Observability Of Linear Time-varying Systems Research Articles

A Resetting Observer for Linear Time-Varying Systems With Application to Dynamic Positioning of Marine Surface Vessels

A Resetting Observer for Linear Time-Varying Systems With Application to Dynamic Positioning of Marine Surface Vessels

Parametric design to reduced-order functional observer for linear time-varying systems

This article studies the parametric design of reduced-order functional observer (ROFO) for linear time-varying (LTV) systems. Firstly, existence conditions of the ROFO are deduced based on the differentiable nonsingular transformation. Then, depending on the solution of the generalized Sylvester equation (GSE), a series of fully parameterized expressions of observer coefficient matrices are established, and a parametric design flow is given. Using this method, the observer can be constructed under the expected convergence speed of the observation error. Finally, two numerical examples are given to verify the correctness and effectiveness of this method and also the aircraft control problem.

Practical Methods to Investigate Observability of Linear Time-Varying Systems

The work proposes a practical methodology to investigate observability of linear time-varying systems. The methodology comprises analytical and numerical methods, as well as a technique to verify results of analytical investigation numerically. Employing reducibility in the analysis of observability is demonstrated.

An Adaptive State Observer for Linear Time-varying Systems with Inaccurate Parameters

The design problem of an adaptive state observer for linear time-varying systems is considered. Some parameters of a time-varying plant are assumed to be unknown numbers multiplied by known functions of time. The approach proposed below is based on identification methods of adaptation. In other words, the main idea is to transform a mathematical model in the form of a linear time-varying differential equation to a static linear regression model containing unknown parameters. In this case, both the unknown parameters of the plant and its initial conditions are the unknown parameters of the regression model under consideration. Further, standard gradient methods or other parametric identification approaches are used to estimate the unknown parameters of the regression model and to construct the observer. The results of computer simulations illustrate the effectiveness of the new state observer design method.

Linear Function Observers for Linear Time-Varying Systems With Time-Delay: A Parametric Approach

In this paper, a parametric approach to design a Luenberger functional observer for linear time-varying (LTV) systems with time-delay is investigated. Based on the solution to generalized Sylvester equation (GSE), the complete general parametric expressions for the functional observer gain matrices are established with the time-varying coefficient matrices, the time-varying closed-loop system and a group of arbitrary parameters. With the parametric method, the observation error system can be transformed into a linear system with the expected eigenstructure. Finally, a numerical simulation is provided to illustrate the effectiveness of the parametric approach.

A Parametric Method of Linear Functional Observers for Linear Time-varying Systems

This paper considers the design of a Luenberger observer to estimate the linear multiple states functional for linear time-varying (LTV) systems. Based on the solutions to a type of full actuated homogeneous generalized Sylvester matrix equations and the conditions for the existence of observers for LTV systems, general parametric solutions to Luenberger functional observers are established. With the proposed approach, the functional observers can be achieved at desired convergence rate of the observation error, and also without any particular transformation for LTV systems. Finally, a numerical example shows the feasibility and effectiveness of the proposed parametric design method for the functional observers in LTV systems.

Observability of Linear Time-Varying Systems with Quasiderivative Coefficients

On the basis of quasiderivatives and the upper triangular Hessenberg form, an approach to investigating the observability problem for linear time-varying systems is proposed. The quasiderivatives are defined for some lower triangular matrix, and the simplest rules of the quasidifferentiation are described. Conditions for linear independence of continuous quasidifferentiable functions are established in terms of the Wronski matrix. The necessary and sufficient conditions for an upper triangular Hessenberg form in the orbit of linear time-varying systems are obtained, and the method to find such systems is described. New efficient conditions for various types of observability (complete, differential, uniform) are obtained.

Receding horizon observer for linear time-varying systems

In this paper, we present a receding horizon observer for linear time-varying systems. Our main contribution is that known deterministic input has been fully dealt with. This poses considerable challenges for recursive formulation of the filter. The suggested observer can be used in closed-loop feedback control systems. The existing finite memory filters lack this ability. First- and second-order statistical convergence analysis carried out in this paper provide an insight into the stochastic behaviour of the observer. Some examples demonstrate the utility of the proposed filter.

On strong structural controllability and observability of linear time-varying systems: a constructive method

In this paper, we consider the controllability and observability of generalized linear time-varying (LTV) systems whose coefficients are not exactly known. All that is known about these systems is the placement of non-zero entries in their coefficient matrices $(A,B)$. We provide the characterizations in order to judge whether the placements can guarantee the controllability/observability of such LTV systems, regardless of the exact value of each non-zero coefficient. We also present a direct and efficient algorithm with an associated time cost of $O(n+m+\nu)$ to verify the conditions of our characterizations, where $n$ and $m$ denote the number of columns of $A$ and $B$, respectively, and $\nu$ is number of non-zero entries in $(A,B)$.

Multi Observer Structure for Rapid State Estimation in Linear Time Varying Systems

A new method to design observers for linear time-varying systems is presented in this paper. The method begins by constructing two layers. The first layer is made up of multiple observers, while the second establishes a relationship between observers via a weighted estimation state. The primary challenge was to find a new feedback process that would determine the second layer weights. The multiple observers of the first layer were investigated to determine a general observation law. The resulting multilayer structure significantly improves the transient characteristics of the observation process, which leads to a more efficient control system.

A Continuous Reconstruction Observer for Sampled-Data Linear Time Varying Systems

In this paper, a novel continuous sampled-data observer for linear time-varying systems is presented. The proposed observer is based on two different impulsive observers. The state estimates of these impulsive observers are fused in a manner such that continuous state estimation is achieved. Another significant contribution is comprehensive stability analysis of the proposed observer. The analysis establishes conditions that guarantee exponential convergence of observers. Contrary to the common understanding, it is revealed that the convergence of associated discrete-time equation for impulsive observers is not a sufficient condition for overall convergence. Contributions are illustrated by simulations.

Strong Structural Controllability and Observability of Linear Time-Varying Systems

In this note we consider continuous-time systems x'(t) = A(t) x(t) + B(t) u(t), y(t) = C(t) x(t) + D(t) u(t), as well as discrete-time systems x(t+1) = A(t) x(t) + B(t) u(t), y(t) = C(t) x(t) + D(t) u(t) whose coefficient matrices A, B, C and D are not exactly known. More precisely, all that is known about the systems is their nonzero pattern, i.e., the locations of the nonzero entries in the coefficient matrices. We characterize the patterns that guarantee controllability and observability, respectively, for all choices of nonzero time functions at the matrix positions defined by the pattern, which extends a result by Mayeda and Yamada for time-invariant systems. As it turns out, the conditions on the patterns for time-invariant and for time-varying discrete-time systems coincide, provided that the underlying time interval is sufficiently long. In contrast, the conditions for time-varying continuous-time systems are more restrictive than in the time-invariant case.

Finite Memory Observers for linear time-varying systems. Part II: Observer and residual sensitivity

Fault detection and diagnosis are important issues in process engineering. Hence, considerable interest is growing in this field from industrial practitioners as well as academic researchers, as opposed to 30years ago. This paper focusses on a model-based approach for fault detection. This approach is based on Finite Memory Observers (FMO), properties of this observer are presented in the first part of our work (Graton et al., 2014 [1]), the main results of this paper are recalled at the beginning of this paper and constitute the basis of this second part. Properties of the Finite Memory Observer (FMO) are studied from a global point of view for the class of linear time-varying (LTV) systems with stochastic noises. FMO performances take their framework from the study of their properties, and from the study of their influences on diagnosis results. Fundamentally, the generation of residuals is essential in a diagnosis procedure. In Graton et al. (2014) [1], the design for the finite memory observer is shown, the determination of its optimal window length is solved, and the generation of residuals for diagnosis is completed. This paper is the second part of this work and is devoted to the study of the observer and residual sensitivity towards model parameter variations and noises.

Finite Memory Observers for linear time-varying systems: Theory and diagnosis applications

Fault detection and diagnosis are important issues in process engineering. Hence, a considerable interest exists in this field now from industrial practitioners as well as academic researchers, as opposed to 30 years ago. The literature on process fault diagnosis, ranging from analytical methods to artificial intelligence and statistical approaches, is largely widespread. In this paper, the modeling of the real process is known, and the state-space representation is used. The properties of the Finite Memory Observer (FMO) are studied from a global point of view for the class of linear time-varying (LTV) systems with stochastic noises. The FMO performances are framed by the study of their properties, and that of their influences on diagnosis results. Fundamentally, the generation of residuals is an essential procedure in diagnosis. So, the determination of the optimal window length of the observer is resolved, and the generation of residuals for diagnosis completed. In the first part, the design of the observer and the residual generation are shown. The second part is devoted to the study of the sensitivity and robustness of the observer and of residuals generated from the observer.

On Functional Observers for Linear Time-Varying Systems

The technical note deals with existence conditions of a functional observer for linear time-varying systems in the case where the order of the observer is equal to the number of observed variables. Constructive procedures for the design of such a linear functional observer are deduced from the existence conditions. As a specific feature, the proposed procedures do not require the solution of a differential Sylvester equation. Some examples illustrate the presented results.

On the Pole-Placement and the Observer for Linear Time-Varying Systems

A simple design method of the Luenberger observer for linear time-varying systems is proposed in this paper. The paper first propose the simple calculation method to derive the pole placement feedback gain vector for linear time-varying systems. For this purpose, it is shown that the pole placement controller can be derived simply by finding some particular "output signal" such that the relative degree from the input to this output is equal to the order of the system. Using this fact, the feedback gain vector can be calculated directly from plant parameters without transforming the system into any standard form. Then, this method is applied to the design of the observer, i.e., because of the duality of linear time-varying system, the state observer can be derived by un-stabilization of the state error equation.

Observers for linear time-varying systems

We give characterizations and necessary and sufficient existence conditions for tracking and asymptotic observers for linear functions of the state of a linear finite-dimensional time-varying state space system. We specialize the results to affine parameter varying systems and bilinear control systems.

A necessary algebraic condition for controllability and observability of linear time-varying systems

In this note, we give an algebraic condition which is necessary for the system x'(t)=A(t)x(t)+B(t)u(t), y(t)=C(t)x(t), either to be totally controllable or to be totally observable, where x/spl isin//spl Ropf//sup d/, u/spl isin//spl Ropf//sup p/, y/spl isin//spl Ropf//sup q/, and the matrix functions A, B and C are (d-2), (d-1) and (d-1) times continuously differentiable, respectively. All conditions presented here are in terms of known quantities and therefore easily verified. Our conditions can be used to rule out large classes of time-varying systems which cannot be controlled and/or observed no matter what the nonzero time-varying coefficients are. This work is motivated by the deep result of Silverman and Meadows.

FURTHER DEVELOPMENTS ON ADAPTIVE OBSERVERS FOR NONLINEAR SYSTEMS WITH APPLICATION IN FAULT DETECTION

From previous studies of (Besançon, 1999; Besançon, 2000) on adaptive observer design for nonlinear systems, and the contribution of (Zhang, 2001) on exponential adaptive observers for linear time-varying systems, the purpose here is to propose some new observer design for a class of nonlinear systems. This observer can in turn be made adaptive, and in particular can help in detecting changes in some parameters.

Minimal-order observer designs for linear time-varying multivariable systems

This note presents two simple approaches for the design of minimal-order observer for linear time-varying systems. Both techniques rely on canonical transformations of the given system. As a consequence, simple expressions are obtained which permit the observer constraint equation to be solved effectively. The observers possess the desirable property of having a time-invariant observer coefficient matrix with arbitrary eigenvalues. A comparison is made between the proposed methods from which conclusions are drawn. An illustrative example is also included.