Two general integral inequalities and their applications to stability analysis for systems with time‐varying delay

Integral inequalities have been widely used in stability analysis for systems with time‐varying delay because they directly produce bounds for integral terms with respect to quadratic functions. This paper presents two general integral inequalities from which almost all of the existing integral inequalities can be obtained, such as Jensen inequality, the Wirtinger‐based inequality, the Bessel–Legendre inequality, the Wirtinger‐based double integral inequality, and the auxiliary function‐based integral inequalities. Based on orthogonal polynomials defined in different inner spaces, various concrete single/multiple integral inequalities are obtained. They can produce more accurate bounds with more orthogonal polynomials considered. To show the effectiveness of the new inequalities, their applications to stability analysis for systems with time‐varying delay are demonstrated with two numerical examples. Copyright © 2016 John Wiley & Sons, Ltd.     

Recursive state estimation for discrete‐time nonlinear systems with event‐triggered data transmission,norm‐bounded uncertainties and multiple missing measurements

In this paper, we consider the recursive state estimation problem for a class of discrete‐time nonlinear systems with event‐triggered data transmission, norm‐bounded uncertainties, and multiple missing measurements. The phenomenon of event‐triggered communication mechanism occurs only when the specified event‐triggering condition is violated, which leads to a reduction in the number of excessive signal transmissions in a network. A sequence of independent Bernoulli random variables is employed to model the multiple measurements missing in the transmission. The norm‐bounded uncertainties that could be considered as external disturbances which lie in a bounded set. The purpose of the addressed filtering problem is to obtain an optimal robust recursive filter in the minimum‐variance sense such that with the simultaneous presence of event‐triggered data transmission, norm‐bounded uncertainties, and multiple missing measurements; the filtering error is minimized at each sampling time. By solving two Riccati‐like difference equations, the filter gain is calculated recursively. Based on the stochastic analysis theory, it is proved that the estimation error is bounded under certain conditions. Finally, two numerical examples are presented to demonstrate the effectiveness of the proposed algorithm. Copyright © 2016 John Wiley & Sons, Ltd.     

Stochastic consensus control with finite frequency specification for Markov jump networks

A stochastic finite frequency consensus protocol for directed networks with Markov jump topologies and external disturbances is proposed in this paper. By introducing the frequency band information into consensus control design, the disagreement dynamics of interconnected networks asymptotically converge to zero with an improved level of disturbance attenuation in the specific frequency band. In addition, the new model transformation approach is presented by exploring certain features of Laplacian matrix in real Jordan form, which leads to more generality of the designed protocol. A numerical example validates the potential of the developed results. Copyright © 2015 John Wiley & Sons, Ltd.     

Pseudo‐predictor feedback control of discrete‐time linear systems with a single input delay

This paper studies the problems of stabilization of discrete‐time linear systems with a single input delay. By developing the methodology of pseudo‐predictor feedback, which uses the (artificial) closed‐loop system dynamics to predict the future state, memoryless state feedback control laws are constructed to solve the problem. Necessary and sufficient conditions are obtained to guarantee the stability of the closed‐loop system in terms of the stability of a class‐difference equations. It is also shown that the proposed controller achieves semi‐global stabilization of the system if its actuator is subject to either magnitude saturation or energy constraints under the condition that the open‐loop system is only polynomially unstable. Numerical examples have been worked out to illustrate the effectiveness of the proposed approaches. Copyright © 2015 John Wiley & Sons, Ltd.     

Stability Margin Determination of Linear Discrete‐Time Systems Described By Fuzzy Convex Sets Uncertainty

This paper proposes a new method for determining the stability margin of uncertain linear discrete‐time systems with uncertainty described by fuzzy convex sets. Nonsymmetrical triangular membership functions describing the uncertainty of characteristic polynomial coefficients are considered. This method is based on transformation of the uncertain discrete systems to the continuous time area and generalization of Kharitonov theorem for determining the uncommon minimum confidence level that guarantees stability of the system.     

Supervised Multi‐Rejector of Periodic Disturbances for Nonlinear Systems Using Decoupled State Multimodel

In this paper, a multi‐rejector of periodic disturbances is proposed for discrete‐time nonlinear systems represented by a decoupled state multimodel. We report a decoupled state multimodel repetitive‐predictive control based on a supervised algorithm to ensure reference trajectory tracking and periodic disturbances rejection. Partial predictors associated to the local controllers make the best choice of the most valid partial controller that meets the desired closed loop performances. The effectiveness of the supervised multi‐rejector is shown via a simulation example. The obtained results are satisfactory and show a good rejection of periodic disturbances and reference trajectory tracking.     

Robust Adaptive Neural Control for a Class of Time‐Varying Delay Systems with Backlash‐like Hysteresis Input

This paper proposes a robust adaptive dynamic surface control (DSC) scheme for a class of time‐varying delay systems with backlash‐like hysteresis input. The main features of the proposed DSC method are that 1) by using a transformation function, the prescribed transient performance of the tracking error can be guaranteed; 2) by estimating the norm of the unknown weighted vector of the neural network, the computational burden can be greatly reduced; 3) by using the DSC method, the explosion of complexity problem is eliminated. It is proved that the proposed scheme guarantees all the closed‐loop signals being uniformly ultimately bounded. The simulation results show the validity of the proposed control scheme.     

Design and Comparison Base Analysis of Adaptive Estimator for Completely Unknown Linear Systems in the Presence of OE Noise and Constant Input Time Delay

In this paper, an adaptive estimator (AE) is introduced to learn the approximate Q‐function and control policy by only using the noisy states and control signals of the unknown linear, discrete time systems having constant input time delay. The system measurements are uncertain owing to output error (OE)‐type noise acting randomly on the system measurements. Therefore, this research differs from the designed AE in the literature since previous research ignores the role of the external random disturbances on AE‐based learning. In order to compare the AE‐based learning results with traditional system identification (SI) approaches, a modified version of the OE model structure for unstable systems is reviewed and parameters of a second‐order unstable system with constant input time delay are identified. The simulation results demonstrate that the designed AE efficiently minimizes the stochastic cost function and the temporal difference error by learning the approximate solution for the Hamilton‐Jacobi‐Bellman (HJB) equation. It is noted that the error in the Q‐function obtained with the AE is slightly larger than the Q‐function attained with the identified OE parameters. However, as the noise standard deviation increases, the error in the AE‐based learning results reduces whereas the error in the OE‐based learning increases. This indicates that even though the added random noise deteriorates the performance of the OE predictor, it improves the learning efficiency of the AE since it acts like exploration noise.     

一种基于DTW的新型故事时间序列相似性度量方法

现有时间序列相似性度量方法在进行股市序列相似性分析时,通常忽略成交量等其他重要因素对股价的影响,从而导致序列聚类、分类不精确。针对这一问题,本文提出了新的股市时间序列相似性度量方法。该方法在动态时间弯曲算法的基础上,通过引进时间衰竭因子,并结合成交量因素,给出了股市序列的最终度量公式。为了证明提出方法的可行性和有效性,本文实验部分通过选取家电等三个行业中的股票数据进行测试。实验结果表明,基于动态时间弯曲(Dynamic time warping,DTW)的新型股市时间序列相似性度量方法能够在保持股票序列形态特征的基础上,较好地解决股市技术分析中量价关系问题,从而更有效地应用于股市技术分析里关于模式发现等领域。