Compensation of time‐varying input delay for discrete‐time nonlinear systems

We consider general discrete‐time nonlinear systems (of arbitrary nonlinear growth) with time‐varying input delays and design an explicit predictor feedback controller to compensate the input delay. Such results have been achieved in continuous time, but only under the restriction that the delay rate is bounded by unity, which ensures that the input signal flow does not get reversed, namely, that old inputs are not felt multiple times by the plant (because on such subsequent occasions, the control input acts as a disturbance). For discrete‐time systems, an analogous restriction would be that the input delay is non‐increasing. In this work, we do not impose such a restriction. We provide a design and a global stability analysis that allow the input delay to be arbitrary (containing intervals of increase, decrease, or stagnation) over an arbitrarily long finite period of time. Unlike in the continuous‐time case, the predictor feedback law in the discrete‐time case is explicit. We specialize the result to linear time‐invariant systems and provide an explicit estimate of the exponential decay rate. Carefully constructed examples are provided to illustrate the design and analytical challenges. Copyright © 2015 John Wiley & Sons, Ltd.     

Time‐varying input delay compensation for nonlinear systems with additive disturbance: An output feedback approach

This paper addresses the output feedback tracking control of a class of multiple‐input and multiple‐output nonlinear systems subject to time‐varying input delay and additive bounded disturbances. Based on the backstepping design approach, an output feedback robust controller is proposed by integrating an extended state observer and a novel robust controller, which uses a desired trajectory‐based feedforward term to achieve an improved model compensation and a robust delay compensation feedback term based on the finite integral of the past control values to compensate for the time‐varying input delay. The extended state observer can simultaneously estimate the unmeasurable system states and the additive disturbances only with the output measurement and delayed control input. The proposed controller theoretically guarantees prescribed transient performance and steady‐state tracking accuracy in spite of the presence of time‐varying input delay and additive bounded disturbances based on Lyapunov stability analysis by using a Lyapunov‐Krasovskii functional. A specific study on a 2‐link robot manipulator is performed; based on the system model and the proposed design procedure, a suitable controller is developed, and comparative simulation results are obtained to demonstrate the effectiveness of the developed control scheme.     

Rejection of mismatched disturbances for systems with input delay via a predictive extended state observer

The problem of output stabilization and disturbance rejection for input‐delayed systems is tackled in this work. First, a suitable transformation is introduced to translate mismatched disturbances into an equivalent input disturbance. Then, an extended state observer is combined with a predictive observer structure to obtain a future estimation of both the state and the disturbance. A disturbance model is assumed to be known but attenuation of unmodeled components is also considered. The stabilization is proved via Lyapunov‐Krasovskii functionals, leading to sufficient conditions in terms of linear matrix inequalities for the closed‐loop analysis and parameter tuning. The proposed strategy is illustrated through a numerical example.     

Output feedback stabilization of stochastic feedforward nonlinear systems with input and state delay

This paper considers the problem of output feedback stabilization for a class of stochastic feedforward nonlinear systems with input and state delay. Under a set of coordinate transformations, we first design a linear output feedback controller for a nominal system. Then, with the aid of feedback domination technique and an appropriate Lyapunov–Krasovskii functional, it is proved that the proposed linear output feedback controller can drive the closed‐loop system globally asymptotically stable in probability. Copyright © 2015 John Wiley & Sons, Ltd.     

一类带不确定输入动态非线性系统的输出反馈鲁棒镇定

研究一类带不确定输入动态非线性系统的输出反馈鲁棒镇定问题.通过在高增益观测器引入新的设计参数,改进了通常的高增益反馈控制的设计方法.在输入动态满足零相对阶最小相位的假设下,基于非分离设计原则给出了动态输出反馈控制器的设计方法,所设计的控制器实现了对任意可允许不确定输入动态的全局鲁棒镇定.     

离散Lipschitz非线性系统状态和未知输入估计

针对含有未知输入和可测噪声的离散Lipschitz非线性系统,研究了状态估计、未知输入以及可测噪声同时估计的问题.首先,对含有未知输入的系统,设计了比例积分观测器,达到同时估计系统状态和未知输入之目的.分析了残差系统的观测性和稳定性,利用H_∞实现该观测器对时变未知输入的有效估计;其次,将观测器增益矩阵的求解转化为求解线性矩阵不等式的形式;进一步地,基于系统状态扩展方法,将所提方法推广至同时含有未知输入和可测噪声的系统;最后,通过两个仿真算例说明了所提方法的正确性和有效性.     

Multiple sliding mode observers and unknown input estimations for Lipschitz nonlinear systems

Multiple sliding mode observers for state and unknown input estimations of a class of MIMO nonlinear systems are systematically developed in this paper. A new nonlinear transformation is formulated to divide the original system into two interconnected subsystems. The unknown inputs are assumed to be bounded and not necessarily Lipschitz, and do not require any matching condition. Under structural assumptions for the unknown input distribution matrix, the sliding mode terms of the nonlinear observer are designed to track their respective unknown inputs. Also, the unknown inputs can be reconstructed from the multiple sliding mode structurally. The conditions for asymptotic stability of estimation error dynamics are derived. Finally, simulation results are given to demonstrate the effectiveness of the proposed method. Copyright © 2011 John Wiley & Sons, Ltd.     

Uniform bounded input bounded output stability of fractional‐order delay nonlinear systems with input

The bounded input bounded output (BIBO) stability for a nonlinear Caputo fractional system with time‐varying bounded delay and nonlinear output is studied. Utilizing the Razumikhin method, Lyapunov functions and appropriate fractional derivatives of Lyapunov functions some new bounded input bounded output stability criteria are derived. Also, explicit and independent on the initial time bounds of the output are provided. Uniform BIBO stability and uniform BIBO stability with input threshold are studied. A numerical simulation is carried out to show the system's dynamic response, and demonstrate the effectiveness of our theoretical results.     

Universal adaptive control of feedforward nonlinear systems with unknown input and state delays

This paper considers the problem of global asymptotic regulation via output feedback for a class of uncertain feedforward nonlinear systems with input and state delays, where the bounds of time delays are unknown. With the help of the high-gain scaling approach and the idea of universal adaptive control, we explicitly construct an adaptive output compensator with a novel positive dynamic gain which compensates simultaneously the unknown delays and the output growth rate with unknown constant. Based on such output compensator, we reduce the conservatism of the restrictive conditions imposed on nonlinearities to generalise the existing results. By the Lyapunov–Krasovskii theorem, a delay-independent controller design scheme is proposed to guarantee that all the closed-loop signals are globally bounded while rendering the states of original system and the estimate states to globally asymptotically converge to zero. Finally, two illustrative examples are given to show the usefulness of the proposed design method.     

带有输入时滞的领导跟随系统扰动抑制一致性

针对一类受到外部干扰且有输入时滞的多智能体系统,讨论了在固定有向拓扑下的领导跟随扰动抑制一致性问题。首先,对于存在外部干扰的多智能体系统,给出分布式状态观测器,使得每个智能体的系统状态和外部干扰被同时估计。其次,基于截取预测方法,利用邻居智能体相对输出信息获得的状态估计和自身干扰估计为每个智能体设计一致性协议。然后,用Lyapunov-Krasovskii理论对系统的观测性和稳定性进行分析,获得满足多智能体系统稳定的充分条件,并将控制器增益和观测器增益求解转化为求解线性矩阵不等式(LMIs)的形式。最后,通过一个仿真例子来验证所得结果的可行性和有效性。     

Delay compensation for linear systems with both state and distinct input delays

This paper is concerned with the stabilization of linear systems with both state and distinct input delays. Nested predictor feedback controllers are designed to predict the future states such that the distinct input delays that can be arbitrarily large yet bounded are compensated completely. It is shown that the compensated closed‐loop system possesses the same characteristic equation as the closed‐loop system without distinct input delays. Both continuous‐time and discrete‐time time‐delay systems are studied in this paper. Moreover, the safe implementation problem for the continuous‐time nested predictor feedback controller is solved via adding input filters. Three numerical examples show the effectiveness of the proposed approaches.     

Fast adaptive fault estimation and accommodation for nonlinear time‐varying delay systems

This paper studies the problem of fault estimation and accommodation for a class of nonlinear time‐varying delay systems using adaptive fault diagnosis observer (AFDO). A novel fast adaptive fault estimation algorithm that does not need the derivative of the output vector is proposed to enhance the performance of fault estimation. Meanwhile, a delay‐dependent criteria is obtained based on free weighting matrix method with the purpose of reducing the conservatism of the AFDO design. On the basis of fault estimation, an observer‐based fault‐tolerant controller is designed to guarantee the stability of the closed‐loop system. In terms of matrix inequality, we derive sufficient conditions for the existence of the adaptive observer and fault‐tolerant controller. Simulation results are presented to illustrate the efficiency of the proposed method. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

输入时滞非线性系统的新型动态面Funnel控制

本文针对一类带有输入时滞的不确定非线性系统, 提出了新型动态面Funnel控制方案. 首先设计补偿动态 变量将输入时滞系统转换成无时滞的系统, 仅需在递归控制的最后一步补偿, 从而优化了控制器设计过程. 其次, 构造Funnel函数, 使系统的瞬态和稳态跟踪误差被限制在给定边界内. 最后, 提出新型非线性动态面控制方法, 不仅 避免了自适应反推控制中的“微分爆炸”问题, 而且消除了边界层误差, 使得系统的跟踪误差最终渐近收敛到零. 理 论分析表明该闭环系统的所有信号一致最终有界, 仿真结果验证了该控制方案的有效性.     

Adaptive neural network tracking control for uncertain nonlinear systems with input delay and saturation

In this article, the adaptive tracking control problem is considered for a class of uncertain nonlinear systems with input delay and saturation. To compensate for the effect of the input delay and saturation, a compensation system is designed. Radial basis function neural networks are directly utilized to approximate the unknown nonlinear functions. With the aid of the backstepping method, novel adaptive neural network tracking controllers are developed, which can guarantee all the signals in the closed‐loop system are semiglobally uniformly ultimately bounded, and the system output can track the desired signal with a small tracking error. In the end, a simulation example is given to illustrate the effectiveness of the proposed methods.     

受饱和输入约束的非线性系统滑模自适应控制

利用神经网络和滑模控制,研究带有饱和输入的一类非线性系统。为了便于问题分析,引入饱和约束模型输出与控制输入的差值这个变量,分5种情况讨论,求得神经网络权值的在线调节律,得到保证闭环系统稳定的控制律。利用Lyapunov函数,证明了闭环系统的稳定性;仿真实验说明了算法的有效性。     

Delay‐range‐dependent control of nonlinear time‐delay systems under input saturation

This paper describes a delay‐range‐dependent local state feedback controller synthesis approach providing estimation of the region of stability for nonlinear time‐delay systems under input saturation. By employing a Lyapunov–Krasovskii functional, properties of nonlinear functions, local sector condition and Jensen's inequality, a sufficient condition is derived for stabilization of nonlinear systems with interval delays varying within a range. Novel solutions to the delay‐range‐dependent and delay‐dependent stabilization problems for linear and nonlinear time‐delay systems, respectively, subject to input saturation are derived as specific scenarios of the proposed control strategy. Also, a delay‐rate‐independent condition for control of nonlinear systems in the presence of input saturation with unknown delay‐derivative bound information is established. And further, a robust state feedback controller synthesis scheme ensuring L₂ gain reduction from disturbance to output is devised to address the problem of the stabilization of input‐constrained nonlinear time‐delay systems with varying interval lags. The proposed design conditions can be solved using linear matrix inequality tools in connection with conventional cone complementary linearization algorithms. Simulation results for an unstable nonlinear time‐delay network and a large‐scale chemical reactor under input saturation and varying interval time‐delays are analyzed to demonstrate the effectiveness of the proposed methodology. Copyright © 2015 John Wiley & Sons, Ltd.     

Reduced‐order observer‐based output‐feedback tracking control of nonlinear systems with state delay and disturbance

In this paper, we investigate the problem of output‐feedback tracking control for a class of nonlinear SISO systems in the strick‐feedback form, which are subject to both uncertain delay‐related functions and disturbances. A reduced‐order observer is first introduced to provide the estimates of the unmeasured states. Then, an output‐feedback controller is recursively designed based on the backsteppng method. By constructing an appropriate Lyapunov–Krasovskii functional, we prove that all the signals in the closed‐loop system are bounded. The tracking performance is guaranteed by suitably choosing the design parameters. Finally, a simulation example is provided to demonstrate the effectiveness of the proposed control algorithm. Copyright © 2009 John Wiley & Sons, Ltd.     

Observer‐predictor feedback for consensus of discrete‐time multiagent systems with both state and input delays

This article is concerned with the consensus problem for discrete‐time multiagent systems with both state and input delays. Single observer‐predictor‐based protocols and multiple observer‐predictors feedback protocols are simultaneously established to predict the future state such that the input delay that can be arbitrarily large yet bounded is completely compensated. It is shown that the consensus of the multiagent system can be achieved by the single/multiple observer‐predictors feedback protocol. Moreover, sufficient conditions guaranteeing the consensus of the multiagent system are provided in terms of the stability of some simple observer‐error systems, and the separation principle is discovered. Finally, a numerical example is worked out to illustrate the effectiveness of the proposed approaches.     

Observers for a class of nonlinear systems with time‐delay

In this paper, the issue of observer designs for a class of nonlinear continuous‐time systems with time‐delay is addressed, where the nonlinear function is not necessarily Lipschitz. It is shown that both full‐order and reduced‐order observers can be obtained by means of the same linear matrix inequality. A numerical example is presented to show the effectiveness of the proposed approach. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society