Nonlinear observer design for state and disturbance estimation

A new systematic framework for nonlinear observer design that allows the concurrent estimation of the process state variables together with key unknown process or sensor disturbances is proposed. The nonlinear observer design problem is addressed within a similar methodological framework as the one introduced in [N. Kazantzis, C. Kravaris, Nonlinear observer design using Lyapunov's auxiliary theorem, Systems Control Lett. 34 (1998) 241; A.J. Krener, M. Xiao, Nonlinear observer design in the Siegel domain, SIAM J. Control Optim. 41 (2002) 932.] for state estimation purposes only. From a mathematical standpoint, the problem under consideration is addressed through a system of first-order singular PDEs for which a rather general set of solvability conditions is derived. A nonlinear observer is then designed with a state-dependent gain that is computed from the solution of the system of singular PDEs. Under the aforementioned conditions, both state and disturbance estimation errors converge to zero with assignable rates. The convergence properties of the proposed nonlinear observer are tested through simulation studies in an illustrative example involving a biological reactor.     

Decentralized state observer scheme for uncertain time-delay T-S fuzzy interconnected systems

This paper focuses on a class of T-S fuzzy interconnected systems with time delays and time-varying parameter uncertainties. Observer-based output feedback decentralized controller is designed such that the closed-loop interconnected system is asymptotically stable in the Lyapunov sense in probability for all admissible uncertainties and time delays. Sufficient conditions for robustly asymptotically stability of the systems are given in terms of a set of linear matrix inequalities （LMIs）.     

Decentralized state observer scheme for uncertain time-delay T-S fuzzy interconnected systems

This paper focuses on a class of T-S fuzzy interconnected systems with time delays and time-varying parameter uncertainties. Observer-based output feedback decentralized controller is designed such that the closed-loop interconnected system is asymptotically stable in the Lyapunov sense in probability for all admissible uncertainties and time delays. Sufficient conditions for robustly asymptotically stability of the systems are given in terms of a set of linear matrix inequalities(LMIs).     

Fault estimation for T-S fuzzy Markovian jumping systems based on the adaptive observer

The adaptive fault estimation problem is studied for a class of stochastic Markovian jumping systems (MJSs) with time delays and nonlinear parameters. By means of Takagi-Sugeno fuzzy models, the dynamics of observer error generator and the fuzzy error dynamical system are constructed. Based on the selected Lyapunov-Krasovskii functional framework, the adaptive fault estimation algorithm is proposed to enhance the rapidity and accuracy performance of fault estimation. In terms of linear matrix inequalities techniques, a sufficient condition on the existence of the adaptive observer is presented and proved. Moreover, the presented results are also extended to multiple time-delayed nonlinear MJSs. A numerical example is given at last to illustrate the effectiveness of the proposed approach.     

Multi-constrained fault estimation observer design with finite frequency specifications for continuous-time systems

The design of a multi-constrained full-order fault estimation observer (FFEO) with finite frequency specifications is studied for continuous-time systems. By constructing an augmented system, a multi-constrained FFEO in finite frequency domain is proposed to achieve fault estimation. Meanwhile, the presented FFEO can avoid the overdesign problem generated by the entire frequency domain by the generalised Kalman–Yakubovich–Popov lemma. Furthermore, by introducing slack variables, improved results on FFEO design in different frequency domains are obtained such that different Lyapunov matrices can be separately designed for each constraint. Simulation results are presented to demonstrate the effectiveness and potentials of the proposed techniques.     

Adjustable parameter-based multi-objective fault estimation observer design for continuous-time/discrete-time dynamic systems

This paper addresses an adjustable parameter (AP)-based multi-objective fault estimation design for continuous-time/discrete-time dynamic systems. First, a fault estimation observer with AP is constructed to on-line identify the size of occurred faults. The fault estimation design not only possesses a wider application compared with adaptive observers, but also uses the current output information to enhance fault estimation performance. Then a multi-objective approach is proposed to determine the gain matrices of fault estimation observer. Moreover, fault estimation results with the slack-variable technique are obtained to further reduce the conservatism. Finally, simulation results of an aircraft application are presented to illustrate the effectiveness of our contribution.     

An uncertainty-based approach to discrete-time fault estimation observer design for nonuniformly sampled systems

This paper considers the fault estimation problem of nonuniformly sampled system in which sensor sampling is performed at aperiodic interval. After being discretized at sampling instant, the nonuniformly sampled system is modeled as an equivalent polytopic system with norm bounded uncertainties. A discrete-time time-varying fault estimation observer with multiple design freedom is then constructed, and a sufficient condition given in linear matrix inequality (LMI) is provided to obtain the constant filter gain and ensure not only the asymptotic stability of fault estimation error but also the robustness of uncertainties. Compared with the existing observer designed based on continuous-time delay approach, the proposed one has a better estimation accuracy and less conservatism and is easy for digital implementation. A numerical simulation and a quadruple-tank benchmark are used to demonstrate the effectiveness and superiority of the proposed method.     

Adaptive observer design for robust fault estimation

In this article, fault diagnosis for a class of linear systems based on adaptive observer is investigated. Linear systems without model uncertainty are first considered, and two adaptive observers are designed for fault identification. The first one uses optimal design for minimizing the estimation error. The second one can achieve asymptotic fault estimation. The general situation where the system is subjected to either model errors or external disturbance is then discussed. Robust adaptive control techniques are applied to guarantee the convergence to a bounded set. Simulation of sensor fault diagnosis for an induction motor is presented to verify the effectiveness of the proposed method.     

Generalized set‐theoretic unknown input observer for LPV systems with application to state estimation and robust fault detection

This paper proposes to design an unknown input observer (UIO) for the linear‐parameter‐varying (LPV) system on the basis of the set theory, which is named as the set‐theoretic UIO (SUIO). The advantage of the SUIO consists in that it combines active and passive approaches to obtain robustness in state estimation (SE) and fault detection (FD). The active approach is based on the use of UIO to decouple unknown inputs, while the passive approach is based on the set theory to bound uncertain factors that cannot be actively decoupled. As a result, the effect of both unknown inputs (process disturbances, modeling errors, etc.) and measurement noises can be appropriately handled in the residual signals compared with the standard UIO‐based SE and FD approaches. The design of SUIO can overcome the limitations of the traditional UIO design conditions, which can significantly broaden the application of the UIO‐based SE and FD theory. Moreover, this paper proposes a generalized framework that can provide more flexibility in the design of SUIO guaranteeing their stability by means of a group of matrix inequalities. Because the LPV system uses a collection of online obtainable scheduling variables to embed nonlinearities, the design of SUIO for the LPV system can be used to address the SE and FD problems of nonlinear systems. At the end of this paper, two case studies are used to illustrate the effectiveness of the proposed approach. Copyright © 2017 John Wiley & Sons, Ltd.     

Unknown disturbance inputs estimation based on a state functional observer design

We consider the problem of function of state plus unknown input estimation of a linear time-invariant system using only the measured outputs. Two reduced-order input estimators built upon a state functional observer are proposed. The first is an extension of a state/input estimator, while the second is based on adaptive observer design technique. The proposed estimator can be designed under less restrictive conditions than those of the previous work, and unlike some of the past studies the proposed observer can be designed for certain nonminimum phase systems.     

Robust fast adaptive fault estimation and tolerant control for T-S fuzzy systems with interval time-varying delay

This paper studies the problem of fault estimation (FE) and the active fault tolerant control (FTC) for Takagi–Sugeno (T-S) fuzzy systems with interval time-varying delay and norm-bounded external disturbance. Based on the fast adaptive fault estimation (FAFE) algorithm, our attention focuses on designing an adaptive observer-based controller to guarantee the filtering error system to be asymptotically stable and satisfy theH_∞ performance index. By constructing a new Lyapunov–Krasovskii functional including the information of the lower and upper delay bounds, the sufficient delay-dependent conditions have been established to guarantee the existence of adaptive observer-based controller in terms of linear matrix inequalities (LMIs). Compared with the constant delay and time-varying delay, the interval time-varying delay is the less conservative form. Furthermore, we make full use of the information of the delay and no terms are ignored when the stability of the system is analysed. In addition, the results for the systems with time-varying structured uncertainties are established. The results of the active FTC are showed in terms of LMIs. Finally, two examples are given to verify the effectiveness of the proposed method.     

Dissipativity-based robust reduced-order fault estimation observer design of multi-agent systems

In this paper, a distributed reduced-order fault estimation observer is studied for both continuous- and discrete-time multi-agent systems with directed communication topologies. Initially, a distributed reduced-order observer is proposed to estimate the occurred faults, which can reduce the number of the fault estimation observer’s order of multi-agent systems. What is more, based on strict dissipativity and pole placement constrains, a multi-constrained design is given to calculate gain matrices of distributed reduced-order observer. Finally, simulation results are presented to demonstrate the effectiveness of the proposed distributed reduced-order fault estimation technique.     

Event-triggered state estimation for T-S fuzzy affine systems based on piecewise Lyapunov-Krasovskii functionals

This paper investigates the problem of event-triggered ${\rm H}_\infty$ state estimation for Takagi-Sugeno (T-S) fuzzy affine systems. The objective is to design an event-triggered scheme and an observer such that the resulting estimation error system is asymptotically stable with a prescribed ${\rm H}_{\infty}$ performance and at the same time unnecessary output measurement transmission can be reduced. First, an event-triggered scheme is proposed to determine whether the sampled measurements should be transmitted or not. The output measurements, which trigger the condition, are supposed to suffer a network-induced time-varying and bounded delay before arriving at the observer. Then, by adopting the input delay method, the estimation error system can be reformulated as a piecewise delay system. Based on the piecewise Lyapunov-Krasovskii functional and the Finsler''s lemma, the event-triggered ${\rm H}_{\infty}$ observer design method is developed. Moreover, an algorithm is proposed to co-design the observer gains and the event-triggering parameters to guarantee that the estimation error system is asymptotically stable with a given disturbance attenuation level and the signal transmission rate is reduced as much as possible. Simulation studies are given to show the effectiveness of the proposed method.     

一类互联非线性系统的分布式故障估计观测器设计

针对一类互联非线性系统,提出一种分布式故障估计观测器设计方法.首先,将状态向量和故障向量进行增广设计,得出等价的增广互联系统;其次,利用互联子系统之间的耦合信息,设计包含关联子系统估计信息的分布式故障估计观测器,用于在线实时估计子系统中出现的故障;再次,提出基于$H_\infty$性能和$L_2-L_\infty$性能的方法求解观测器增益矩阵;最后,通过一个仿真实验表明所提出方法的可行性和有效性.     

A fuzzy disturbance observer and its application to control

In this paper, a fuzzy disturbance observer (FDO) is developed and its application to the control of a nonlinear system under the internal and external disturbances is presented. To construct the FDO, two parameter tuning methods are proposed and shown to be useful in adjusting the parameters of the FDO. The first tuning method employs the disturbance observation error to guarantee that the FDO monitors the unknown disturbance. The next one enlarges the concept of error and introduces augmented error to guarantee that the FDO monitors the disturbance and the control objective is achieved. In addition, the relationships between the suggested FDO-based control and the conventional adaptive fuzzy controls reported in the previous literatures are discussed and it is shown in a rigorous manner that the disturbance observation error or the augmented error converges to a region of which size can be kept arbitrarily small. Finally, some examples and computer simulation results are presented to illustrate the effectiveness and the applicability of the FDO     

Fuzzy observer design using linear matrix inequalities for fuzzy closed-loop control systems

Linear observers play an important role in modern control theory and practice. A systematic design method of fuzzy observers would be important for fuzzy control as well. The fuzzy observer is designed by solving linear matrix inequalities (LMI) that represent control performance such as disturbance rejection and robust stability. Our approach in designing the fuzzy observer is based on the LMI formulation of the stability conditions for closed-loop Takagi-Sugeno (T-S) fuzzy systems, when states are not available for measurement of feedback. We present a new approach, which is to design an observer based on fuzzy implications, with fuzzy sets in the antecedents, and an asymptotic observer in the consequents. Each fuzzy rule is responsible for observing the states of a locally linear subsystem. An example illustrates the design procedure.     

模糊系统H∞控制器设计的LMI方法

应用LMI(线性矩阵不等式)方法,研究了T-S模糊系统H_∞控制器的设计问题.首先给出了T-S模糊系统基于状态反馈H_∞控制存在的两个新的充分条件.新条件不但简洁而且把模糊子系统间的相互作用表示为由子系统的系数矩阵构成的矩阵不等式.然后新条件被转化为可直接应用Matlab求解的线性矩阵不等式.最后应用线性矩阵不等式方法和Matlab,给出了T-S模糊系统H_∞控制器的设计方法.     

约束T-S模糊系统设计的模糊Lyapunov方法

通过引入模糊Lyapunov函数,研究一类执行器饱和的离散T-S模糊系统.对系统设计模糊抗积分饱和补偿器,得到系统稳定的充分条件,并扩大了系统的吸引域.这种方法避免了寻求一个满足系统所有模糊规则的公共正定矩阵P.最后,抗积分饱和补偿器增益通过迭代优化算法得到.