Observability of Singular Systems with Commensurate Time-Delays and Neutral terms

International audienceThis paper deals with the observability problem of a sort of singular systems with commensurate time-delays in the trajectories of the system, in the time derivative of the trajectories (neutral terms), and in the output system. By using a recursive algorithm, sufficient conditions (easy testable) are proposed for guaranteeing the backward and the algebraic observability of the system. This condition implies that the trajectories of the system can be reconstructed by using the actual and past values of the system output

A nonlinear Luenberger-like observer for nonlinear singular systems

International audienceThis paper investigates observer design problem for a large class of nonlinear singular systems with multiple outputs. We firstly regularize the singular system by injecting the derivative of outputs into the system. Then differential geometric method is applied to transform the regularized system into a simple normal form, for which a Luenberger-like observer is proposed

Unknown Input Functional Observability of Descriptor Systems with Neutral and Distributed Delay Effects

International audienceIn this paper a general class of linear systems with time-delays is considered, which includes linear classical systems, linear systems with commensurate delays, neutral systems and singular systems with delays. After given a formal definition of functional backward observability (BO), an easily testable condition is found. The fulfillment of the obtained condition allows for the reconstruction of the trajectories of the system under consideration using the actual and past values of the system output and some of its derivatives. The methodology we follow consists in an iterative algorithm based upon the classical Silverman algorithm used for inversion of linear systems. By using basic module theory we manage to prove that the proposed algorithm is convergent. A direct application of studying functional observability is that a condition can be derived for systems with distributed delays also, we do this as a case of study. The obtained results are illustrated by two examples, one is merely academic but illustrates clearly the kind of systems which the proposed methodology works for and the other is a practical system with distributed delays

Observability and Detectability of Singular Linear Systems with Unknown Inputs

International audienceIn this paper the strong observability and strong detectability of a general class ofsingular linear systems with unknown inputs are tackled. The case when the matrix pencil is non-regular is comprised (i.e., more than one solution for thedifferential equation is allowed). It is shown that, under suitableassumptions, the original problem can be studied by means of a regular(non-singular) linear system with unknown inputs and algebraic constraints.Thus, it is shown that for purposes of analysis, the algebraic equations canbe included as part of an extended system output. Based on this analysis, weobtain necessary and sufficient conditions guaranteeing the observability (or detectability) of the system in terms of the zeros of the system matrix.Corresponding algebraic conditions are given in order to test theobservability and detectability. A formula is provided that expresses thestate as high order derivative of a function of the output, which allows forthe reconstruction of the actual state vector. It is shown that the unknown inputs may be reconstructed also

Observability and Detectability of Singular Linear Systems with Unknown Inputs

International audienceIn this paper the strong observability and strong detectability of a general class of singular linear systems with unknown inputs are tackled. The case when the matrix pencil is non-regular is comprised (i.e., more than one solution for the differential equation is allowed). It is shown that, under suitable assumptions, the original problem can be studied by means of a regular (non-singular) linear system with unknown inputs and algebraic constraints. Thus, it is shown that for purposes of analysis, the algebraic equations can be included as part of an extended system output. Based on this analysis, we obtain necessary and sufficient conditions guaranteeing the observability (or detectability) of the system in terms of the zeros of the system matrix. Corresponding algebraic conditions are given in order to test the observability and detectability. A formula is provided that expresses the state as high order derivative of a function of the output, which allows for the reconstruction of the actual state vector. It is shown that the unknown inputs may be reconstructed also

Fault estimation algorithms: design and verification

The research in this thesis is undertaken by observing that modern systems are becoming more and more complex and safety-critical due to the increasing requirements on system smartness and autonomy, and as a result health monitoring system needs to be developed to meet the requirements on system safety and reliability. The state-of-the-art approaches to monitoring system status are model based Fault Diagnosis (FD) systems, which can fuse the advantages of system physical modelling and sensors' characteristics. A number of model based FD approaches have been proposed. The conventional residual based approaches by monitoring system output estimation errors, however, may have certain limitations such as complex diagnosis logic for fault isolation, less sensitiveness to system faults and high computation load. More importantly, little attention has been paid to the problem of fault diagnosis system verification which answers the question that under what condition (i.e., level of uncertainties) a fault diagnosis system is valid. To this end, this thesis investigates the design and verification of fault diagnosis algorithms. It first highlights the differences between two popular FD approaches (i.e., residual based and fault estimation based) through a case study. On this basis, a set of uncertainty estimation algorithms are proposed to generate fault estimates according to different specifications after interpreting the FD problem as an uncertainty estimation problem. Then FD algorithm verification and threshold selection are investigated considering that there are always some mismatches between the real plant and the mathematical model used for FD observer design. Reachability analysis is drawn to evaluate the effect of uncertainties and faults such that it can be quantitatively verified under what condition a FD algorithm is valid. First the proposed fault estimation algorithms in this thesis, on the one hand, extend the existing approaches by pooling the available prior information such that performance can be enhanced, and on the other hand relax the existence condition and reduce the computation load by exploiting the reduced order observer structure. Second, the proposed framework for fault diagnosis system verification bridges the gap between academia and industry since on the one hand a given FD algorithm can be verified under what condition it is effective, and on the other hand different FD algorithms can be compared and selected for different application scenarios. It should be highlighted that although the algorithm design and verification are for fault diagnosis systems, they can also be applied for other systems such as disturbance rejection control system among many others