On the capability of the T‐S model in describing nonlinear systems

The Takagi‐Sugeno (T‐S) model is one of the most powerful methods in describing nonlinear systems. Because the T‐S model can be easily converted into an LPV system, Lyapunov stability analysis and controller design reduce to solving an LMI problem. However, since the constructed T‐S model is generally approximation, how to construct a T‐S model with less approximation error is important. In this paper, we propose a modeling method for T‐S model which yields no error for some class of nonlinear systems, and discuss some expansion as well as estimation of error bound for general nonlinear systems. © 2008 Wiley Periodicals, Inc. Electr Eng Jpn, 166(1): 52–59, 2009; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.20503     

Identification in nonlinear systems by using an automatic choosing function and a genetic algorithm

This paper deals with an identification method based on an automatic choosing function (ACF) for nonlinear systems. A full data region or an entire domain is partitioned into subdomains and the unknown nonlinear function to be estimated is approximately described by a linear equation on each subdomain. These linear equations are smoothly united into a single expression by the ACF, and the resulting model is linear in its parameters. Hence these parameters are easily evaluated by the linear least-squares method. The subdomains and the ACF are properly determined by a genetic algorithm that has a high potential for global optimization. Numerical experiments demonstrate the effectiveness of the proposed method. © 1998 Scripta Technica, Electr Eng Jpn, 125(4): 43–51, 1998     

Analysis of the effect of metal oxide arresters on system resonanceusing the describing function method

A theoretical analysis of the effect of gapless metal oxide arresters on power system resonance is presented. The describing function method is used to approximately evaluate fundamental and harmonic resonant conditions for systems involving metal oxide arresters. The study shows that the presence of metal oxide arresters not only introduces no new resonant conditions, but also can help to eliminate some old ones. Computer simulations were performed to verify these theoretical results     

一类非线性系统渐近稳定控制方法及其应用

研究了某一类非线性系统渐近稳定控制问题,首先对非线性系统模型的状态变量进行非线性变换,然后采用非线性状态反馈方法将原非线性系统变换为一渐近稳定的线性系统,得到了相应的非线性控制律。把本文研究的结果应用于某飞行器的姿态控制系统中,得到渐近稳定姿态控制律。最后通过仿真证明了本控制方法的有效性。     

The asymptotic stability of nonlinear autonomous systems

In this paper a new general method is developed by means of which one can ascertain whether a nonlinear autonomous system is asymptotically stable. The method is essentially an extension to nonlinear systems of a theorem developed earlier by the first author for linear autonomous systems. Necessary and sufficient conditions are specified, the satisfaction of which guarantees that the system being studied is asymptotically stable. The new method, by design, always uses a positive-definite function which satisfies Lyapunov?s stability theorem. However, the new method uses only one positive-definite function, in contrast to Lyapunov?s stability theorem, which requires two functions to be definite at the same time. In addition, the new method specifies the stability function at the outset once a mathematical system model has been obtained.     

Determining the periodic response of nonlinear systems by a gradient method

For systems of differential equations of the form ? = f(x) or x = f(x, t) , a periodic response may be identified by the requirement that x(kT) = x(0) , where k = 1, 2, … and T is the period, x(0) = x₀ being the initial-condition vector. We describe a gradient method for finding this x₀ vector by minimizing the square magnitude of the ‘discrepancy vector’ δ(x₀) = x(T)–x₀. The gradient of the scalar function P(x₀) = δ^t(x₀)δ(x₀) with respect to x₀ is calculated by one full-period forward integration of the original differential equation to obtain δ(x₀), and then one full-period backward integration of the adjoint variational equations, using δ(x₀) as the initial-condition vector. The gradient of P(x₀) is then twice the adjoint discrepancy vector. We use Fletcher's method of optimization to minimize P(x₀) .     

一种基于非线性模型的OFDM信道估计

导频辅助的信道估计方法是OFDM系统中应用最为广泛的一类信道估计方法,其中的2-D维纳滤波是最小均方误差意义下的最佳线性估计器,但是由于其计算量非常大,因而在实际中不能得到很好的应用。2×1-D的维纳滤波器利用信道相关函数的可分离性,对2-D维纳滤波器进行了简化,一定程度地降低了其复杂性,但仍然需要知道或估计信道的统计特性。文中介绍了一种基于非线性模型的信道估计方法,对其算法进行了仿真并与2×1-D维纳滤波的误比特率(BER)性能进行了比较。仿真结果表明,此方法能以较低的复杂性达到与2×1-D维纳滤波相近的性能,且无需对信道特性估计,是一种较实用的信道估计方法。     

一类不确定非线性系统的有限时间输出调节方法

针对一类外系统是中性稳定的不确定非线性系统的输出调节问题,提出一种有限时间收敛的输出调节器的设计方法。该方法结合内模原理和有限时间稳定性理论,先根据输出调节问题可解的必要条件,将原受控系统和外系统的输出调节问题转化为增广系统的镇定问题;再利用动态面技术设计一种鲁棒有限时间稳定的镇定器,从而保证闭环系统的信号是全局最终有界的,并且使调节误差在有限的时间内收敛至任意给定的范围内。仿真结果说明了所设计调节器的有效性和可行性。     

Modulated carriers in nonlinear systems

The systems to be considered consist of linear and nonlinear elements and are driven by a priori known periodic signals (carriers). The present theory deals with small perturbations from the periodic steady state. Use has been made of the ‘amplitude-phase’ representation of the perturbations. The operator (jω₀ + λ) is used, in which jω₀ indicates the time differentiation of the carrier components and the operator λ ( = d/dt) affects the perturbation only. The perturbations will be related by a ‘sensitivity’ matrix H. In order to illustrate the applicability of this theory, the performance of the dynamic limiter of Zaalberg van Zelst will be treated.     

A distributed state estimation method for power systems incorporating linear and nonlinear models

High-voltage transmission networks are commonly equipped with phasor measurement units (PMU), and some of them are PMU observable. However, PMUs are seldom installed in distribution networks due to budget limitations. The state estimation equations of PMU observable areas are linear, while those of other areas remain nonlinear. This paper proposes a new distributed state estimation method for solving multi-area state estimation problems, in which linear models are used for high-voltage transmission network, while nonlinear models are adopted for other areas. In PMU observable area, we select coordinating variables as generalized cost functions which accurately represent the sensitivity between the linear SE objective function and boundary states. Consequently, SE results identical to a centralized estimator can be obtained without iterations at the coordination level. This paper presents the problem model and theoretical analysis of the proposed method, and shows its effectiveness by numerical tests.     

Low-frequency noise in nonlinear systems

Excess noise degrades circuit performance in linear and nonlinear operation. The linear case, obviously, is much easier to analyze, understand, and model. Things get much more involved when nonlinear operation is involved. An analytical investigation is usually not feasible, thus it is necessary to resort to numerical circuit simulation.     

一类不确定非线性系统的动态面输出调节方法

针对一类由线性中性稳定的外系统驱动的具有未建模动态和外界扰动的非线性不确定系统的输出调节问题,结合动态面控制法和内模原理提出一种具有动态面控制的设计方法.根据非线性输出调节问题可解的必要条件,运用状态变换和标准内模将输出调节问题转化为镇定问题.运用动态面控制法将一阶滤波器引入反步设计中,避免了反步设计中所存在的"膨胀项...     

一类非线性混沌系统的RBF神经网络控制

设计了一种基于径向基函数网络(RBFNs)的混沌非线性动力系统控制方法，将嵌入在混沌吸引子中不稳定周期轨道镇定到稳定不动点。用Logistic方程和Henon映射作数值仿真实验，证明了该方法的有效性。     

A set‐based model‐free reinforcement learning design technique for nonlinear systems

In this study, we propose an extremum‐seeking approach for the approximation of optimal control problems for a class of unknown nonlinear dynamical systems. The technique combines a phasor extremum‐seeking controller with a reinforcement learning strategy. The learning approach is used to estimate the value function of an optimal control problem of interest. The phasor extremum‐seeking controller implements the approximate optimal controller. The approach is shown to provide reasonable approximations of optimal control problems without the need for a parameterization of the nonlinear system's dynamics. A simulation example is provided to demonstrate the effectiveness of the technique.     

An efficient method for combining adaptive echo and noise canceller in hands‐free systems

Acoustic interferences severely degrade the quality and the intelligibility of the desired speech signal, thus posing a severe problem for many speech applications. Several acoustic echo cancellation (AEC) techniques have been proposed with a view to solving this problem. There are, however, few reports of AEC methods working under real noisy conditions. In this paper, we investigate the maximum positive synergies of the combination of acoustic echo canceller with a new adaptive beamformer. The proposed system achieves both the AEC and noise reduction of speech in an actual environment with real noise sources. Since the AEC is located behind the fixed beamformer of the new adaptive beamformer only one AEC is required for an arbitrary number of array elements, and the AEC does not feel any repercussions from the new adaptive beamformer. The proposed system was implemented in a real environment using National Instruments NI‐PXI‐1042Q controller system and data acquisition card PXI‐4472. Experimental results show that the proposed system has successfully improved the performance of hands‐free systems. Copyright © 2008 John Wiley & Sons, Ltd.     

Indirect adaptive fuzzy control for input and output constrained nonlinear systems using a barrier Lyapunov function

In this paper, a novel indirect adaptive fuzzy controller is proposed for a class of uncertain nonlinear systems with input and output constrains. To address output and input constraints, a barrier Lyapunov function and an auxiliary design system are employed, respectively. The proposed approach is explored by employing fuzzy logic systems to tackle unknown nonlinear functions and combining the adaptive backstepping technique with adaptive fuzzy control design. Especially, the number of the online learning parameters are reduced to 2n in the closed‐loop system. It is proved that the proposed control approach can guarantee that all the signals in the closed‐loop system are bounded, and the input and output constraints are circumvented simultaneously. A numerical example with comparisons is provided to illustrate the effectiveness of the proposed approach. Copyright © 2013 John Wiley & Sons, Ltd.