Original Descriptor System Research Articles

Joint unknown input observer for descriptor system based on interval observer

In this paper, a novel joint unknown input observer (JUIO) is proposed for a class of descriptor systems. The unknown input (UI) to be estimated injects additively into both the state and output equations in a state space model. To the best of our knowledge, only a few contributions in existing work address this problem directly. To begin with, by introducing an auxiliary UI, the original system is transformed into a normal form in which the output is no longer affected by UI. In this way, the negative effect brought by the UI occurring in the output measurement is removed. An interval observer is developed to obtain upper and lower boundary estimates of the output of the reformulated system. After that, an algebraic relationship between the auxiliary UI and the states is established, and a UI reconstruction (UIR) method is developed. Based on the UIR, a JUIO comprising the UIR and a Luenberger-like state observer is developed to achieve asymptotic estimations of the UI and state simultaneously. Verifiable conditions for the existence of the proposed JUIO are given with respect to the original descriptor system. Finally, a simulation example is presented to verify the effectiveness of the proposed method.

An Identification Approach for Descriptor Systems

This letter proposes a novel identification approach for linear time-invariant descriptor systems based on input-state-output data. Under the assumption of regularity, the equivalent inverse form of the descriptor system is firstly introduced. Then two groups of data experiments are designed, and corresponding input, state and output data are collected. Furthermore, the parameters of the inverse form are uniquely identified based on those data sets. Since the inverse form possesses the same state, input, output signals and input-output transfer function as the original descriptor system, the identification is completed. Finally, an electrical circuit system is provided to illustrate the effectiveness of our method.

Robust fusion filter for multisensor descriptor system with uncertain‐variance noises and packet dropout

AbstractFor the multisensor linear stochastic descriptor system with uncertain‐variance noises and packet dropout, the standard state space model of the new reduced‐order augmented state is obtained based on the singular value decomposition (SVD) approach and augmented state approach. By applying the min‐max robust estimation principle and Kalman filtering theory, the local robust time‐varying Kalman filters of the reduced‐order augmented state and fictitious process noise are proposed. Then, the local robust time‐varying filters of the original descriptor system are presented according to the relation of the reduced‐order augmented state and the original state. And the distributed and covariance intersection (CI) fusion robust time‐varying filters are presented, and the actual and conservative filtering error variances are obtained. Further, the robustness of the local and fused robust filters are proved by applying Lyapunov equation approach, and the accuracy relation between them is analyzed. A simulation example applied to a circuit system shows its effectiveness and applicability.

Robust time‐varying estimator for descriptor system with random one‐step measurement delay

AbstractFor the linear stochastic descriptor system with random one‐step measurement delay and uncertain‐variance correlated noises, the robust estimation problem is addressed. Applying the singular value decomposition method, augmented state approach and fictitious noise approach, the original descriptor system is transformed to new standard system only with uncertain‐variance fictitious noises. Based on Kalman filtering and the minimax robust estimation principle, the actual Kalman estimator for the proposed standard system with actual measurement and the upper bounds of the variances is presented, including the Kalman predictor, filter, smoother and white noise deconvolution estimator. According to the relation of the new standard system and the original system, the actual estimator of original state of descriptor system and actual estimation error variance are presented. Further, the robustness of the actual estimator is proved by the Lyapunov equation approach, that is, the actual estimation error variance is guaranteed to have minimal upper bound for all admissible uncertainties. A simulation example about circuits system verifies the correctness and effectiveness of the proposed results.

Formal Control Synthesis via Simulation Relations and Behavioral Theory for Discrete-Time Descriptor Systems

The control and verification of industrial processes, modeled as discrete-time descriptor systems, is often computationally hard due to the presence of both algebraic couplings and difference equations. In this article, we introduce a new control synthesis method for descriptor systems which is based on formal abstractions and enables control design over related reduced-order models. We leverage notions of exact and approximate similarity relations, which hold for the algebraic couplings that are inherent to descriptor systems. Using the behavioral framework, we extend a control refinement scheme for classical dynamical systems and develop a corresponding notion for descriptor systems: We show that any given well-posed controller of the abstract (reduced-order) descriptor system can be refined to a controller for the original descriptor system. The resulting controlled system preserves the same controlled output behavior in the case of exact similarity, whereas in the case of approximate similarity, the output behavior of the controlled descriptor system is shown to have a bounded deviation from that of the abstract model where the controller is designed.

Impulse Elimination and Fault-Tolerant Preview Controller Design for a Class of Descriptor Systems

In this paper, a fault-tolerant preview controller is designed for a class of impulse controllable continuous time descriptor systems with sensor faults. Firstly, the impulse is eliminated by introducing state prefeedback; then an algebraic equation and a normal control system are obtained by restricted equivalent transformation for the descriptor system after impulse elimination. Next, the model following problem in fault-tolerant control is transformed into the optimal regulation problem of the augmented system which is constructed by a general method. And the final augmented system and its corresponding performance index function are obtained by state feedback for the augmented system constructed above. The controller with preview effect for the final augmented system is attained based on the existing conclusions of optimal preview control; then, the fault-tolerant preview controller for the original system is obtained through integral and backstepping. The relationships between the stabilisability and detectability of the final augmented system and the corresponding characteristics of the original descriptor system are also strictly discussed. The effectiveness of the proposed method is verified by numerical simulation.

Luenberger-like interval observer design for discrete-time descriptor linear system

In this paper, the problem of Luenberger-like interval observer design for discrete-time descriptor linear system is investigated. In the first place, two ways in which the original descriptor system is transformed into general systems are given and the detectability of the equivalent general systems is discussed in detail. A new equivalent general system construction is developed and we prove that the detectability can be kept under this new equivalent transformation. After this, based on the new equivalent general system, a Luenberger-like interval observer is proposed. Finally, two simulation examples are given to demonstrate the correctness and the effectiveness of the proposed interval observer.

Interpolatory model reduction for quadratic-bilinear systems using error estimators

Purpose The purpose of this paper is to propose an interpolation-based projection framework for model reduction of quadratic-bilinear systems. The approach constructs projection matrices from the bilinear part of the original quadratic-bilinear descriptor system and uses these matrices to project the original system. Design/methodology/approach The projection matrices are constructed by viewing the bilinear system as a linear parametric system, where the input associated with the bilinear part is treated as a parameter. The advantage of this approach is that the projection matrices can be constructed reliably by using an a posteriori error bound for linear parametric systems. The use of the error bound allows us to select a good choice of interpolation points and parameter samples for the construction of the projection matrices by using a greedy-type framework. Findings The results are compared with the standard quadratic-bilinear projection methods and it is observed that the approximations through the proposed method are comparable to the standard method but at a lower computational cost (offline time). Originality/value In addition to the proposed model order reduction framework, the authors extend the one-sided moment matching parametric model order reduction (PMOR) method to a two-sided method that doubles the number of moments matched in the PMOR method.

Reduced-order switched UIO design for switched discrete-time descriptor systems

In this paper, a reduced-order switched unknown input observer design is investigated for switched discrete-time descriptor systems. By a series of equivalent transformations, the original descriptor system with unknown inputs is transformed into a reduced-order standard system without unknown inputs, and then a switched reduced-order unknown input observer is designed by using standard switched system stability analysis techniques. Besides, the sufficient condition for the existence of the switched observer is also discussed in detail. Moreover, based on the state estimation, a delayed unknown input reconstruction method is also proposed. Finally, two simulation examples are given to show the effectiveness of the proposed methods.

Computation of State Reachable Points of Second Order Linear Time-Invariant Descriptor Systems

This paper considers the problem of computing the state reachable points (from the origin) of a linear constant coefficient second order descriptor system. A new method is proposed to compute the reachable set in a numerically stable way. The original descriptor system is transformed into a strangeness-free system within the behavioral framework followed by a projection that separates the system into different order differential and algebraic equations while keeping the original state variables. This reformulation is followed by a first order formulation that avoids all unnecessary smoothness requirements. For the resulting first order system, it is shown that the computation of the image space of two matrices, associated with the projected system, is enough to numerically compute the reachable set. Moreover, a characterization is presented of all the inputs by which one can reach an arbitrary point in the reachable set. These results are used to compute two different types of reachable sets for second order systems. The new approach is demonstrated through a numerical example.

Optimal recursive estimation for networked descriptor systems with packet dropouts, multiplicative noises and correlated noises

This paper addresses the optimal linear estimation problem for a class of networked descriptor systems with multiple packet dropouts, measurement multiplicative noises and finite-step correlated process and measurement noises. Based on a fast–slow subsystem decomposition approach (FSD), the descriptor system is transformed into two reduced-order linear nonsingular subsystems with finite-step correlated noises. Optimal linear estimators including filter, predictor and smoother with corresponding estimation error covariance matrices for the states and noises of new systems are developed via the innovation analysis approach. Then, the optimal linear estimators are obtained for the original descriptor system. An example shows the effectiveness of the proposed algorithms.

Weighted measurement fusion Kalman estimator for multisensor descriptor system

For the multisensor linear stochastic descriptor system with correlated measurement noises, the fused measurement can be obtained based on the weighted least square (WLS) method, and the reduced-order state components are obtained applying singular value decomposition method. Then, the multisensor descriptor system is transformed to a fused reduced-order non-descriptor system with correlated noise. And the weighted measurement fusion (WMF) Kalman estimator of this reduced-order subsystem is presented. According to the relationship of the presented non-descriptor system and the original descriptor system, the WMF Kalman estimator and its estimation error variance matrix of the original multisensor descriptor system are presented. The presented WMF Kalman estimator has global optimality, and can avoid computing these cross-variances of the local Kalman estimator, compared with the state fusion method. A simulation example about three-sensors stochastic dynamic input and output systems in economy verifies the effectiveness.

Preview control for impulse-free continuous-time descriptor systems

This paper studies the preview control problem of impulse-free linear continuous-time descriptor systems. The system is first decomposed into a normal system (i.e., slow subsystem) and an algebraic equation set, by restricted equivalent linear transformation. Then, applying the method of preview control theory to the slow subsystem, by taking derivatives on both the error vector and the state function, and with the error vector being a part of the new state vector, the augmented system is constructed and the tracking problem is transformed into a regulation problem. According to preview control theory, the controller of the augmented system can be obtained and the control input of the original descriptor system with preview function can be acquired by integrating on the controller of the augmented system. Both the stabilisability and detectability of the augmented system are discussed. Numerical simulation verifies the presented results.

Recursive estimation for descriptor systems with multiple packet dropouts and correlated noises

In this paper, the problem of recursive estimation is studied for a class of descriptor systems with multiple packet dropouts and correlated noises. The multiple packet dropouts phenomenon is considered to be random and described by a binary switching sequence that obeys a conditional probability distribution. The autocorrelated measurement noise is characterized by the covariances between different time instants. The descriptor system is transformed into a regular line system with an algebraic constraint. By using an innovation analysis method and the orthogonal projection theorem, recursive estimators including filter, predictor and smoother are developed for each subsystem and the process noise. Further, the recursive filter, predictor and smoother are obtained for the original descriptor system with possible multiple packet dropouts phenomenon and correlated noises. Simulation results are provided to demonstrate the effectiveness of the proposed approaches.

Full-Order Filters and Smoothers for Descriptor Systems with Delayed Measurements

This paper is concerned with the filtering problem for descriptor system with measurement delays. Using full-order transformation, the original descriptor system with delayed measurements is transferred to the normal system with delayed state and delayed measurements. Based on the projection theory, the filter and smoother of the normal system are derived. Then, the full-order filter and smoother of the original descriptor system are given. The proposed estimators avoid the high-dimensional computation from state augmentation. Simulation research verifies the effectiveness of the proposed algorithm.

Descriptor recursive estimation for multiple sensors with different delay rates

In this article, the problem of recursive estimation is studied for a class of descriptor systems measured by multiple sensors with different delay rates. The delay phenomenon occurs in a random way and the delay rate for each sensor is characterised by an individual binary switching sequence obeying a conditional probability distribution. The original descriptor system is transformed into two non-descriptor stochastic subsystems with autocorrelated and cross-correlated noises by using the singular-value decomposition and the state augmentation. Applying an innovation analysis approach and the orthogonal projection theorem, recursive estimators including filter, predictor and smoother are first derived for each subsystem and the process noise. Then, based on the newly obtained recursive state estimators and process noise estimators, the recursive filter, predictor and smoother are obtained for the original descriptor system measured by multiple sensors with different delay rates. A numerical simulation example is exploited to show the effectiveness of the proposed approaches.