线性系统对偶Luenberger观测器设计

提出了线性系统对偶Luenberger观测器的参数化设计方法.基于一类广义Sylvester矩阵方程的显式参数化解,根据一些自由参数给出了对偶Luenberger观测器所有增益矩阵的参数化表达.该设计方法能提供所有的设计自由度,它们能进一步用来实现系统的其他性能指标.数值例子显示了该方法的设计过程.     

离散线性系统高阶积分观测器设计

针对离散线性系统提出一类高阶积分观测器。并且显示这类观测器满足极点配置分离原理，同时给出了这类观测器的存在条件．基于Sylvester矩阵方程的显式参数化通解提出了这类观测器的参数化设计方法．该方法不仅给出了观测器增益矩阵的参数表达式，而且还提供了观测器系统矩阵左特征向量的参数表达式．该设计方法给出了所有的设计自由度，为实现系统的其他性能提供了方便且强有力的工具．数值例子说明了设计过程，并表明了该方法的有效性．     

Full‐Order and Reduced‐order Observer Design for a Class of Fractional‐order Nonlinear Systems

The paper is concerned with problem of the full‐order and reduced‐order observer design for a class of fractional‐order one‐sided Lipschitz nonlinear systems. By introducing a continuous frequency distributed equivalent model and using indirect Lyapunov approach, the sufficient condition for asymptotic stability of the full‐order observer error dynamic system is presented. Furthermore, the proposed design method was extended to reduced‐order observer design for fractional‐order nonlinear systems. All the stability conditions are obtained in terms of LMI, which are less conservative than some existing ones. Finally, a numerical example demonstrates the validity of this approach.     

Unified parametric approaches for high-order integral observer design for matrix second-order linear systems

A type of high-order integral observers for matrix second-order linear systems is proposed on the basis of generalized eigenstructure assignment via unified parametric approaches. Through establishing two general parametric solutions to this type of generalized matrix second-order Sylvester matrix equations, two unified complete parametric methods for the proposed observer design problem are presented. Both methods give simple complete parametric expressions for the observer gain matrices. The first one mainly depends on a series of singular value decompositions, and is thus numerically simple and reliable; the second one utilizes the right factorization of the system, and allows eigenvalues of the error system to be set undetermined and sought via certain optimization procedures. A spring-mass-dashpot system is utilized to illustrate the design procedure and show the effect of the proposed approach.     

Unified parametric approaches for high-order integral observer design for matrix second-order linear systems

A type of high-order integral observers for matrix second-order linear systems is proposed on the basis of generalized eigenstructure assignment via unified parametric approaches. Through establishing two general parametric solutions to this type of generalized matrix second-order Sylvester matrix equations, two unified complete parametric methods for the proposed observer design problem are presented. Both methods give simple complete parametric expressions for the observer gain matrices. The first one mainly depends on a series of singular value decompositions, and is thus numerically simple and reliable; the second one utilizes the right factorization of the system, and allows eigenvalues of the error system to be set undetermined and sought via certain optimization procedures. A spring-mass-dashpot system is utilized to illustrate the design procedure and show the effect of the proposed approach.     

Observer‐based finite‐time stabilization for discrete‐time switched singular systems with quadratically inner‐bounded nonlinearities

This paper discusses the observer‐based finite‐time stabilization for discrete‐time switched singular systems with quadratically inner‐bounded nonlinear terms. Firstly, based on the Luenberger‐like observer, by using the average dwell time approach, sufficient conditions are proposed to make closed‐loop systems be regular, be causal, as having a unique solution, and be uniformly finite‐time bounded. Then, a new linear matrix inequality sufficient condition for the existence of an observer‐based controller is obtained by using certain matrix decoupling techniques, and the controller is designed. In this paper, the conditions proposed not only give the observer‐based controller design methods but also guarantee the existence and uniqueness of solution for the systems. Since the quadratically inner‐bounded nonlinearities are more general than Lipschitz nonlinearities and one‐sided Lipschitz nonlinearities, compared with previous works, the proposed controller design methods in this paper are also more general than the existing ones. Finally, numerical examples are provided to illustrate the effectiveness of the methods proposed in this paper.     

Non‐parametric linear time‐invariant extensions of non‐invertible and backlash plant

A rigorous validation for the use of a set of linear time‐invariant models as a surrogate in the design of controllers for uncertain nonlinear systems, which are invertible as one‐to‐one operators, such as used in the nonlinear quantitative feedback theory (NLQFT) design methodology has been given by Baños and Bailey. This paper presents a similar validation but weakens the requirement on the invertibility of the nonlinear plant by application of Kakutani's fixed‐point theorem and an incremental gain constraint on the plant within its operational envelope. The set of linear time‐invariant models to be used for design is shown to be an extension (termed here the linear time‐invariant extension—LTIE) of the nonlinear plant restricted to the desired output operating space. A new non‐parametric approach to the modelling of the LTIE is proposed which is based on Fourier transforms of the plant I/O data and which accordingly may be based solely on experimental testing without the need for an explicit parametric plant model. This new approach thus extends the application of robust linear controller design methods (including those of NLQFT) to nonlinear plants with set‐valued (multi‐valued) inverses such as those containing backlash and also to plants for which explicit parametric models are difficult to obtain. The method is illustrated by application of the non‐parametric approach to an NLQFT tracking controller design for a mechanical backlashed servomechanism problem. Copyright © 2013 John Wiley & Sons, Ltd.     

Sliding Mode Disturbance Observer‐based Motion Control for a Piezoelectric Actuator‐based Surgical Device

This paper presents a sliding mode disturbance observer‐based motion tracking control methodology. In particular, the methodology is applied to control a semi‐automated hand‐held ear surgical device for the treatment of otitis media with effusion. The proposed control methodology is utilised to deal with the undesirable effects in the motion system, such as non‐linear dynamics, parametric uncertainties and external disturbances. It employs a proportional‐derivative control scheme together with a sliding mode disturbance observer for rejecting the undesirable effects. The stability of the proposed control methodology is proven theoretically and its effectiveness is evaluated experimentally. In addition, promising motion tracking experimental results are shown, and it can be observed that the proposed approach offers more robust performance for controlling the hand‐held surgical device and other similar instruments.     

Eigenstructure assignment design for proportional-integral observers: the discrete-time case

A complete parametric design approach for proportional-integral observers of multivariable discrete-time linear systems is proposed based on an eigenstructure assignment technique. Complete parameterizations for all the observer gains as well as the eigenvector matrix of the observer system matrix are established in terms of three sets of design parameters that satisfy three basic and simple constraints. The proposed approach provides all the degrees of freedom and has great potential in applications. An illustrative example shows the effect of the proposed approach.     

H ∞ observer design for uncertain nonlinear discrete‐time systems with time‐delay: LMI optimization approach

We present a robust H _∞ observer for a class of nonlinear discrete‐time systems. The class under study includes an unknown time‐varying delay limited by upper and lower bounds, as well as time‐varying parametric uncertainties. We design a nonlinear H _∞ observer, by using the upper and lower bounds of the delay, that guarantees asymptotic stability of the estimation error dynamics and is also robust against time‐varying parametric uncertainties. The described problem is converted to a standard optimization problem, which can be solved in terms of linear matrix inequalities (LMIs). Then, we expand the problem to a multi‐objective optimization problem in which the maximum admissible Lipschitz constant and the minimum disturbance attenuation level are the problem objectives. Finally, the proposed observer is illustrated with two examples. Copyright © 2014 John Wiley & Sons, Ltd.     

Robust fault detection in linear systems based on PI observers

A parametric approach for robust fault detection in linear systems with unknown disturbances is presented. The residual is generated using full-order proportional-integral (PI) observers. The approach is based on a result for PI observer design recently proposed. In terms of the design degrees of freedom provided by the parametric PI observer design and a group of introduced parameter vectors, a sufficient and necessary condition for PI observer design with disturbance decoupling is established. By properly constraining the design parameters according to this proposed condition, the effect of the disturbance to the residual signal is decoupled, and a simple algorithm is presented. The presented approach offers all the degrees of design freedom. A numerical example illustrates the effect of the proposed approach.     

Disturbance‐prediction–based control of input time delay systems for rejection of unknown frequency disturbances

In this paper, a novel disturbance rejection approach is presented for a class of input time‐delay systems subject to sinusoidal disturbances with unknown frequency. In particular, an auxiliary observer is proposed to represent the periodic disturbance in a parametric uncertainty form, where the unknown factor related to disturbance frequency can be estimated. Furthermore, the correlation between the future disturbance and the auxiliary observer output is analyzed, such that the future disturbances can be predicted and rejected through the input channel. Based on the aforementioned observer and predictor structure, the overall control architecture can be established as a framework of disturbance‐prediction–based control for systems with input time delays, where the conditions on the asymptotic stability of the closed‐loop systems are also derived. Finally, numerical examples are provided to illustrate the effectiveness of the proposed control approach.     

Robust output‐control for uncertain linear systems: Homogeneous differentiator‐based observer approach

This paper deals with the design of a robust control for linear systems with external disturbances using a homogeneous differentiator‐based observer based on a implicit Lyapunov function approach. Sufficient conditions for stability of the closed‐loop system in the presence of external disturbances are obtained and represented by linear matrix inequalities. The parameter tuning for both controller and observer is formulated as a semi‐definite programming problem with linear matrix inequalities constraints. Simulation results illustrate the feasibility of the proposed approach and some improvements with respect to the classic linear observer approach. Copyright © 2016 John Wiley & Sons, Ltd.     

Improved exponential observer design for one‐sided Lipschitz nonlinear systems

This paper investigates the exponential observer design problem for one‐sided Lipschitz nonlinear systems. A unified framework for designing both full‐order and reduced‐order exponential state observers is proposed. The developed design approach requires neither scaling of the one‐sided Lipschitz constant nor the additional quadratically inner‐bounded condition. It is shown that the synthesis conditions established include some known existing results as special cases and can reduce the intrinsic conservatism. For design purposes, we also formulate the observer synthesis conditions in a tractable LMI form or a Riccati‐type inequality with equality constraints. Simulation results on a numerical example are given to illustrate the advantages and effectiveness of the proposed design scheme. Copyright © 2016 John Wiley & Sons, Ltd.     

Fixed‐Time Synchronization of a Class of Second‐Order Nonlinear Leader‐Following Multi‐Agent Systems

The fixed‐time synchronization problem for a class of second‐order nonlinear multi‐agent systems with a leader‐follower architecture is investigated in this paper. To achieve the fixed‐time tracking task, the design procedure is divided into two steps. At the first step, a distributed fixed‐time observer is designed for each agent to estimate the leader's state in a fixed time. Then, at the second step, based on the technique of adding a power integrator, a fixed‐time tracking controller for each agent is proposed such that the estimate leader's state can be tracked in a fixed time. Finally, an observer‐based fixed‐time controller is developed such that the leader can be tracked by all the followers in a fixed time, which can be predetermined. Simulations are presented to verify the effectiveness of the proposed approach.     

Adaptive tracking for MIMO nonlinear systems with Unknown fast time‐varying parameters

In this paper, we consider a class of MIMO nonlinear systems with fast time‐varying parametric uncertainties. First, the tracking problem of general nonlinearly time‐varyingly parameterized systems is solved. Then, a Lyapunov‐based singularity free adaptive controller is proposed for the considered system. Specifically, an estimation approach with a proportional plus integral adaptation scheme is utilized to update the estimations of the unknown parameters under a mild assumption that the signs of the leading minors of the input gain matrix are known. The asymptotic stability is achieved with full state feedback. Furthermore, we design an output feedback controller by utilizing a standard high‐gain observer and achieve uniformly ultimately bounded convergence. Simulation examples illustrate the effectiveness of the proposed methods.     

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.