Partial state observers for linear systems with unknown inputs

We consider the problem of constructing partial state observers for discrete-time linear systems with unknown inputs. Specifically, for any given system, we develop a design procedure that characterizes the set of all linear functionals of the system state that can be reconstructed through a linear observer with a given delay. By treating the delay as a design parameter, we allow greater flexibility in estimating state functionals, and are able to obtain a procedure that directly produces the corresponding observer parameters. Our technique is also applicable to continuous-time systems by replacing delayed outputs with differentiated outputs.     

Interval estimation for uncertain systems with time-varying delays

The estimation problem for uncertain time-delay systems is addressed. A design method of reduced-order interval observers is proposed. The observer estimates the set of admissible values (the interval) for the state at each instant of time. The cases of known fixed delays and uncertain time-varying delays are analysed. The proposed approach can be applied to linear delay systems and nonlinear time-delay systems in the output canonical form. It involves the properties of quasi-monotone/Metzler/cooperative systems. In this framework, it is shown that if under a suitable coordinate transformation the delay-free subsystem is cooperative, then the delayed estimation error dynamics inherits this property. The conditions to find the observer gains are formulated in the form of LMI. The framework efficiency is demonstrated on examples of nonlinear systems.     

具有积分测量和时延的离散线性变参数系统故障与状态估计

故障检测与诊断(FDD)技术可以有效地提高系统的安全性和可靠性,因此受到越来越多的关注.目前,关于离散系统的状态和故障估计问题的研究还不够充分.本文针对具有积分测量和时延的线性变参数(LPV)系统,提出了一种同时估计执行器/传感器故障和状态的方法.首先,系统当前状态、系统延迟状态和传感器故障构造一个扩维状态,得到广义离...     

基于凸空间收缩滤波的噪声不确定时滞系统状态估计

针对受未知但有界噪声干扰的噪声不确定时滞系统, 提出了一种基于凸空间收缩滤波的系统状态估计方法. 首先, 利用凸空间定义包裹系统真实状态的可行集, 求解下一时刻的凸空间体形状矩阵; 随后从凸空间收缩角度, 利用当前时刻噪声和扰动构造带空间, 得到满足状态预测和量测更新条件的凸空间结构; 进而, 依据时滞系统约束条件构造线性规划不等式方程组, 利用线性规划求解该凸空间, 得到包裹状态可行集的最紧致凸空间体; 最后, 通过数值仿真与电池化成工艺变换器案例仿真, 验证了本文所提方法解决不确定时滞系统状态估计问题的有效性和准确性.     

Simultaneous state and input estimation of hybrid systems with unknown inputs

This paper addresses the problem of the simultaneous state and input estimation for hybrid systems when subject to input disturbances. The proposed algorithm is based on the moving horizon estimation (MHE) method and uses mixed logical dynamical (MLD) systems as equivalent representations of piecewise affine (PWA) systems. So far the MHE method has been successfully applied for the state estimation of linear, hybrid, and nonlinear systems. The proposed extension of the MHE algorithm enables the estimation of unknown inputs, or disturbances, acting on the hybrid system. The new algorithm is shown to improve the convergence characteristics of the MHE method by reducing the delay of convergent estimates, while assuring convergence for every possible sequence of input disturbances. To ensure convergence the system is required to be incrementally input observable, which is an extension to the classical incremental observability property.     

A practical functional observer scheme for interconnected time-delay systems

This paper proposes a partially distributed functional observer scheme for a class of interconnected linear systems with very strong non-instantaneous subsystems interaction and with time delays in the local states and in the transmission of output information from the remote subsystems. A set of easily verifiable existence conditions is established and upon its satisfaction, simple distributed observers are designed using a straightforward design procedure. Simulation results of a numerical example are given to substantiate the feasibility of the approach.     

Simultaneous state and unknown input reconstruction using cascaded high-gain observers

This paper presents a systematic routine for jointly reconstruct the state variables and the unknown inputs (UIs) for a large class of nonlinear MIMO systems. After an appropriate change of state coordinates, a set of cascade high-gain observers (CHGO) are designed in such a way that each of them provides an estimation of only one component of the UI vector, except the last one which gives a final adjustment of the whole state variables. Such design achieves a boundary of the state estimation error which can be arbitrarily small by properly specifying the sole synthesis parameter. An illustrative example verifies the effectiveness of the proposed scheme.     

Unbiased minimum-variance state estimation for linear systems with unknown input

The problem of state estimation for a linear system with unknown input, which affects both the system and the output, is discussed in this paper. A recursive optimal filter with global optimality in the sense of unbiased minimum variance over all linear unbiased estimators, is provided. The necessary and sufficient condition for the convergence and stability is also given, which is milder than existing approaches.     

Event-based input and state estimation for linear discrete time-varying systems

In this paper, the joint input and state estimation problem is considered for linear discrete-time stochastic systems. An event-based transmission scheme is proposed with which the current measurement is released to the estimator only when the difference from the previously transmitted one is greater than a prescribed threshold. The purpose of this paper is to design an event-based recursive input and state estimator such that the estimation error covariances have guaranteed upper bounds at all times. The estimator gains are calculated by solving two constrained optimisation problems and the upper bounds of the estimation error covariances are obtained in form of the solution to Riccati-like difference equations. Special efforts are made on the choices of appropriate scalar parameter sequences in order to reduce the upper bounds. In the special case of linear time-invariant system, sufficient conditions are acquired under which the upper bound of the error covariance of the state estimation is asymptomatically bounded. Numerical simulations are conducted to illustrate the effectiveness of the proposed estimation algorithm.     

Extension of unbiased minimum-variance input and state estimation for systems with unknown inputs

This paper extends the existing results on joint input and state estimation to systems with arbitrary unknown inputs. The objective is to derive an optimal filter in the general case where not only unknown inputs affect both the system state and the output, but also the direct feedthrough matrix has arbitrary rank. The paper extends both the results of Gillijns and De Moor [Gillijns, S., & De Moor, B. (2007b). Unbiased minimum-variance input and state estimation for linear discrete-time systems with direct feedthrough. Automatica, 43, 934–937] and Darouach, Zasadzinski, and Boutayeb [Darouach, M., Zasadzinski, M., & Boutayeb, M. (2003). Extension of minimum variance estimation for systems with unknown inputs. Automatica, 39, 867–876]. The resulting filter is an extension of the recursive three-step filter (ERTSF) and serves as a unified solution to the addressed unknown input filtering problem. The relationship between the ERTSF and the existing literature results is also addressed.     

Robust state estimation for a class of uncertain time-delay systems

This paper considers a robust state estimation problem for a class of uncertain time-delay systems. In this problem, the noise and uncertainty are modelled deterministically via an integral quadratic constraint. The robust state estimation problem involves constructing the set of all possible states at the current time consistent with given output measurements and the integral quadratic constraint. This set is found to be an ellipsoid which is constructed via a linear state estimator.     

Design of LPV observers for LPV time-delay systems: an algebraic approach

The design of reduced order observer for linear parameter varying (LPV) time-delay systems is addressed. Necessary conditions guaranteeing critical structural properties for the observation error dynamics are first provided through nonlinear algebraic matrix equalities. An explicit parametrisation of the family of observers fulfilling these necessary conditions is then derived. Finally, an approach based on linear matrix inequalities is provided and used to select a suitable observer within this family, according to some criterion; e.g. maximisation of the delay margin or guaranteed suboptimal ?₂-gain. Examples from the literature illustrate the efficiency of the approach.     

Reduced-order observer-based output feedback control of nonlinear time-delay systems with prescribed performance

This paper studies the problem of output feedback control for a class of nonlinear time-delay systems with prescribed performance. The system is in the form of triangular structure with unmodelled dynamics. First, we introduce a reduced-order observer to provide the estimate of the unmeasured states. Then, by setting a new condition with the performance function, we design the state transformation with prescribed performance control. By employing backstepping method, we construct the output feedback controller. It is proved that the resulting closed-loop system is asymptotically stable and both transient and steady-state performance of the output are preserved with the changing supply function idea. Finally, a simulation example is conducted to show the effectiveness of the main results.     

含未知输入的广义系统的状态与输入估计

研究了含未知输入的广义系统的输入解耦观测器设计问题. 在系统脉冲能控的条件下通过系统输入-状态对的非奇异变换, 把此问题等价地转化为正常状态空间系统的相应问题. 用大家熟知的方法设计正常状态空间系统的观测器, 从而得到广义系统的输入解耦观测器. 然后用广义系统的观测器状态和系统输出的线性组合渐近估计系统的状态与未知输入.     

Adaptive state observation of linear time-varying systems with delayed measurements and unknown parameters

In this article, we address the problem of adaptive state observation of linear time-varying systems with delayed measurements and unknown parameters. Our new developments extend the results reported in our recently works. The case with known parameters has been studied by many researchers. However in this article we show that the generalized parameter estimation-based observer design provides a very simple solution for the unknown parameter case. Moreover, when this observer design technique is combined with the dynamic regressor extension and mixing estimation procedure the estimated state and parameters converge in fixed-time imposing extremely weak excitation assumptions.     

Local nonlinear unknown input observer

This paper proposes a new nonlinear unknown input observer. The observer design approach utilizes the first order Taylor expansion. The observer gains are then obtained by a systematic method. In this paper, we added some improvements to this method. The developed approach also can enable observer design for a large class of differentiable nonlinear systems. The necessary and sufficient conditions for the existence of the observer are given. A numerical example is given to illustrate the attractiveness and the simplicity of the new design procedure.     

Partial unknown input reconstruction for linear systems

The problem of partial unknown input (UI) reconstruction is addressed. It is considered that a linear functional of the UI vector has to be reconstructed using output information only. Necessary and sufficient conditions are given allowing for the reconstruction in finite time of the required UI’s; analogous conditions are obtained for the asymptotic reconstruction of the required UI’s. The solution of the problem under consideration provides a means to solve the problem of fault detection and isolation for disturbed linear systems.     

Global output feedback control of nonlinear time-delay systems with input matching uncertainty and unknown output function

This paper studies the problem of global output feedback control for nonlinear time-delay systems with input matching uncertainty and the unknown output function, whose nonlinearities are bounded by lower triangular linear unmeasured states multiplying the unknown constant, polynomial-of-output and polynomial-of-input growth rates. By constructing a new extended state observer and skillfully combining the dynamic gain method, backstepping method and Lyapunov–Krasovskii theorem, a delay-independent output feedback controller can be developed with only one dynamic gain. It is proved that all the signals of the closed-loop system are bounded, the states of the original system and the corresponding observer converge to zero, and the estimation of input matching uncertainty converges to its actual value. Two examples demonstrate the effectiveness of the control scheme.