Dynamic observer-based controllers for linear uncertain systems

This paper addresses robust controller design for uncertain linear systems via a dynamic observer-based controller. A dynamic observer is an alternative structure for a classical observer which can be regarded as a general form of a usual observer and has additional degrees of freedom in the observer structure. Using this new observer structure, a new observer-based controller for linear systems is proposed. Some strict linear matrix inequalities (LMIs) have been given to find the dynamic observer parameters and controller gain. It is shown that dynamic observer can be used effectively for tackling the drawbacks of the classical observer-based robust controller design methods. As an advantage, LMIs are derived even in the presence of uncertainties in system, input and output matrices simultaneously, whereas by using the traditional observer, bilinear matrix inequalities (BMIs) are given in the presence of such uncertainties. Moreover, the proposed LMIs do not imply the equality constraint. Simulation results are used to illustrate the effectiveness of the proposed design technique.     

线性广义系统的区间观测器设计

本文研究了连续时间线性广义系统的区间观测器设计问题.首先根据正系统的稳定性判据提出了一种基于线性矩阵不等式的广义区间观测器直接设计法,然后通过引入更多的设计自由度进一步放宽了区间观测器的设计条件,扩大了设计方法的适用范围.所提出的设计方法无需坐标变换,是一种直接设计方法.最后,通过两个仿真算例验证了所提出方法的有效性.     

Control design based on a linear state function observer

A control design method based on a linear state function observer is proposed. The method is a semi-inverse design procedure in that the control law is not designed before the observer system, but is a result of the observer design. However, the observer design is not completely independent of the control design, but seeks to yield a feedback signal that is close to a prescribed control law. First, the observer design problem is considered as the reconstruction of a linear function of the state vector. The linear state function to be reconstructed is the given control law. Then, based on the derivation for linear state function observers, the observer design is formulated as a parameter optimization problem. The optimization objective is to generate a matrix that is close to the given feedback gain matrix. Based on that matrix, the form of the observer and a new control law can be determined. The semi-inverse design procedure can yield a reduced-order observer with dimension considerably smaller than that of the system. Two numerical examples are used to demonstrate the proposed design procedure.     

Sliding mode control-based linear functional observers for discrete-time stochastic systems

Sliding mode control (SMC) is one of the most popular techniques to stabilise linear discrete-time stochastic systems. However, application of SMC becomes difficult when the system states are not available for feedback. This paper presents a new approach to design a SMC-based functional observer for discrete-time stochastic systems. The functional observer is based on the Kronecker product approach. Existence conditions and stability analysis of the proposed observer are given. The control input is estimated by a novel linear functional observer. This approach leads to a non-switching type of control, thereby eliminating the fundamental cause of chatter. Furthermore, the functional observer is designed in such a way that the effect of process and measurement noise is minimised. Simulation example is given to illustrate and validate the proposed design method.     

Robust reduced-order sliding mode observer design

In this article, a triple state and output variable transformation-based method combined with linear matrix inequality (LMI) techniques to design a new robust reduced-order sliding mode observer for perturbed linear multiple-input and multiple-output systems is developed. The state and output variables of the original system are triple transformed into suitable canonical form coordinates to facilitate the design of a reduced-order observer. The existing transformations are summarised in this study and presented systematically. A new combined observer configuration is proposed and compared with another type of observers. Global asymptotical stability LMI and sliding mode existence conditions for the coupled observer error system are derived using Lyapunov full quadratic form. Reaching and sliding modes of motion of decoupled observer error system are discussed as well. Two numerical and simulation examples are given to illustrate the usefulness of the proposed design techniques.     

Finite-time estimation for linear time-delay systems via homogeneous method

This paper presents a finite-time observer for linear time-delay systems with commensurate delay. Unlike the existing observers in the literature which converge asymptotically, the proposed observer provides a finite-time estimation. This is realised by using the well-known homogeneous technique, and the results are also extended to investigate the estimation problem for linear time-delay systems with unknown inputs. Simulation results are presented in order to illustrate the feasibility of the proposed method.     

Functional observer-based sliding mode control for linear discrete-time-delayed stochastic systems

Functional observers are the primary solution to sundry estimation problems, wherein full- or reduced-order observer cannot be directly applied. This paper presents a functional observer-based sliding mode control method for the linear discrete-time delayed stochastic system. Stability analysis of sliding function is presented for the delayed stochastic system with a linear matrix inequality approach. The functional observer method for the linear discrete-time-delayed stochastic system is proposed based on the Kronecker product approach. Sliding mode controller is estimated using the functional observer method. Finally, to demonstrate the efficacy of the proposed design, comparison of its performance with some of the well-known existing state feedback controller is presented.     

Disturbance-observer-based robust control for time delay uncertain systems

A robust control scheme is proposed for a class of systems with uncertainty and time delay based on disturbance observer technique. A disturbance observer is developed to estimate the disturbance generated by an exogenous system, and the design parameters of the disturbance observer are determined by solving linear matrix inequalities (LMIs). Based on the output of the disturbance observer, a robust control scheme is proposed for the time delay uncertain system. The disturbance-observer-based robust controller is combined of two parts: one is a linear feedback controller designed using LMIs and the other is a compensatory controller designed with the output of the disturbance observer. By choosing an appropriate Lyapunov function candidate, the stability of the closed-loop system is proved. Finally, simulation example is presented to illustrate the effectiveness of the proposed control scheme.     

A state observer for nonlinear systems

A state observer design methodology for a class of nonlinear systems is proposed. The nonlinear observer design methodology is, in fact, an extension of linear observer design techniques using transformations related to linear observability matrices     

非线性微分——代数系统的输出反馈镇定控制

对满足线性增长条件的非线性微分--代数系统, 研究了其输出反馈镇定控制问题. 通过将状态观测器与控制器耦合在一起设计, 构造出一种非初始化的线性高增益状态观测器, 具有良好的鲁棒性. 基于反推设计方法构造出一个线性的动态输出补偿器, 使得整个闭环系统是渐近稳定的. 仿真结果验证了本文所提控制方法的有效性.     

用B-样条神经网络设计非线性观测器

对线性部分已知、非线性部分未知的一类非线性系统,提出了一种新的状态观测器 的设计方法.首先针对线性部分设计线性观测器,随后在线性观测器中加入非线性补偿项.该 补偿项先由"反卷积"的方式确定,再用B-样条神经网络拟合.对三个非线性系统设计了观测 器,通过与已有的解析方法进行比较,说明了该方法的优越性.     

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.     

Disturbance localization and pole shifting by dynamic compensation

This paper concerns the problem of disturbance localization and pole shifting by dynamic compensation in multivariable linear systems with inaccessible state vector. A necessary and sufficient condition for the solvability of the problem is given. Two synthesis procedures of the compensator are presented: one is based on an observer and the other is based on a dual observer. The observer designed by the proposed procedure acts as as unknown input observer for a linear function. An improved procedure of designing a reduced order unknown input observer is also given. The result may be applicable to reducing the compensator order.     

A novel sth‐order observer for linear system: Application to state and fault estimation of spacecraft control system

In this paper, a fault estimation problem for linear system is considered. A novel sth‐order observer is proposed to cope with this problem. The advantages of the proposed observer are that (i) the observer matching condition is not required to be satisfied in practical systems, (ii) if the sth derivative of fault is unknown and/or unbounded and the (s + 1)th derivative of fault f (t) is naught or bounded, it can simultaneously estimate the state and fault. The sufficient existence condition of the proposed observer is given by a linear matrix inequality. In addition, a feasible method to obtain the design parameters is discussed. Finally, two numerical examples are presented to illustrate the effectiveness of the proposed method.     

Time averaged consensus in a direct coupled coherent quantum observer network

This paper considers the problem of constructing a direct coupling quantum observer for a closed linear quantum system. The proposed distributed observer consists of a network of quantum harmonic oscillators and it is shown that the observer network converges to a consensus in a time averaged sense in which each element of the observer estimates the specified output of the quantum plant. An example and simulations are included to illustrate the properties of the observer network.     

Observer design and output feedback stabilization for linear singular time-delay systems with unknown inputs

The design of a functional observer and reduced-order observer with internal delay for linear singular timedelay systems with unknown inputs is discussed. The sufficient conditions of the existence of observers, which are normal linear time-delay systems, and the corresponding design steps are presented via linear matrix inequality（LMI）. Moreover, the observer-based feedback stabilizing controller is obtained. Three examples are given to show the effectiveness of the proposed methods.     

一类非线性系统的控制器和观测器设计

研究一类非线性系统的全状态反馈控制问题、观测器设计问题及输出反馈控制设计问题.首先设计出非线性全状态反馈控制器,获得了系统指数镇定的充分条件.然后提出了非线性观测器,并证明了该观测器是指数稳定观测器.进一步,在控制器和观测器问题的充分条件满足的假设下,证明了提出的带估计状态的反馈控制能达到指数镇定.最后,仿真实例验证了所得结果的有效性.     

New scheme for discrete observer design with estimation error covariance assignment

This article presents an innovative method for solving an estimation error covariance assignment problem to design an observer for a stochastic linear system. In the proposed method, the covariance assignment problem is converted to the problem of finding an extra noise-like input to the observer. Using appropriate matrix manipulation, the Riccati equation of the estimation error covariance assignment problem, is converted to a new deterministic linear state-space model. Also, the extra noise-like input to the observer is modelled as an input to the new deterministic linear state-space model. Therefore, all the conventional and well-defined control strategies could be applied and there is no need to solve a complicated Riccati equation. Moreover, using the proposed method, a multi-objective estimation error covariance tracking problem would be easily converted to the problem of controlling a standard deterministic linear state-space system. Based on the integral control method, which is applied to the new state-space model, formulations for the proposed covariance feedback law are presented. The control law results in a stable closed-loop covariance system and assigns a pre-specified covariance matrix to the estimation errors.