Interval observers for linear functions of state vectors of linear fractional‐order systems with delayed input and delayed output

This paper addresses the problem of interval observer design for linear functions of state vectors of linear fractional‐order systems, which are subjected to time delays in the measured output as well as the control input. By using the information of both the delayed output and input, we design two linear functional state observers to compute two estimates, an upper one and a lower one, which bound the unmeasured linear functions of state vectors. As a particular case with output delay only, we design a linear functional state observer to estimate (asymptotically) the unmeasured linear functions of state vectors. Existence conditions of such observers are provided, and some of them are translated into a linear programming problem, in which the observers' matrices can be effectively computed. Constructive design algorithms are introduced. Numerical examples are provided to illustrate the design procedure, practicality, and effectiveness of the proposed design method.     

Adaptive observers for a class of multi-output non-linear systems

Sufficient differential geometric conditions are given for the existence of global adaptive observers for a class of multi-output non-linear systems which are linear with respect to a vector of unknown constant parameters. They extend to multi-output systems earlier results on adaptive observers for single-output systems; they also extend to systems with unknown parameters results obtained previously on the existence of non-adaptive observers with linear error dynamics.     

Design of unknown‐input reduced‐order observers for a class of nonlinear fractional‐order time‐delay systems

This paper considers the design of reduced‐order state observers for fractional‐order time‐delay systems with Lipschitz nonlinearities and unknown inputs. By using the Razumikhin stability theorem and a recent result on the Caputo fractional derivative of a quadratic function, a sufficient condition for the asymptotic stability of the observer error dynamic system is presented. The stability condition is obtained in terms of linear matrix inequalities, which can be effectively solved by using existing convex algorithms. Numerical examples and simulation results are given to illustrate the effectiveness of the proposed design approach.     

Observers for a Class of Chaotic Systems

The design of observers for a class of practical physical chaotic systems is discussed. By using only one state variable and its time derivatives, a control law is constructed to achieve the synchronization between the investigated chaotic systems and their observers, and the results are proved theoretically. Several observers of chaotic systems are designed by using this method. Translated from “Observers for a Class of Chaotic Systems” published in Journal of Southwest China Normal University (Natural Science), 2004, 29(1): 53–57 (in Chinese)     

Decentralized bounded input bounded output stabilization of perturbed interconnected time-delay power systems with energy storages

This paper presents a new decentralized bounded input bounded output (BIBO) stabilization problem for a class of interconnected time-delay systems and its application to power systems with energy storages. We first provide conditions for the derivation of an ellipsoid that bounds a given linear functions of the state vector. Then, a design procedure is proposed to synthesize decentralized static output feedback controllers. The designed controllers guarantee that a given linear functions of the state vector, starting from any initial condition, converges exponentially to its prescribed zones. To deal with the time-delay issue, we use an improved weighted integral inequality recently reported in the literature to derive less conservative exponential stability conditions. Then, our presented control approach is applied to an interconnected power system integrated energy storages with multiple time delays. We synthesis decentralized static output feedback load frequency controllers to guarantee that the system frequency and interchanged power converge to their prescribed zones exponentially from any initial conditions. The controller’s construction is simpler and easier for implementation due to only the local output measurements are required. In order to systematically obtain the controller gains, an effective procedure using linear matrix inequality based stabilisation criteria, which can be solved by various computation tools, is provided. Finally, the effectiveness of the proposed control scheme is verified by comprehensive simulations.     

Neural observer-based small fault detection and isolation for uncertain nonlinear systems

Small faults (some weak faults with a tiny magnitude) are difficult to detect and may cause severe problems leading to degrading the system performance. This paper proposes an approach to estimate, detect, and isolate small faults in uncertain nonlinear systems subjected to model uncertainties, disturbances, and measurement noise. A robust observer is developed to alleviate the lack of full state measurement. Using the estimated state, a dynamical radial basis function neural networks observer is designed in form of LMI problem to accurately learn the function of the inseparable mixture between modeling uncertainty and the small fault. By exploiting the knowledge obtained by the learning phase, a bank of observers is constructed for both normal and fault modes. A set of residues is achieved by filtering the differences between the outputs of the bank of observers and the monitored system output. Due to the noise dampening characteristics of the filters and according to the smallest residual principle, the small faults can be detected and isolated successfully. Finally, rigorous analysis is performed to characterize the detection and isolation capabilities of the proposed scheme. Simulation results are used to prove the efficacy and merits of the proposed approach.     

Luenberger-type cubic observers for state estimation of linear systems

This article introduces a new nonlinear observer for state estimation of linear time invariant systems. The proposed observer contains a (nonlinear) cubic term to enhance observer response. Unlike previously proposed observers, the cubic observer has nonlinear estimation error dynamics. Convergence criteria, performance advantages, and observer-based feedback control with cubic observers are addressed. Simulation examples demonstrating performance improvement compared with linear observers, are included.     

具滞后的离散广义系统的无源控制

将无源的概念引入到滞后离散广义系统中，进而研究具滞后的离散广义系统在有界能量外部输入作用下的无源控制问题．基于广义Lyapunov函数，利用线性矩阵不等式和广义代数Riccati不等式，首先给出具滞后的离散广义系统E-渐近稳定且具有无源性的充分条件，然后在此基础上，得到存在状态反馈控制器，使得闭环系统E-渐近稳定且具有无源性的充分条件，并且由矩阵不等式的解给出相应的控制器构造方法。最后的数值算例说明了文中结论的有效性。     

一类具有高增益观测器的非线性系统的输出调节

针对具有由非线性外部系统产生的未知不确定性函数和未建模动态的非线性不确定系统,研究了其跟踪和干扰抑制问题。首先运用状态变换将输出调节问题转化为非线性系统的镇定问题,接着引入动态信号解决了动态扰动,并设计出高增益的状态观测器去估计不可测的状态。然后根据外系统信息设计自适应的非线性内模,结合自适应控制理论、Backstepping设计方法、模糊控制方法和Lyapunov法给出了输出反馈的自适应模糊控制器和自适应控制律,所提出的输出反馈控制器和自适应律能够实现整个闭环系统的跟踪和干扰抑制,并使得跟踪误差能渐近收敛到给定的任意小的领域内。最后仿真结果验证了所提出的控制器的有效性。     

Lipschitz非线性系统观测器设计

运用微分方程方法,讨论了一类满足Ｌｉｐｓｃｈｉｔｚ条件的非线性系统观测器的设计,结论表明,稳定观测器的存在不仅与系统矩阵的特征值有关,而且与矩阵对距离不可观测性的大小有关,给出代数设计方法以条件数量小为目标准则,根据梯度下降法原理,用ＭＡＴＬＡＢ写代码,设计者只须提供初值,程序即自动完成观测器设计,文末咄了释例。     

具有传输通道时间延迟的一类混沌系统脉冲控制同步

针对一类混沌系统同步控制问题,利用脉冲微分方程的稳定理论,研究了传榆信号具有时间延迟的混沌系统脉冲同步问题,给出了两个混沌系统实现全局渐进同步的判据方法。该方法仅采用具有时间延迟的驱动系统与响应系统输出偏差的线性反馈作为脉冲控制信号,驱动两个混沌系统达到全局渐进同步,且适用于绝大多数混沌系统的同步控制。所设计的控制器结构简单,收敛速度快,易于实现。Roessler混沌系统的仿真实验进一步验证了该方法的有效性和可行性。     

A synthesized design of sliding‐mode and Luenberger observers for early detection of incipient faults

In this paper, a new design of sliding mode observers (SMOs) for the purpose of early detection of incipient faults is presented. This work is motivated by the fact that the strong robustness of the conventional SMO to bounded disturbances inevitably makes it insensitive to incipient faults when they are small in size during the initial phase; as a result, the fault‐detection residual generated through the SMO is not sensitive to incipient faults for a certain length of time until they have become severe. On the contrary, the new design proposed in this paper ensures that the overall system is sensitive to incipient faults while remaining robust to disturbances. The design presented in this paper is based on the transformation of the system into two subsystems. One of these subsystems is free from disturbances and/or modeling errors: for this subsystem, a Luenberger observer is constructed; the other subsystem is subject to disturbances: an SMO is designed for this subsystem so that the effect of the disturbances is eliminated. Together, the entire system achieves both robustness to disturbances and sensitivity to incipient faults. Stability and convergence of the proposed SMO and Lueneberger observer are proved, and an aircraft example is employed to demonstrate the effectiveness of the proposed design approach. Copyright © 2010 John Wiley & Sons, Ltd.     

Adaptive observer design for uncertain nonlinear ODE-PDE cascades

We are revisiting the problem of adaptive observer design for systems that are constituted of an Ordinary Differential Equation (ODE), containing a globally Lipschitz function of the state, and a linear Partial Differential Equation (PDE) of a diffusion–reaction heat type. The ODE and PDE are connected in series and both are subject to parametric uncertainties. In addition to nonlinearity and uncertainty, the system complexity also lies in the fact that no sensor can be implemented at the junction point between the ODE and the PDE. In the absence of parameter uncertainty, nonadaptive state observers are available featuring exponential convergence. However, convergence is guaranteed only under the condition that either the Lipschitz coefficient is sufficiently small or the PDE domain length is sufficiently small. To get around this limitation, and also to account for parameter uncertainty, we develop a design that involves two concatenated adaptive observers, covering the two subintervals of the PDE domain. The proposed design employs one extra sensor, providing the measurement of the PDE state at an inner position close to the ODE-PDE junction point. Both observers are shown to be exponentially convergent, under ad-hoc persistent excitation (PE) conditions, with no limitation on the Lipschitz coefficient and domain length.     

State estimation of system with bounded uncertain parameters: Interval multimodel approach

The objective of this study is the analysis of dynamic systems represented by a multimodel expression with variable parameters. Changes in these parameters are unknown but bounded. Since it is not possible to estimate these parameters over time, the simulation of such systems requires the consideration of all possible values taken by these parameters. More precisely, the goal is to determine, at any moment, the smallest set containing all the possible values of the state vector simultaneously compatible with the state equations and with a priori known bounds of the uncertain parameters. This set will be characterized by two trajectories corresponding to the lower and upper limits of the state at every moment. This characterization can be realized by a direct simulation of the system, given the bounds of its parameters. It can also be implemented with a Luenberger‐type observer, fed with the system measurements.     

Hybrid adaptive observers for locally Lipschitz systems

An adaptive observer design approach is proposed for the class of nonlinear locally Lipschitz systems. The case of disturbances affecting the state equations is considered. The proposed solution is applicable to the systems with bounded solutions and hyperminimum phase linear part. It is based on the logic‐based control approach. Efficiency of the proposed observer design is demonstrated through computer simulations for Duffing and satellite system. Copyright © 2010 John Wiley & Sons, Ltd.     

Adaptive observer for a class of nonlinear systems with time‐varying delays

The adaptive observer design problems have been extensively studied in literature for both linear and nonlinear systems. Some researches have also been carried out on adaptive observer design for linear time‐delay systems, but there is no significant work on adaptive observer design for nonlinear time‐delay systems. In this work, the adaptive observer design problem for a class of nonlinear time‐delay systems is considered. The observer is designed for the nonlinear systems whose nonlinear functions satisfy Lipschitz condition. Like conventional adaptive observers for the systems without time delays, this observer also estimates both states and unknown parameters simultaneously. For this property, it will be very much useful for many real‐time systems where time delays cannot be avoided. The sufficient conditions for existence of the observer are derived using the linear matrix inequality approach. With the help of a numerical example, effectiveness of the proposed observer is demonstrated. Copyright © 2012 John Wiley & Sons, Ltd.     

Decentralized stabilization of large‐scale systems with interval time‐varying delays in interconnections

This paper considers decentralized stabilization problem for a class of large‐scale systems with interval time‐varying delays in interconnections. The time delay is assumed to be a continuous function belonging to a given interval but not necessary to be differentiable. On the basis of constructing a set of improved Lyapunov–Krasovskii functionals, new sufficient conditions for the existence of decentralized state feedback controller are established in terms of linear matrix inequalities. The decentralized control design guarantees the system exponential stability. An illustrative example is given to show the validity of the results obtained in this paper. Copyright © 2012 John Wiley & Sons, Ltd.     

Separable multi-innovation stochastic gradient estimation algorithm for the nonlinear dynamic responses of systems

This article is concerned with the parameter identification problem of nonlinear dynamic responses for the linear time-invariant system by means of an impulse excitation signal and discrete observation data. Using the impulse signal as the input, the impulse response experiment is carried out and the dynamical moving sampling is designed to generate the measured data for deriving new identification algorithms. By applying the moving window data that contain the dynamical information of the system to be identified, an objective function with respect to the parameters of the systems is constructed according to the impulse response. In accordance with different functional relations between the system parameters and the system output response, the unknown parameter vector of the system is separated into a linear parameter vector and a nonlinear parameter vector. Based on the separated parameter vectors, two subidentification models are constructed and a separable identification algorithm is presented through the gradient search to improve the accuracy. Moreover, for the purpose of enhancing the estimation accuracy and capturing the dynamical feature of the systems, the moving window data are employed to develop the separable identification algorithm. The performance of the proposed separable identification method is illustrated via a numerical example.     

Compound conditions event-triggered tracking control for nonlinear multiagent systems with nonlinear output faults

This article is devoted to investigating the compound conditions event-triggered prescribed performance tracking problem for strict-feedback nonlinear multiagent systems with nonlinear output faults and unknown disturbances. A simplified event-triggered sampling condition is designed to successfully reduce the number of state triggered design parameters. Besides, a compound conditions event-triggered mechanism is constructed, which integrates state triggered and controller triggered simultaneously to reduce communication burden. Furthermore, by using disturbance observers and prescribed performance functions, unknown external disturbances are compensated and the tracking errors can converge into the prescribed boundary, respectively. Moreover, all the signals of the closed-loop system are semiglobally uniformly ultimately bounded. Finally, the availability of the proposed control strategy is testified via simulation results.