The variable structure controller design for a class of nonlinear uncertain systems based on robust observer

The variable structure controller is designed for a class of nonlinear uncertain time-delay system by using robust observer, and incorporating H-infinity control technique, the controller can guarantee the H-infinity performance of sliding mode dynamics and satisfy the reaching condition, which also does not require uncertainties to satisfy matching condition and linear boundary condition. The simulation example is given to illustrate the method.

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.

Polynomial robust observer implementation based passive synchronization of nonlinear fractional-order systems with structural disturbances

A robust polynomial observer is designed based on passive synchronization of a given class of fractional-order Colpitts(FOC)systems with mismatched uncertainties and disturbances.The primary objective of the proposed observer is to minimize the effects of unknown bounded disturbances on the estimation of errors.A more practicable output-feedback passive controller is proposed using an adaptive polynomial state observer.The distributed approach of a continuous frequency of the FOC is considered to analyze the stability of the observer.Then we derive some stringent conditions for the robust passive synchronization using Finsler’s lemma based on the fractional Lyapunov stability theory.It is shown that the proposed method not only guarantees the asymptotic stability of the controller but also allows the derived adaptation law to remove the uncertainties within the nonlinear plant’s dynamics.The entire system using passivity is implemented with details in PSpice to demonstrate the feasibility of the proposed control scheme.The results of this research are illustrated using computer simulations for the control problem of the fractional-order chaotic Colpitts system.The proposed approach depicts an efficient and systematic control procedure for a large class of nonlinear systems with the fractional derivative.

Robust guaranteed cost observer design for linear uncertain jump systems with state delays

This paper deals with the robust guaranteed cost observer with guaranteed cost performance for a class of linear uncertain jump systems with state delay.The transition of the jumping parameters in systems is governed by a finite-state Markov process.Based on the stability theory in stochastic differential equations,a sufficient condition on the existence of the proposed robust guaranteed cost observer is derived.Robust guaranteed cost observers are designed in terms of a set of linear coupled matrix inequalities.A convex optimization problem with LMI constraints is formulated to design the suboptimal guaranteed cost observers.

Robust fault diagnosis for linear time-delay systems with uncertainty

This paper deals with the problem of fault diagnosis problem for a class of linear systems with delayed state and uncertainty. The systems are transformed into two different subsystems. One is not affected by actuator faults so that a robust observer can be designed under certain conditions. The other whose states can be measured is affected by the faults. The proposed observer is utilized in an analytical-redundancy-based approach for actuator and sensor fault detection and diagnosis in time-delay systems. Finally, the applicability and effectiveness of the proposed method is illustrated through numerical examples.

Robust adaptive observer for nonlinear time-delay systems with disturbances and uncertainties

A method of designing robust adaptive observer for nonlinear continuous-time systems with time-delays is presented.It is assumed that the nonlinear functions of the system satisfy Lipschitz condition.The observer is derived considering plant disturbances,structured parameter uncertainties and unknown parameters.Like any other adaptive observer for nonlinear systems with ideal working conditions,it also simultaneously estimates both the states and unknown parameters.This property is very much useful for many applications like fault diagnosis.The convergence of the state errors and estimated unknown parameters are analysed by H_(∞)-control.The sufficient conditions for the existence of the observer are determined and expressed in linear matrix inequality form.With the help of a numerical example,the effectiveness of the proposed observer is demonstrated.

Nonlinear robust H-infinity filtering for a class of uncertain systems via convex optimization

A new approach for robust H-infinity filtering for a class of Lipschitz nonlinear systems with time-varying uncertainties both in the linear and nonlinear parts of the system is proposed in an LMI framework. The admissible Lipschitz constant of the system and the disturbance attenuation level are maximized simultaneously through convex multi-objective optimization. The resulting H-infinity filter guarantees asymptotic stability of the estimation error dynamics with exponential convergence and is robust against nonlinear additive uncertainty and time-varying parametric uncertainties. Explicit bounds on the nonlinear uncertainty are derived based on norm-wise and element-wise robustness analysis.

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.

Detection and Estimation of False Data Injection Attacks for Load Frequency Control Systems

False data injection attacks(FDIAs)against the load frequency control(LFC)system can lead to unstable operation of power systems.In this paper,the problems of detecting and estimating the FDIAs for the LFC system in the presence of external disturbances are investigated.First,the LFC system model with FDIAs against frequency and tie-line power measurements is established.Then,a design procedure for the unknown input observer(UIO)is presented and the residual signal is generated to detect the FDIAs.The UIO is designed to decouple the effect of the unknown external disturbance on the residual signal.After that,an attack estimation method based on a robust adaptive observer(RAO)is proposed to estimate the state and the FDIAs simultaneously.In order to improve the performance of attack estimation,the H¥technique is employed to minimize the effect of external disturbance on estimation errors,and the uniform boundedness of the state and attack estimation errors is proven using Lyapunov stability theory.Finally,a two-area interconnected power system is simulated to demonstrate the effectiveness of the proposed attack detection and estimation algorithms.