Asynchronous Observer Design for Switched Linear Systems: A Tube-Based Approach

This paper proposes a tube-based method for the asynchronous observation problem of discrete-time switched linear systems in the presence of amplitude-bounded disturbances.Sufficient stability conditions of the nominal observer error system under mode-dependent persistent dwell-time(MPDT)switching are first established. Taking the disturbances into account, a novel asynchronous MPDT robust positive invariant(RPI) set and an asynchronous MPDT generalized RPI(GRPI)set are determined for the difference system between the nominal and disturbed observer error systems. Further, the global uniform asymptotical stability of the observer error system is established in the sense of converging to the asynchronous MPDT GRPI set, i.e., the cross section of the tube of the observer error system. Finally, the proposed results are validated on a space robot manipulator example.

Sensor Fault Diagnosis Observer Design for Linear Sampled-Data Descriptor System with Time-Vary Delay

In this paper, a robust sensor fault diagnosis observer with non-singular structure is proposed for a class of linear sampled-data descriptor system with state time-vary delay. Firstly, a sampled-data descriptor model with time-vary delay is proposed and transformed into a discrete-time non-singular one. Then, a robust sensor fault diagnosis observer is proposed based on the state estimation error and the measurement residual, this observer can guarantee the robustness of the residual against the augmented disturbance and the sensor fault, which means the H∞ performance index is satisfied. As the confining matrix of the designed observer parameters does not meet the Linear Matrix Inequality (LMI), a cone complementary linearization (CCL) algorithm is proposed to solve this problem. The decision logic of the residual is obtained by the residual evaluation function. Simulation results show the effectiveness of the method.

A novel observer design method for neural mass models

Neural mass models can simulate the generation of electroencephalography（EEG） signals with different rhythms,and therefore the observation of the states of these models plays a significant role in brain research. The structure of neural mass models is special in that they can be expressed as Lurie systems. The developed techniques in Lurie system theory are applicable to these models. We here provide a new observer design method for neural mass models by transforming these models and the corresponding error systems into nonlinear systems with Lurie form. The purpose is to establish appropriate conditions which ensure the convergence of the estimation error. The effectiveness of the proposed method is illustrated by numerical simulations.

Observer design and interval estimation of time-delay discrete-time linear systems with external disturbance and measurement noise

For a class of time-delay discrete-time linear systems with external disturbance and measurement noise, the interval estimation problems of state and measurement noise are investigated in this paper. First, the system state together with the time-delay term and measurement noise is augmented as a new state, and a singular system is then constructed. Subsequently, a kind of decoupling technique is employed to eliminate the effect of external disturbance, and an observer is designed to simultaneously estimate the system state and measurement noise. Based on the estimated state and measurement noise, the interval estimations of system state and measurement noise are obtained by reachability analysis technique. Finally, the effectiveness of the proposed method is verified by a four-tank liquid level system.

Non-fragile Observer Design for Fractional-order One-sided Lipschitz Nonlinear Systems

This paper is concerned with the problem of the full-order observer design for a class of fractional-order Lipschitz nonlinear systems. By introducing a continuous frequency distributed equivalent model and using an indirect Lyapunov approach, the sufficient condition for asymptotic stability of the full-order observer error dynamic system is presented. The stability condition is obtained in terms of LMI, which is less conservative than the existing one. A numerical example demonstrates the validity of this approach.

Controller-based observer design for distributed consensus of multi-agent systems with fault and delay

The object of this article is to study the consequences of occurrence both fault in input and multiple time-varying delays simultaneously while designing observer to estimate the states of agents and also unknown nonlinear fault of system.Two delay dependent criteria are established to show the states of observer reach to states of MAS and also states of observer reach to consensus.From two obtained criteria,it can be deduced,by constructing a distributed controller-based observer design,MAS reach to consensus exponentially.Finally,the advantages of the obtained results are shown by solving an illustrative example.

Robust Observer Design of Nonlinear Systems

A design method of robust observer is proposed for a class of nonlinear systems.The advantages of the designed observer,such as simpler design process, strong robustness and wider scope or application,are indicated.Finally,some examples are given to show the efectiveness of the design method.

Observer Design —— A Survey

This paper surveys the results of observer design for linear time-invariant(L-T-I) deterministic irreducible open-loop systems(OLS), the most basic type of OLS. An observer estimates Kxx(t) signal where K is a constant and x(t) is the state vector of the OLS. Thus, an observer can be used as a feedback controller that implements state feedback control(SFC) or Kxx(t)-control,and observer design is therefore utterly important in all feedback control designs of state space theory. In this survey, the observer design results are divided into three categories and for three respective main purposes. The first category of observers estimate signal Kxx(t) only with a given K, and this survey has four conclusions: 1) Function observer that estimates Kxx(t) directly is more general than state observer that estimates x(t), and may be designed with order lower than that of state observer, and the additional design objective is to minimize observer order; 2) The function observer design problem has already been simplified to the solving of a single set of linear equations only while seeking the lowest possible number of rows of the solution matrix, and an apparently most effective and general algorithm of solving such a problem can guarantee unified upper and lower bounds of the observer order; 3) Because such a single set of linear equations is the simplest possible theoretical formulation of the design problem and such theoretical observer order bounds are the lowest possible, and because the general, simple, and explicit theoretical formula for the function observer order itself do not exist, the theoretical part of this design problem is solved; 4) Because the function observer order is generically near its upper bound, further improvement on the computational design algorithm so that the corresponding observer order can be further reduced,is generically not worthwhile. The second category of observers further realize the loop transfer function and robustness properties of the direct SFC, and the conclusion of this survey is also fourfold: 1) To fully realize the loop transfer function of a practically designed Kxx(t)-control, the observer must be an output feedback controller(OFC) which has zero gain to OLS input; 2) If parameter K is separately designed before the observer design, as in the separation principle which has been followed by almost all people for over half of a century, then OFC that estimates Kxx(t) does not exist for almost all OLS s; 3) As a result, a synthesized design principle that designs an OFC first and is valid for almost all OLS s, is proposed and fully developed, the corresponding K will be designed afterwards and will be constrained by the OFC order as well as the OFC parameters; 4) Although the Kxx(t)-control is constrained in this new design principle and is therefore called the "generalized SFC"(as compared to the existing SFC in which K is unconstrained), it is still strong enough for most OLS s and this new design principle overcomes many fundamental drawbacks of the existing separation principle. The third category of observers estimate Kxx(t) signal at special applications such as fault detection and identification and systems with time delay effects. Using directly the result of OFC that estimates Kxx(t) of the second category, these observers can be generally and satisfactorily designed.

On “Over-Sized” High-Gain Practical Observers for Nonlinear Systems

In this paper,it is shown that the performances of a class of high-gain practical observers can be improved by estimating the time derivatives of the output up to an order that is greater than the dimension of the system, which is assumed to be in observability form and, possibly, time-varying. Such an improvement is achieved without increasing the gain of the observers, thus allowing their use in a wide variety of control and identification applications.

Influence of fault slip on mining-induced pressure and optimization ofroadway support design in fault-influenced zone

This paper presents an investigation on the characteristics of overlying strata collapse and mining-induced pressure in fault-influenced zone by employing the physical modeling in consideration of fault structure. The precursory information of fault slip during the underground mining activities is studied as well. Based on the physical modeling, the optimization of roadway support design and the field verification in fault-influenced zone are conducted. Physical modeling results show that, due to the combined effect of mining activities and fault slip, the mining-induced pressure and the extent of damaged rock masses in the fault-influenced zone are greater than those in the uninfluenced zone. The sharp increase and the succeeding stabilization of stress or steady increase in displacement can be identified as the precursory information of fault slip. Considering the larger mining-induced pressure in the fault-influenced zone, the new support design utilizing cables is proposed. The optimization of roadway support design suggests that the cables can be anchored in the stable surrounding rocks and can effectively mobilize the load bearing capacity of the stable surrounding rocks. The field observation indicates that the roadway is in good condition with the optimized roadway support design.

Robust fault diagnosis with disturbance rejection and attenuation for systems with multiple disturbances

The fault diagnosis problem is investigated for a class of nonlinear neutral systems with multiple disturbances.Time-varying faults are considered and multiple disturbances are supposed to include the unknown disturbance modeled by an exo-system and norm bounded uncertain disturbance.A nonlinear disturbance observer is designed to estimate the modeled disturbance.Then,the fault diagnosis observer is constructed by integrating disturbance observer with disturbance attenuation and rejection performances.The augmented Lyapunov functional approach,which involves the tuning parameter and slack variable,is applied to make the solution of inequality more flexible.Finally,applications for a two-link robotic manipulator system are given to show the efficiency of the proposed approach.

Detecting and diagnosing faults in dynamic stochastic distributions using a rational B-splines approximation to output PDFs

This paper presents a novel approach to detect and diagnose faults in the dynamic part of a class of stochastic systems . the Such a group of systems are subjected to a set of crisp inputs but the outputs considered are the measurable probability density functions (PDFs) of the system output, rather than the system output alone. A new approximation model is developed for the output probability density functions so that the dynamic part of the system is decoupled from the output probability density functions. A nonlinear adaptive observer is constructed to detect and diagnose the fault in the dynamic part of the system. Conver-gency analysis is performed for the error dynamics raised from the fault detection and diagnosis phase and an applicability study on the detection and diagnosis of the unexpected changes in the 2D grammage distributions in a paper forming process is included.

Optimal State Estimation and Fault Diagnosis for a Class of Nonlinear Systems

This study proposes a scheme for state estimation and,consequently,fault diagnosis in nonlinear systems.Initially,an optimal nonlinear observer is designed for nonlinear systems subject to an actuator or plant fault.By utilizing Lyapunov's direct method,the observer is proved to be optimal with respect to a performance function,including the magnitude of the observer gain and the convergence time.The observer gain is obtained by using approximation of Hamilton-Jacobi-Bellman(HJB)equation.The approximation is determined via an online trained neural network(NN).Next a class of affine nonlinear systems is considered which is subject to unknown disturbances in addition to fault signals.In this case,for each fault the original system is transformed to a new form in which the proposed optimal observer can be applied for state estimation and fault detection and isolation(FDI).Simulation results of a singlelink flexible joint robot(SLFJR)electric drive system show the effectiveness of the proposed methodology.

Increasingly important role of numerical modeling in oceanic observation design strategy: A review

Oceanic observation design is of considerable significance and has made remarkable progress during the past several decades.This study addresses the critical role of numerical modeling in oceanic observation design.Following a brief introduction of the characteristics of existing oceanic observation design studies,we present the advantages of the model-based observation design strategy and further review its decisive contribution.To demonstrate the effectiveness of this strategy,the targeted observation applications using the conditional nonlinear optimal perturbation(CNOP)approach for improving the Kuroshio predictions are introduced.Finally,the authors present their consideration for correcting model errors by targeted observations of sensitive model parameters and mitigating the model-dependency problem by utilizing multiple modeling systems.Suggestions on using observing system simulation experiments to validate the designed observations and extending the model-based observation design strategy into observing oceanic climatological mean states are also discussed.