L∞ Observer for Uncertain Linear Systems

In this paper, an L_∞ observer design method is proposed for linear system subject to parameter uncertainty and bounded disturbance. The proposed L_∞ observer, which satisfies a peak‐to‐peak disturbances attenuation performance, is designed to overbound the estimation error. Moreover, sufficient conditions for the design of L_∞ observer are derived and expressed in terms of linear matrix inequalities (LMIs). The novelty of the proposed method is that we develop an L_∞ observer that not only can attenuate bounded disturbance but also provides an upper bound of estimation error norm. Simulation results are presented to illustrate the effectiveness of the proposed method.     

Robust State‐and‐Disturbance Observer Design for Linear Non‐minimum‐phase Systems

When there are external disturbances acting on the system, the conventional Luenberger observer design for state estimation usually results in a biased state estimate. This paper presents a robust state and disturbance observer design that gives both accurate state and disturbance estimates in the face of large disturbances. The proposed robust observer is structurally different from the conventional one in the sense that a disturbance estimation term is included in the observer equation. With this disturbance estimation term, the robust observer design problem is skillfully transformed into a disturbance rejection control problem. We then can utilize the standard H_∞ control design tools to optimize the robust observer between the disturbance rejection ability and noise immune ability. An important advantage of the proposed robust observer is that it applies to both minimum‐phase systems and non‐minimum phase systems.     

Asynchronous fault detection observer design for discrete‐time piecewise linear systems

This paper studies the problem of asynchronous fault detection (FD) observer design for piecewise linear systems. Considering that the states of the FD observer and the system may stay at different regions of the state space, asynchronous FD observers are designed at different instants to cope with the challenges incurred by exogenous disturbances and fault signals. By employing new piecewise Lyapunov functions that depend on the different regions where the states are located, it is proved that the proposed asynchronous FD observers ensure the stability and H_∞ performance of the error systems. Three examples are given to show that the new design scheme provides better FD results than the existing design methods.     

Sensor fault estimation for Lipschitz nonlinear systems in finite-frequency domain

In this study, the problem of sensor fault estimation observer design for Lipschitz nonlinear systems with finite-frequency specifications is investigated. First, the sensor fault is considered as an auxiliary state vector and an augmented system is established. Then, by transforming the nonlinear error dynamics into a linear parameter varying system, a sufficient condition for the observer-error system with a finite-frequency H_∞ performance is derived in terms of linear matrix inequalities (LMIs). Based on the obtained condition, novel nonlinear observers are designed to simultaneously estimate the system states and the fault signals and attenuate the disturbances in the finite-frequency domain. The proposed design method can provide less restrictive LMI conditions and get a better disturbance-attenuation performance when the frequency ranges of disturbances are known beforehand. A numerical example is given to show the effectiveness and superiority of the new results.     

Robust consensus tracking of double‐integrator dynamics by bounded distributed control

This paper studies the robust consensus tracking problem of multiple second‐order systems with additive disturbances and a direct communication topology. We design a continuous, bounded and distributed controller that is composed of a tracker and an uncertainty and disturbance estimator. The tracker makes the nominal closed‐loop system globally asymptotically stable, while the output of uncertainty and disturbance estimator attenuates the effect of disturbances. We show that if the disturbances converge to constants, the tracking error converges asymptotically to zero, whereas for other types of disturbances, the obtained error system is small‐signal L_∞ stable. Some inequalities are developed to show the relationship between the ultimate bounds of tracking errors and the design parameters. Finally, simulation results for four cases are presented to demonstrate the performance of the controller. Copyright © 2015 John Wiley & Sons, Ltd.     

Composite disturbance‐observer‐based control and H ∞ control for nonlinear time‐delay systems

A novel type of control scheme combined the distance‐observer‐based control (DOBC) with H_∞ control is proposed for a class of nonlinear time‐delay systems subject to disturbances. The disturbances are supposed to include two parts. One in the input channel is generated by an exogenous system with uncertainty, which can represent the harmonic signals with modeling perturbations. The other is supposed to have the bounded H₂ norm. The disturbance observers based on regional pole placement and D‐stability theory are presented, which can be designed separately from the controller design. By integrating disturbance‐observer‐based control with H_∞ control laws, the disturbances can be rejected and attenuated, simultaneously, the desired dynamic performances can be guaranteed for nonlinear time‐delay systems with unknown nonlinear dynamics. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Unknown Input Observer-based Actuator and Sensor Fault Estimation Technique for Uncertain Discrete Time Takagi-Sugeno Systems

This paper presents an Unknown Input robust Observer (UIO) capable of simultaneously estimate both sensor fault and system states. The system is assumed to be discrete-time Takagi-Sugeno (T-S) Fuzzy with uncertainties. An augmented system is obtained from the dynamic fault model and original system. Afterward, a UIO is designed for the augmented system aiming at decoupling process disturbances. Its design is obtained by using an H_∞ optimization technique and developed to maintain the observer stable, reducing the non-decoupled process disturbances effect. The proposed method is validated by two numerical examples as it is compared to a regular UIO technique and the extended Kalman filter. Results show the proposed technique presents better performance when the dynamic system is not purely nonlinear even if the same tuning parameters are chosen. Although other techniques are not able to ensure the error limitation, the proposed one is capable of it even in nonlinear systems.

     

Elegant antidisturbance fault‐tolerant control for stochastic systems with multiple heterogeneous disturbances

In this article, the elegant antidisturbance fault‐tolerant control (EADFTC) problem is studied for a class of stochastic systems in the simultaneous presence of multiple heterogeneous disturbances and time‐varying faults. The multiple heterogeneous disturbances include white noise, norm bounded uncertain disturbances and uncertain modeled disturbances with multiple nonlinearities and unknown amplitudes, frequencies, and phases. The time‐varying fault signals are caused by lose efficacy of actuator. To online estimate uncertain modeled disturbances and time‐varying faults, a novel composite observer structure consisting of the adaptive nonlinear disturbance observer and the fault diagnosis observer is constructed. The novel EADFTC strategy is proposed by integrating composite observer structure with adaptive disturbance observer‐based control theory and H_∞ technology. It is proved that all the signals of closed‐loop system are asymptotically bounded in mean square under the circumstances of multiple heterogeneous disturbances and time‐varying faults occur simultaneously. Finally, the effectiveness and availability of proposed strategy are demonstrated by means of the numerical simulation and a doubly fed induction generators system simulation, respectively.     

Robust H∞ fuzzy observer‐based tracking control design for a class of nonlinear stochastic Markovian jump systems

This paper investigates the stochastic H_∞ tracking control problem for a class of nonlinear stochastic Markovian jump systems. The attention is focused on the design of a fuzzy observer‐based fuzzy controller such that an H_∞ model reference tracking performance is guaranteed for admissible disturbances. A sufficient condition is established to guarantee the existence of the desired robust controller, which is given in terms of a set of coupled matrix inequalities. Moreover, a novel decoupled method is proposed to transform the sufficient condition into some linear matrix inequality (LMI) form such that observer gains and control gains can be simultaneously obtained by solving a set of LMIs. Finally, a simulation example is presented to illustrate the effectiveness of the proposed design method. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Observer‐based H ∞ control on nonhomogeneous Markov jump systems with nonlinear input

This paper considers the problem of observer‐based H _∞ controller design for a class of discrete‐time nonhomogeneous Markov jump systems with nonlinear input. Actuator saturation is considered to be a nonlinear input of such system and the time‐varying transition probability matrix in the system is described as a polytope set. Furthermore, a mode‐dependent and parameter‐dependent Lyapunov function is investigated, and a sufficient condition is derived to design observer‐based controllers such that the resulting error dynamical system is stochastically stable and a prescribed H _∞ performance is achieved. Finally, estimation of attraction domain of such nonhomogeneous Markov jump systems is also made. A simulation example shows the effectiveness of developed techniques. Copyright © 2013 John Wiley & Sons, Ltd.     

Nonlinear H∞ observer design for one‐sided Lipschitz discrete‐time singular systems with time‐varying delay

This paper investigates the H_∞ observer design problem for a class of nonlinear discrete‐time singular systems with time‐varying delays and disturbance inputs. The nonlinear systems can be rectangular and the nonlinearities satisfy the one‐sided Lipschitz condition and quadratically inner‐bounded condition, which are more general than the traditional Lipschitz condition. By appropriately dealing with these two conditions and applying several important inequalities, a linear matrix inequality–based approach for the nonlinear observer design is proposed. The resulting nonlinear H_∞ observer guarantees asymptotic stability of the estimation error dynamics with a prescribed performance γ. The synthesis condition of H_∞ observer design for nonlinear discrete‐time singular systems without time delays is also presented. The design is first addressed for one‐sided Lipschitz discrete‐time singular systems. Finally, two numerical examples are given to show the effectiveness of the present approach.     

H∞ optimal design of robust observer against disturbances

This paper considers the robust observer design problem for linear dynamic systems subject to the interference of external disturbances. For such systems, the state estimate from the conventional Luenberger is normally biased with respect to the true system state. To remedy this situation, this paper proposes a new structure for robust observers. With this new structure, the robust observer design problem is skillfully transformed into the well-known disturbance rejection control problem. The H_∞ optimal control design technique can then be applied to shape the proposed robust observer in the frequency domain. The proposed robust observer is a joint state and disturbance observer, which simultaneously estimates both the system state and unknown disturbances, and can be applied to non-minimum-phase systems.     

LMI optimization approach to robust H∞ observer design and static output feedback stabilization for discrete‐time nonlinear uncertain systems

A new approach for the design of robust H_∞ observers for a class of Lipschitz nonlinear systems with time‐varying uncertainties is proposed based on linear matrix inequalities (LMIs). The admissible Lipschitz constant of the system and the disturbance attenuation level are maximized simultaneously through convex multiobjective optimization. The resulting H_∞ observer guarantees asymptotic stability of the estimation error dynamics and is robust against nonlinear additive uncertainty and time‐varying parametric uncertainties. Explicit norm‐wise and element‐wise bounds on the tolerable nonlinear uncertainty are derived. Also, a new method for the robust output feedback stabilization with H_∞ performance for a class of uncertain nonlinear systems is proposed. Our solution is based on a noniterative LMI optimization and is less restrictive than the existing solutions. The bounds on the nonlinear uncertainty and multiobjective optimization obtained for the observer are also applicable to the proposed static output feedback stabilizing controller. Copyright © 2008 John Wiley & Sons, Ltd.     

Composite anti‐disturbance resilient control for Markovian jump nonlinear systems with partly unknown transition probabilities and multiple disturbances

In this paper, the problem of composite anti‐disturbance resilient control is studied for Markovian jump nonlinear systems with partly unknown transition probabilities and multiple disturbances. The multiple disturbances include two types: one is in the input channel generated by an exogenous system with perturbations, and the other is belong to L ₂[0,∞ ). The first class of disturbances is estimated by designing a disturbance observer. Combining the disturbance estimation with conventional L ₂ ? L _∞ resilient control law, a composite anti‐disturbance control scheme is constructed such that the closed‐loop system is stochastically stable, and different types of disturbances can be attenuated and rejected. By using Lyapunov function method and linear matrix inequalities technique, some sufficient conditions for the desired controller and observer gains are developed. Finally, an application example is provided to demonstrate the effectiveness of the proposed method. Copyright © 2016 John Wiley & Sons, Ltd.     

Anti-disturbance control for time-varying delay Markovian jump nonlinear systems with multiple disturbances

In this paper, the problem of composite anti-disturbance resilient control is addressed for time-varying delay Markovian jump nonlinear systems with multiple disturbances. The disturbances are assumed to include two parts: the first one in the input channel is described by an external system with perturbations; the second one is supposed to be bounded H₂ norm. By combining disturbance observer and L₂–L_∞ control method, the disturbances are attenuated and rejected, simultaneously, and the desired dynamic performance can be obtained for time-varying delay Markovian jump nonlinear systems. Moreover, the gains of the resilient controller and the observer are acquired by applying linear matrix inequalities (LMIs) technology. Finally, an application example is presented to show the effectiveness of the proposed approach.     

ℋ︁∞ sliding mode observers for uncertain nonlinear Lipschitz systems with fault estimation synthesis

This paper presents a scheme to design robust sliding mode observers(SMO) with ??_∞ performance for uncertain nonlinear Lipschitz systems where both faults and disturbances are considered. We study the necessary conditions to achieve insensitivity of the proposed sliding mode observer to the unknown input(fault). The objective is to derive a sufficient condition using linear matrix inequality(LMI) optimization for minimizing the ??_∞ gain between the estimation error and disturbances, while at the same time the design method guarantees that the solution of the LMI optimization satisfies the so‐called structural matching condition. The sliding motion affects only a part of the system through a novel reduced‐order sliding mode controller. Furthermore, the so‐called equivalent control concept is discussed for fault estimation. Finally, a numerical example of MCK chaos demonstrates the high performance of the results compared with a pure SMO. Copyright © 2010 John Wiley & Sons, Ltd.     

H−/L∞ fault detection observer for linear parameter‐varying systems with parametric uncertainty

This paper considers H_?/L_∞ fault detection for discrete‐time linear parameter‐varying (LPV) systems with parametric uncertainty. In H_?/L_∞ fault detection scheme, residual generation and threshold computation are simultaneously designed. With consideration of H_?/L_∞ performance indices, the generated residual is sensitive to faults while robust against unknown disturbances. Furthermore, the L_∞ performance provides a time‐varying threshold for residual evaluation. This paper proposes a novel H_?/L_∞ fault detection observer design method to handle actuator fault detection for LPV systems with parametric uncertainty. Sufficient conditions of the fault detection observer design in the finite‐frequency domain are derived as linear matrix inequalities. Numerical simulations are used to illustrate the effectiveness and superiority of the proposed fault detection observer design approach.     

Fault detection problem for discrete-time impulsive system using mixed dissipativity approach

This article studies the fault detection problem for a class of discrete-time impulsive systems using mixed dissipativity theory. First, under the impulsive effects, a fault diagnosis observer is designed such that it is insensitive to disturbances, and sensitive to faults. Then, a mixed dissipativity concept is introduced to deal with impulsive effects, disturbances insensitivity condition and faults sensitive condition in one framework such that the impulsive error dynamic is dissipative with respect to the proposed mixed supply rate. Based on the proposed mixed supply rate, sufficient conditions are obtained to guarantee the dissipativity of the impulsive estimation error dynamic. Moreover, sufficient conditions are established for the existence of the desired fault observer. The corresponding solubility conditions for the designs of the desired observer are also obtained. Finally, simulation results are proposed to demonstrate the effectiveness of our proposed strategy.