State estimation for discrete-time neural networks with time-varying delay

This article deals with the problem of delay-dependent state estimation for discrete-time neural networks with time-varying delay. Our objective is to design a state estimator for the neuron states through available output measurements such that the error state system is guaranteed to be globally exponentially stable. Based on the linear matrix inequality approach, a delay-dependent condition is developed for the existence of the desired state estimator via a novel Lyapunov functional. The obtained condition has less conservativeness than the existing ones, which is demonstrated by a numerical example.     

A time-varying extremum-seeking control approach for discrete-time systems

This paper considers the solution of a real-time optimization problem using adaptive extremum seeking control for a class of unknown discrete-time nonlinear systems. It is assumed that the equations describing the dynamics of the nonlinear system and the cost function to be minimized are unknown and that the objective function is measured. The main contribution of the paper is to formulate the extremum-seeking problem as a time-varying discrete-time estimation problem. The proposed approach is shown to avoid the need for averaging results which minimizes the impact of the choice of dither signals on the performance of the extremum seeking control system. Several examples are used to illustrate the effectiveness of the proposed technique.     

Robust discrete-time control design with time-varying parametric uncertainties

A novel multiplier approach for robust controller design in discrete-time systems with real, time-varying parametric uncertainty is presented. An important feature of our approach is that bounds on the rate of variation of the uncertain parameters are assumed and, unlike in most related approaches, dynamic multipliers are obtained that utilize this information. A convex minimization procedure formulated as an LMI problem is presented to obtain multipliers that satisfy the robustness conditions derived. Such conditions are transformed to an equivalent scaled H_∞ norm condition and a μ/k_m-synthesis approach is proposed to design robust controllers. Copyright © 1999 John Wiley & Sons, Ltd.     

Stochastic dissipativity analysis on discrete-time neural networks with time-varying delays

In this paper, the problems of global dissipativity and global exponential dissipativity are investigated for discrete-time stochastic neural networks with time-varying delays and general activation functions. By constructing appropriate Lyapunov-Krasovskii functionals and employing stochastic analysis technique, several new delay-dependent criteria for checking the global dissipativity and global exponential dissipativity of the addressed neural networks are established in linear matrix inequalities (LMIs). Furthermore, when the parameter uncertainties appear in the discrete-time stochastic neural networks with time-varying delays, the delay-dependent robust dissipativity criteria are also presented. Two examples are given to show the effectiveness and less conservatism of the proposed criteria.     

A new admissibility condition of discrete-time singular systems with time-varying delays

This paper gives a novel delay-dependent admissibility condition of discrete-time singular systems with time-varying delays. For convenience, the time-varying delay is assumed to be the sum of delay lower bound and the integral multiples of a constant delay. Specially, if the constant delay is of unit length, the delay is an interval-like time-varying delay. The proposed admissibility condition is presented and expressed in terms of linear matrix inequality (LMI) by Lyapunov approach. Generally, the uncertainty of time-varying delay would lead to conservatism. In this paper, this critical issue is tackled by accurately estimating the time-varying delay. Consequently, the proposed admissibility condition is less conservative than the existing results, which is demonstrated by a numerical example.     

Fuzzy linear pulse-transfer function-based sliding-mode control fornonlinear discrete-time systems

In this paper, a nonlinear discrete-time system in the presence of input disturbance and measurement noise is approximated by N subsystems described by the linear pulse-transfer functions. Although the input disturbance and the measurement noise are unknown, they are modeled as known pulse-transfer functions. The approximation error between the nonlinear discrete-time system and the fuzzy linear pulse-transfer function system is represented by the linear time-invariant dynamic system in every subsystem, whose degree can be larger than that of the corresponding subsystem. Besides the input disturbance and the measurement noise, uncertainties are caused by the approximation error of the fuzzy-model and the interconnected dynamics resulting from the other subsystems. Owing to the presence of input disturbance, measurement noise, or uncertainties, a disadvantageous response occurs. Based on Lyapunov redesign, the switching control in every subsystem is designed to reinforce the system performance. Due to the time-invariant feature for a constant reference input, the operating point can approach the sliding surface in the manner of finite-time steps. The stability of the overall system is verified by Lyapunov stability theory     

Minimax control for discrete-time time-varying stochastic systems

This paper gives a self-contained presentation of minimax control for discrete-time time-varying stochastic systems under finite- and infinite-horizon expected total cost performance criteria. Suitable conditions for the existence of minimax strategies are proposed. Also, we prove that the values of the finite-horizon problem converge to the values of the infinite-horizon problems. Moreover, for finite-horizon problems an algorithm of calculation of minimax strategies is developed and tested by using time-varying stochastic systems.     

Adaptive neural control of MIMO nonlinear state time-varying delay systems with unknown dead-zones and gain signs

In this paper, adaptive neural control is proposed for a class of uncertain multi-input multi-output (MIMO) nonlinear state time-varying delay systems in a triangular control structure with unknown nonlinear dead-zones and gain signs. The design is based on the principle of sliding mode control and the use of Nussbaum-type functions in solving the problem of the completely unknown control directions. The unknown time-varying delays are compensated for using appropriate Lyapunov-Krasovskii functionals in the design. The approach removes the assumption of linear functions outside the deadband as an added contribution. By utilizing the integral Lyapunov function and introducing an adaptive compensation term for the upper bound of the residual and optimal approximation error as well as the dead-zone disturbance, the closed-loop control system is proved to be semi-globally uniformly ultimately bounded. Simulation results demonstrate the effectiveness of the approach.     

时变参数不确定离散时间系统的预见控制

基于具有参数依赖的Lyapunov函数方法及LMI技巧,研究一类时变参数不确定离散时间系统的预见跟踪控制问题.首先,采用预见控制理论中误差系统的方法,引入两个与状态变量和输入变量有关的辅助信号,构造出包含未来目标值信号和干扰信号的信息的扩大误差系统,将原系统的预见跟踪问题转化为扩大误差系统的镇定问题;然后,针对扩大误差系统,考虑输出反馈时,通过改造输出方程融合可预见信号的未来信息.研究表明,通过求解LMI,即可确定静态输出反馈预见控制器增益矩阵的参数矩阵.数值仿真表明了结果的有效性.     

非仿射非线性离散系统的数据驱动二阶滑模解耦控制

针对传统二阶离散滑模变结构控制方法很难应用于模型未知系统的问题,提出了一种数据驱动二阶滑模解耦控制算法.该控制算法采用数据驱动的策略,运用系统的I/O数据,实时计算二阶离散滑模控制(2–DSMC)律.同时,运用观测器的思想,在控制器设计中引入离散扩张状态观测器(DESO),在线估计系统各回路间耦合、不确定性和外部扰动,进一步实现系统的解耦,改善控制品质.最后的理论分析和仿真结果表明,所提出的方法对于一般带有扰动和不确定性的非仿射非线性离散多入多出(MIMO)系统具有较好的解耦效果、渐进收敛的稳定性和较强的鲁棒性.     

Synthesis of the sliding-mode neural network controller for unknown nonlinear discrete-time systems

This paper develops a sliding-mode neural network controller for a class of unknown nonlinear discrete-time systems using a recurrent neural network (RNN). The control scheme is based on a linearized expression of the nonlinear system using a linear neural network (LNN). The control law is proposed according to the discrete L yapunov theory. With a modified real-time recurrent learning algorithm, the RNN as an estimator is used to estimate the unknown part in the control law in on-line fashion. The stability of the control system is guaranteed owing to the on-line learning ability of the RNN algorithm. The proposed control scheme is applied to numerical problems and simulation results that it is very effective.     

Robust extended dissipativity criteria for discrete-time uncertain neural networks with time-varying delays

In this draft, we consider the problem of robust extended dissipativity for uncertain discrete-time neural networks (DNNs) with time-varying delays. By constructing appropriate Lyapunov–Krasovskii functional (LKF), sufficient conditions are established to ensure that the considered time-delayed uncertain DNN is extended dissipative. The derived conditions are presented in terms of linear matrix inequalities (LMIs). Numerical examples are provided to illustrate the superiority of this result.

     

Passivity analysis for uncertain discrete-time stochastic BAM neural networks with time-varying delays

This paper is concerned with the passivity analysis problem for a class of discrete-time stochastic bidirectional associative memory neural networks with time-varying delays. Furthermore, the results are extended to the robust passivity analysis with mixed time delays that consist of both the discrete and distributed time delays, and the uncertainties are assumed to be time-varying norm bounded parameter uncertainties. By constructing a new Lyapunov–Krasovskii functional and introducing some appropriate free-weighting matrices, a delay-dependent passivity criterion is derived in terms of LMIs whose feasibility can be easily checked by some available software packages. Finally, two numerical examples with simulation results are given to demonstrate the effectiveness and usefulness of the proposed results.     

Delay-dependent exponential stability analysis for discrete-time switched neural networks with time-varying delay

In this paper, we focus on the stability problem for discrete-time switched neural networks with time-varying delay resorting to the average dwell time method. In terms of linear matrix inequality approach, a delay-dependent sufficient condition of exponential stability is developed for a kind of switching signal with average dwell time. A numerical example is given to show the validness of the established result.     

New delay-dependent stability results for discrete-time recurrent neural networks with time-varying delay

This paper studies the problem of stability analysis for discrete-time recurrent neural networks (DRNNs) with time-varying delays. By using the discrete Jensen inequality and the sector bound conditions, a new less conservative delay-dependent stability criterion is established in terms of linear matrix inequalities (LMIs) under a weak assumption on the activation functions. By using a delay decomposition method, a further improved stability criterion is also derived. It is shown that the newly obtained results are less conservative than the existing ones. Meanwhile, the computational complexity of the newly obtained stability conditions is reduced since less variables are involved. A numerical example is given to illustrate the effectiveness and the benefits of the proposed method.     

Delay-distribution-dependent stability of stochastic discrete-time neural networks with randomly mixed time-varying delays

In this paper, the stability analysis problem for a new class of discrete-time neural networks with randomly discrete and distributed time-varying delays has been investigated. Compared with the previous work, the distributed delay is assumed to be time-varying. Moreover, the effects of both variation range and probability distribution of mixed time-delays are taken into consideration in the proposed approach. The distributed time-varying delays and coupling term in complex networks are considered by introducing two Bernoulli stochastic variables. By using some novel analysis techniques and Lyapunov–Krasovskii function, some delay-distribution-dependent conditions are derived to ensure that the discrete-time complex network with randomly coupling term and distributed time-varying delay is synchronized in mean square. A numerical example is provided to demonstrate the effectiveness and the applicability of the proposed method.     

Adaptive control based on fast online algebraic identification and GPI control for magnetic levitation systems with time-varying input gain

This paper considers the position tracking problem of a voltage-controlled magnetic levitation system (MLS) in the presence of modelling errors caused by uncertainties in the system’s physical parameters. An adaptive control based on fast online algebraic parameter estimation and generalised proportional integral (GPI) output feedback control is considered as a control scheme candidate. The GPI controller guarantees an asymptotically exponentially stable behaviour of the controlled ball position and the possibilities of carrying out rest-to-rest trajectory tracking tasks. The nature of the control input gain in an MLS is that of a state-dependent time-varying gain, reflecting the nonlinear character of the magnetic force with regard to the distance and the properties of the metallic ball. The system gain has therefore been locally approximated using a periodically updated time polynomial function (of second degree), where the coefficients of the polynomial are estimated during a very short period of time. This estimation is achieved using the recently introduced algebraic online parameter estimation approach. The stability of the closed-loop system is demonstrated under the assumption that no external factors cause changes in the parameter during the time interval in which the stability is analysed. Finally, experimental results are presented for the controlled MLS demonstrating the excellent stabilisation and position tracking performance of the control system designed in the presence of significant nonlinearities and uncertainties of the underlying system.     

A new neural network-based approach for self-tuning control of nonlinear SISO discrete-time systems

This article presents a new neural network-based approach for self-tuning control of nonlinear single-input single-output (SISO) discrete-time dynamic systems. According to the approach, a neural network ARMAX (NN-ARMAX) model of the system is identified and continuously updated, using an online training algorithm. Control design is accomplished by solving an optimal discrete-time linear quadratic tracking problem using an observer-type linear state-space Kalman innovation model, which is built from the parameters of a local linear version of the NN-ARMAX model. The state-feedback control law is implemented using the Kalman state, which is calculated without estimating the noise covariance properties. The proposed control approach is shown to be very effective and outperforms the self-tuning control approach based on a linear ARMAX model on two simulation examples.     

Adaptive discrete-time sliding-mode control of nonlinear systems described by Wiener models

In this paper, we propose an adaptive control scheme that can be applied to nonlinear systems with unknown parameters. The considered class of nonlinear systems is described by the block-oriented models, specifically, the Wiener models. These models consist of dynamic linear blocks in series with static nonlinear blocks. The proposed adaptive control method is based on the inverse of the nonlinear function block and on the discrete-time sliding-mode controller. The parameters adaptation are performed using a new recursive parametric estimation algorithm. This algorithm is developed using the adjustable model method and the least squares technique. A recursive least squares (RLS) algorithm is used to estimate the inverse nonlinear function. A time-varying gain is proposed, in the discrete-time sliding mode controller, to reduce the chattering problem. The stability of the closed-loop nonlinear system, with the proposed adaptive control scheme, has been proved. An application to a pH neutralisation process has been carried out and the simulation results clearly show the effectiveness of the proposed adaptive control scheme.     

Adaptive neural complementary sliding-mode control via functional-linked wavelet neural network

Chaos control can be applied in the vast areas of physics and engineering systems, but the parameters of chaotic system are inevitably perturbed by external inartificial factors and cannot be exactly known. This paper proposes an adaptive neural complementary sliding-mode control (ANCSC) system, which is composed of a neural controller and a robust compensator, for a chaotic system. The neural controller uses a functional-linked wavelet neural network (FWNN) to approximate an ideal complementary sliding-mode controller. Since the output weights of FWNN are equipped with a functional-linked type form, the FWNN offers good learning accuracy. The robust compensator is designed to eliminate the effect of the approximation error introduced by the neural controller upon the system stability in the Lyapunov sense. Without requiring preliminary offline learning, the parameter learning algorithm can online tune the controller parameters of the proposed ANCSC system to ensure system stable. Finally, it shows by the simulation results that favorable control performance can be achieved for a chaotic system by the proposed ANCSC scheme.