribed bound on the approximation error. Here we give some general results concerning the problem of finding the structure. Our setting is as follows. There is a large family 𝒢 of causal time‐invariant approximately‐finite‐memory input‐output maps G from a set S of real d‐vector‐valued discrete‐time inputs (with d⩾1) to the set of ℝ‐valued discrete‐time outputs, with both the inputs and outputs defined on the non‐negative integers 𝒵₊. We show that for each ϵ>0, any Gϵ𝒢 can be uniformly approximated by a structure map H(G, ·) to within tolerance ϵ, and we give analytical results and an example to illustrate how such a H(G, ·) can be determined in principle. Copyright © 2000 John Wiley & Sons, Ltd.     

一类不确定线性离散系统有限时间观测器设计

针对一类不确定线性离散系统有限时间观测器最优设计问题,利用线性矩阵不等式方法以及有限时间有界的概念,给出了具有不确定外部扰动输入的线性离散系统有限时间有界的充分条件.对具有状态反馈和输出的线性不确定离散系统引入有限时间观测器的概念,可以保证在给定的有限时间区间内,观测误差小于一个给定的界,并给出了最优有限时间观测器的具体设计方案.此方案的有效性可以通过仿真实验得到验证.     

Model reference adaptive control system design for linear time‐varying systems with unstructured and bounded varying functions

In recent years, many methods of model reference adaptive control system (MRACS) for a linear time‐varying (LTV) plant have been proposed. These methods assumed that the structure of plant parameters is known in advance. However, it is difficult to get a priori information of plant parameters. In this paper, an MRACS design for an LTV system based on high‐order estimator (HOE) is proposed. By applying dynamic certainty equivalence (DyCE) to LTV plants, a new MRAC law of LTV system is derived without knowing the structure of the plant parameters. The MRACS law is generated by using high‐order derivatives of an estimated parameter, so that robust HOE with a normalization signal and σ modification for the system introduced. Our proposed method can attain better performance than conventional methods, such as estimation with variable forgetting factor (VF) and the gradient projection method (GPM). The robust HOE establishes the boundedness of all of the estimated parameters under the condition that the estimated parameter and the first derivative of the parameter are bounded. It is shown that all signals in the adaptive loop are bounded and the output error converges to a closed set. The proposed method is compared to the familiar schemes, the gradient projection method and the estimation based on forgetting factor through numerical simulations, and the effectiveness of our proposed method is shown. © 2000 Scripta Technica, Electr Eng Jpn, 130(4): 87–98, 2000     

Threshold computation for fault detection in a class of discrete‐time nonlinear systems

In this paper, we address the problem of designing robust thresholds for fault detection in discrete‐time nonlinear uncertain systems in the presence of process disturbances. Both constant and dynamic thresholds are proposed. For the computation of constant thresholds, a generalized framework based on signal norms is developed. Different kinds of constant thresholds are studied in the framework proposed. Using linear matrix inequalities (LMI) techniques, algorithms are derived for the computation of these thresholds. Similarly, the dynamic threshold is designed by deriving an inequality on the upper bound of the modulus of the residual signal. This inequality is based on the solution of discrete‐time nonlinear uncertain systems. The simulation examples illustrate that false alarms are successfully eliminated using the proposed thresholds. Copyright © 2010 John Wiley & Sons, Ltd.     

Time‐varying linear systems and input–output stability

One useful strategy for establishing input–output stability is to seek conditions on the system map so that a certain lower‐bound condition is met. We show here that, for a large class of time‐varying linear systems, the lower‐bound condition for stability is in fact necessary. Copyright © 2000 John Wiley & Sons, Ltd.     

A design method for robust model matching control of nonminimum‐phase discrete‐time systems

This paper presents a design method for robust model matching control of nonminimum‐phase discrete‐time systems. This scheme can robustly control the nominal model in the presence of unmodeled dynamics and can achieve the desired model matching simultaneously. Furthermore, the sufficient condition for stabilizing the nominal model in the presence of the unmodeled dynamics is derived and the existence of bounds for all signals is proved. Finally, computer simulation results are presented to illustrate the effectiveness of the proposed method. © 1999 Scripta Technica, Electr Eng Jpn, 128(2): 36–44, 1999     

A note on global convergence of adaptive control in a discrete‐time non‐linear case

Adaptive control is applied to a particular class of SISO discrete‐time non‐linear systems. Global boundedness and convergence are obtained by introducing a modification to a classical adaptive scheme. Copyright © 1999 John Wiley & Sons, Ltd.     

Guaranteed cost control with pole constraints for uncertain discrete-time switched systems

For a class of discrete-time switched systems with norm-bounded uncertainties and a quadratic cost index, the problem of designing a guaranteed cost state feedback controller with pole constraints is considered. A sufficient condition on the existence of robust guaranteed controllers is derived by a quadratic Lyapunov function approach together with linear matrix inequality (LMI) technique. Based on a constructed switching law, the closed-loop system is quadratic D-stable and the closed-loop cost function value is not more than a specified upper bound. Furthermore, the design of suboptimal guaranteed cost controllers is turned into a convex optimization problem with linear matrix inequalities constraints. A numerical example demonstrates the effect of the proposed design approach. __________ Translated from Control and Decision, 2007, 22(11): 1269–1273 [译自: 控制与决策]     

一类切换系统的动态输出反馈控制器设计

针对一类非线性扰动项不满足匹配条件的蚤确定切换系统鲁棒动态输出反馈镇定问题,采用单李雅普诺夫函数方法和变量替换方法,研究了状态矩阵和控制输入矩阵同时带有未知、时变但有界的不确定性,且有外界干扰的切换系统,给出了不确定切换系统鲁棒可稳的充分备件。仿真结果表明,所设计的动态输出反馈控制器及相应的切换策略保证了闭环系统渐近稳定。     

一类离散时滞不确定系统的鲁棒控制

讨论了一类离散线性时滞不确定系统的鲁棒控制问题,利用Lyapunov方法,结合矩阵不等式性质,给出离散时滞系统对所有允许不确定性鲁棒稳定的充分条件,并设计出系统的状态反馈鲁棒控制器,所得结构分别基于相应的线性矩阵不等式（LMI）的解。     

感应电机速度和电阻自适应辨识的LMI方法(英文)

该文研究了一种感应电机无速度传感器模型参考自适应系统(model reference adaptive system,MRAS),提出一种新型的基于自适应磁链观测器的常数增益速度辨识方法。首先,运用李亚普诺夫(Lyapunov)稳定性理论设计出自适应磁链观测器及速度估算方法,通过MATLAB中的线性矩阵不等式(linear matrix inequality,LMI)工具箱求解线性矩阵不等式获得磁链观测器的增益矩阵,保证了此磁链观测器的稳定性,同时也克服了运用极点配置方法带来不稳定区域的问题。该文还研究了基于自适应观测器的电阻辨识问题。基于给出的自适应磁链估计方法,设计了感应电机无速度传感器直接转矩控制系统,并进行了MATLAB仿真和实验,结果表明,提出的无速度传感器速度方法在全速范围内具有很好的动态和静态性能。     

Construction of Lyapunov function for power system based on solving linear matrix inequality

This paper presents construction of Lyapunov functions for power systems based on solving the Linear Matrix Inequality (LMI) derived from the Lyapunov stability theorem considering the dynamics of load characteristic and AVR control system. The proposed Lyapunov function is constructed as a quadratic form of state variables and an integral term which satisfies the curl equation and the sector condition. An induction machine and a synchronous machine are considered as load characteristics. One‐machine one‐load infinite bus system is considered taking into account the flux decay effects and AVR with one time constant of the generator. To verify the proposed Lyapunov function, the transient stability assessment is shown. The critical clearing times given by the proposed Lyapunov function are compared with those obtained by the numerical integration method, and they are shown to be practical. © 2007 Wiley Periodicals, Inc. Electr Eng Jpn, 158(4): 42– 50, 2007; Published online in Wiley InterScience ( www.interscience. wiley.com ). DOI 10.1002/eej.20328     

A method for determining pseudo‐measurement state values for topology observability of state estimation in power systems

This paper proposes a new technique for determining state values in power systems. Recently, it has been useful for carrying out state estimation with PMU (Phasor Measurement Unit) data. The authors have developed a method for determining state values with an artificial neural network (ANN) considering topology observability in power systems. The ANN has the advantage of approximating nonlinear functions with high precision. The method evaluates pseudo‐measurement state values of data which are lost in power systems. The method has been successfully applied to the IEEE 14‐bus system. © 2012 Wiley Periodicals, Inc. Electr Eng Jpn, 179(2): 27–34, 2012; Published online in Wiley Online Library ( wileyonlinelibrary.com ). DOI 10.1002/eej.21235