Observer design for neutral‐type neural networks with discrete and distributed time‐varying delays

This paper is concerned with the problem of state estimation for a class of neural networks with discrete and distributed interval time‐varying delays. We propose a new approach of nonlinear estimator design for the class of neutral‐type neural networks. By constructing a newly augmented Lyapunov‐Krasovskii functional, we establish sufficient conditions to guarantee the estimation error dynamics to be globally exponentially stable. The obtained results are formulated in terms of linear matrix inequalities (LMIs), which can be easily verified by the MATLAB LMI control toolbox. Then, the desired estimators gain matrix is characterized in terms of the solution to these LMIs. Three numerical examples are given to show the effectiveness of the proposed design method.     

Composite learning fuzzy synchronization for incommensurate fractional‐order chaotic systems with time‐varying delays

This paper presents a composite learning fuzzy control to synchronize two different uncertain incommensurate fractional‐order time‐varying delayed chaotic systems with unknown external disturbances and mismatched parametric uncertainties via the Takagi‐Sugeno fuzzy method. An adaptive controller together with fractional‐order composite learning laws is designed based on both a parallel distributed compensation technology and a fractional Lyapunov criterion. The boundedness of all variables in the closed‐loop system and the Mittag‐Leffler stability of tracking error can be guaranteed. T‐S fuzzy systems are provided to tackle unknown nonlinear functions. The distinctive features of the proposed approach consist in the following: (1) a supervisory control law is designed to compensate the lumped disturbances; (2) both the prediction error and the tracking error are used to estimate the unknown fuzzy system parameters; (3) parameter convergence can be ensured by an interval excitation condition. Finally, the feasibility of the proposed control strategy is demonstrated throughout an illustrative example.     

On‐line parameter estimation for a class of time‐varying continuous systems with bounded disturbances

In this paper, we proposed an on‐line parameter estimation algorithm for a class of time‐varying continuous systems with bounded disturbance. In this method, a novel polynomial approximator with a bounded regressor vector is constructed and utilized to approximate the time‐varying parameters. The direct least‐squares algorithm is employed to acquire the on‐line estimates, so that several useful properties of the direct estimation, such as fast convergence and robustness to the bounded disturbance, are reflected in our method. We have proved that the estimation error of this method is bounded. Furthermore, the bound on the Euclidean norm of the estimation error is derived. The simulation results demonstrate that this method can provide accurate estimates of time‐varying parameters even under the influence of bounded disturbance. Copyright © 2010 John Wiley & Sons, Ltd.     

Adaptive neural tracking control for high angle of attack maneuver with average dwell time

This article attempts to study the high angle of attack maneuver from the perspective of switched system control. In view of the complex aerodynamic characteristics, an improved longitudinal attitude motion model is presented, which is a switched stochastic nonstrict feedback nonlinear system with distributed delays. The significant design difficulty is the completely unknown diffusion and drift terms and distributed delays with all state variables. Based on a technical lemma and neural networks, an improved smooth state feedback control law for nonstrict feedback systems is proposed without any growth assumptions. To eliminate the influence of distributed delays, an improved Lyapunov–Krasovskii function is constructed, which skillfully removes the constraint of the upper bound of the delay change rate. Then, by combining the average dwell-time scheme and stochastic backstepping technique, an adaptive neural network tracking control law is designed, which extends a newly proposed switched system stability condition to the stochastic switched system. Theoretical analysis and flight control simulation experiments are provided to illustrate the effectiveness of the proposed control method.     

Less conservative criteria for fault accommodation of time‐varying delay systems using adaptive fault diagnosis observer

This paper studies the problem of fault accommodation of time‐varying delay systems using adaptive fault diagnosis observer. Based on the proposed fast adaptive fault estimation (FAFE) algorithm using only a measured output, a delay‐dependent criteria is first established to reduce the conservatism of the design procedure, and the FAFE algorithm can enhance the performance of fault estimation. On the basis of fault estimation, the observer‐based fault‐tolerant tracking control is then designed to guarantee tracking performance of the closed‐loop systems. Furthermore, comprehensive analysis is presented to discuss the calculation steps using linear matrix inequality technique. Finally, simulation results of a stirred tank reactor model are presented to illustrate the efficiency of the proposed techniques. Copyright © 2009 John Wiley & Sons, Ltd.     

Maximum likelihood gradient identification for multivariate equation‐error moving average systems using the multi‐innovation theory

For the multivariate equation‐error moving average system, a multivariate maximum likelihood multi‐innovation extended stochastic gradient (M‐ML‐MIESG) algorithm is delivered. The key is to decompose the system into several regressive identification subsystems according to the number of the system outputs. Then, a multivariate maximum likelihood extended stochastic gradient algorithm is presented to estimate the parameters of these subsystems. The M‐ML‐MIESG algorithm has higher parameter estimation accuracy than the multivariate extended stochastic gradient algorithm. The simulation examples indicate that the proposed methods work well.     

H∞ filtering for continuous‐time singular systems with time‐varying delay

This paper focuses on H_∞ filter design for continuous‐time singular systems with time‐varying delay. A delay‐dependent H_∞ performance analysis result is first established for error systems via a novel estimation method. By combining a well‐known inequality with a delay partition technique, the upper bound of the derivative of the Lyapunov functional is estimated more tightly and expressed as a convex combination with respect to the reciprocal of the delay rather than the delay. Based on the derived H_∞ performance analysis results, a regular and impulse‐free H_∞ filter is designed in terms of linear matrix inequalities (LMIs). A numerical example is given to demonstrate the merits of the proposed method. Copyright © 2010 John Wiley & Sons, Ltd.     

Fault detection for discrete‐time switched singular time‐delay systems: an average dwell time approach

In this paper, the fault detection problem is investigated for a class of discrete‐time switched singular systems with time‐varying state delays. The residual generator is firstly constructed based on a switched filter, and the design of fault detection filter is formulated as an H _∞ filtering problem, that is, minimizing the error between residual and fault in the H _∞ sense. Then, by constructing an appropriate decay‐rate‐dependent piecewise Lyapunov function and using the average dwell time scheme, a sufficient condition for the residual system to be regular, causal, and exponential stable while satisfying a prescribed H _∞ performance is derived in terms of linear matrix inequalities (LMIs). The corresponding solvability condition for the desired fault detection filters is also established via LMI approach. Finally, a numerical example is presented to show the effectiveness of the developed theoretical results.Copyright © 2012 John Wiley & Sons, Ltd.     

Parameter identification for Wiener-finite impulse response system with output data of missing completely at random mechanism and time delay

In this paper, the parameter estimation issue of Wiener system with random time delay and missing output data is studied. The linear part of Wiener system is described by Finite Impulse Response (FIR) model. The mathematical formula of the Expectation Maximum algorithm to identify Wiener-FIR system that contains the random time delay and the nonlinear output data in missing completely at random mechanism is derived, which is never considered before. To obtain the unmeasurable intermediate variable in Wiener-FIR system, the idea of auxiliary model is adopted. The time delay and system parameters can be estimated simultaneously by this method. Numerical example and the identification of water tank system example are carried out, the effectiveness of the algorithm is proved.     

Convergence of the recursive identification algorithms for multivariate pseudo‐linear regressive systems

The performance analysis of the recursive algorithms for the multivariate systems with an autoregressive moving average noise process is still open. This paper analyzes the convergence of two recursive identification algorithms, the multivariate recursive generalized extended least squares algorithm and the multivariate generalized extended stochastic gradient algorithm, for pseudo‐linear multivariate systems and proves that the parameter estimation errors consistently converge to zero under persistent excitation conditions. The simulation results show that the proposed algorithms work well. Copyright © 2015 John Wiley & Sons, Ltd.     

Identification of NARMAX Hammerstein models with performance assessment using brain storm optimization algorithm

In this paper, brain storm optimization (BSO)‐based efficient identification approach has been applied to different types of stable and practically useful Nonlinear Auto Regressive Moving Average with exogenous noise (NARMAX) Hammerstein models with various performance criteria‐based assessments. Different performance measures of the estimation process like accuracy, precision and consistency have been established to ensure the general applicability and practical usefulness of the proposed approach. The accuracy and the precision of the parameter estimation are established with the corresponding bias and variance information, while the consistency has been justified with the help of hypothesis test results. BSO‐based optimum values of the output mean square errors and the parameters and their corresponding convergences ensure the stability and robustness of the proposed identification scheme. The comparative studies of the performance of the BSO algorithm with the other basic evolutionary algorithms have been reported with optimum values of the mean square errors, estimated values of the parameters, corresponding computational times and hypothesis test outcomes. Copyright © 2016 John Wiley & Sons, Ltd.     

Dissipativity and passivity analysis for discrete‐time complex‐valued neural networks with leakage delay and probabilistic time‐varying delays

In this paper, the problem of dissipativity and passivity analysis is investigated for discrete‐time complex‐valued neural networks with time‐varying delays. Both leakage and discrete time‐varying delays have been considered. By constructing a suitable Lyapunov–Krasovskii functional and by using discretized Jensen's inequality approach, sufficient conditions have been established to guarantee the (Q ,S ,R ) ? γ dissipativity and passivity of the addressed discrete‐time complex‐valued neural networks. These conditions are derived in terms of complex‐valued linear matrix inequalities (LMIs), which can be checked numerically using Yet Another LMI Parser toolbox in Matrix Laboratory. Finally, three numerical examples are established to illustrate the effectiveness of the obtained theoretical results. Copyright © 2016 John Wiley & Sons, Ltd.     

Filter‐based fault detection and diagnosis using output PDFs for stochastic systems with time delays

In this paper, a fault detection and diagnosis (FDD) scheme is studied for general stochastic dynamic systems subjected to state time delays. Different from the formulation of classical FDD problems, it is supposed that the measured information for the FDD is the probability density function (PDF) of the system output rather than its actual value. A B‐spline expansion technique is applied so that the output PDF can be formulated in terms of the dynamic weights of the B‐spline expansion, by which a time delay model can be established between the input and the weights with non‐linearities and modelling errors. As a result, the concerned FDD problem can be transformed into a classic FDD problem subject to an uncertain non‐linear system with time delays. Feasible criteria to detect the system fault are obtained and a fault diagnosis method is further presented to estimate the fault. Simple simulations are given to demonstrate the efficiency of the proposed approach. Copyright © 2006 John Wiley & Sons, Ltd.     

Combined state and parameter estimation for Hammerstein systems with time delay using the Kalman filtering

This paper discusses the state and parameter estimation problem for a class of Hammerstein state space systems with time delay. Both the process and the measurement noises are considered in the system. On the basis of the observable canonical state space form and the key term separation, a pseudolinear regressive identification model is obtained. For the unknown states in the information vector, the Kalman filter is used to search for the optimal state estimates. A Kalman filter–based least squares iterative and a recursive least squares algorithms are proposed. Extending the information vector to include the latest information terms, which are missed for the time delay, the Kalman filter–based recursive extended least squares algorithm is derived to obtain the estimates of the unknown time delay, parameters, and states. The numerical simulation results are given to illustrate the effectiveness of the proposed algorithms.     

A novel variable‐length sliding window blockwise least‐squares algorithm for on‐line estimation of time‐varying parameters

Motivated by the advances in computer technology and the fact that the batch/block least‐squares (LS) produces more accurate parameter estimates than its recursive counterparts, several important issues associated with the block LS have been re‐examined in the framework of on‐line identification of systems with abrupt/gradual change parameters in this paper. It is no surprise that the standard block LS performs unsatisfactorily in such a situation. To overcome this deficiency, a novel variable‐length sliding window‐based LS algorithm, known as variable‐length sliding window blockwise least squares, is developed. The algorithm consists of a change detection scheme and a data window with adjustable length. The window length adjustment is triggered by the change detection scheme. Whenever a change in system parameters is detected, the window is shortened to discount ‘old’ data and place more weight on the latest measurements. Several strategies for window length adjustment have been considered. The performance of the proposed algorithm has been evaluated through numerical studies. In comparison with the recursive least squares (RLS) with forgetting factors, superior results have been obtained consistently for the proposed algorithm. Robustness analysis of the algorithm to measurement noise have also been carried out. The significance of the work reported herein is that this algorithm offers a viable alternative to traditional RLS for on‐line parameter estimation by trading off the computational complexity of block LS for improved performance over RLS, because the computational complexity becomes less and less an issue with the rapid advance in computer technologies. Copyright © 2004 John Wiley & Sons, Ltd.