M. Zasadzinski

Reduced-order observer design for descriptor systems with unknown inputs

A new method for the design of reduced-order observers for descriptor systems with unknown inputs is presented. The approach is based on the generalized constrained Sylvester equation. Sufficient conditions for the existence of the observer are given.

Brief Extension of minimum variance estimation for systems with unknown inputs

In this paper, we address the problem of minimum variance estimation for discrete-time time-varying stochastic systems with unknown inputs. The objective is to construct an optimal filter in the general case where the unknown inputs affect both the stochastic model and the outputs. It extends the results of Darouach and Zasadzinski (Automatica 33 (1997) 717) where the unknown inputs are only present in the model. The main difficulty in treating this problem lies in the fact that the estimation error is correlated with the systems noises, this fact leads generally to suboptimal filters. Necessary and sufficient conditions for the unbiasedness of this filter are established. Then conditions under which the estimation error and the system noises are uncorrelated are presented, and an optimal estimator and a predictor filters are derived. Sufficient conditions for the existence of these filters are given and sufficient conditions for their stability are obtained for the time-invariant case. A numerical example is given in order to illustrate the proposed method.

Brief Residual generator design for singular bilinear systems subjected to unmeasurable disturbances: an LMI approach

In this paper, a method to design a bank of unknown input residual generator for fault detection and isolation is investigated. The plant model is assumed to be a bounded control inputs singular bilinear systems subjected to unknown disturbances. The measurements can be bilinear.

Kalman filtering for continuous descriptor systems

This paper deals with the problem of the state estimation for continuous stochastic descriptor systems. A new method, based on linear transformations which lead to a stochastic differential algebraic equation, is developed. Uniqueness of the estimate is achieved by choosing the optimum gain matrix which minimizes the trace of the error covariance matrix for the static subsystem, while the standard Kalman filter is derived for the dynamic subsystem. Necessary and sufficient conditions for the convergence and stability of the proposed estimator are established.

REDUCED-ORDER OBSERVER-BASED POINT-TO-POINT AND TRAJECTORY CONTROLLERS FOR ROBOT MANIPULATORS

This paper presents a design procedure for a reduced-order observer-based controller dedicated to n-joint robot manipulators. It is assumed that only the joint angular positions are measured. The joint angular velocities are estimated via an exponential reduced-order observer. Two types of control laws based on this observer are studied: point-to-point control with gravity compensation and trajectory control. Sufficient conditions to ensure the closed-loop stability are given. Performances of the reduced-order observer used with these two control laws are illustrated in a simulation study of a two-degrees-of-freedom robot manipulator.

Connection between the three-block generalized Riccati equation and the standard Riccati equation

Nikoukhah et al. (1992) developed a maximum likelihood descriptor Kalman filter the properties of which are governed by a three-block generalized Riccati difference equation (GRDE). The convergence of this GRDE has been studied and the generalization of the eigenvector approach to solving the associated generalized algebraic Riccati equation has been carried out. In this paper, the authors connect the GRDE to the standard Riccati equation to point out Nikoukhahs results from well-known results obtained in standard Kalman filtering. Moreover, while the previous study provides only sufficient conditions on the convergence and stability of the three-block descriptor Kalman filter, the relationship established herein allows the authors to derive necessary and sufficient conditions. In addition, several descriptor Kalman filtering problems can be treated as in the standard case. >

Robust reduced order unbiased filtering for uncertain systems

This paper presents a simple solution to the robust unbiased functional reduced order filtering problem in the case of uncertain systems described by Integral Quadratic Constraint (IQC). The existence condition of the unbiased filter is expressed through a rank relation. Then the filter is designed via Linear Matrix Inequalities coupled with an equality constraint. The results obtained in this paper are applicable to unstable systems. The approach is illustrated by a numerical example.

Disturbance decoupled diagnostic observer for singular bilinear systems

In this paper, a method to design a bank of unknown input residual generator for fault detection and isolation is investigated. The plant model is assumed to be a bounded controlled input singular bilinear system, subjected to unknown disturbances. The measurements can be bilinear.

Unknown input reduced order observer for singular bilinear systems with bilinear measurements

In this paper, a method to design a reduced-order unknown input observer (UIO) for bounded control input singular bilinear systems (SBS) with bilinear measurements and subjected unknown disturbances is investigated. The design of this UIO is divided into two parts. The first one consists in solving some algebraic constraints to obtain an observation error which is decoupled from the unknown disturbances. In the second part, an LMI is solved to ensure the exponential stability of the reconstruction error for all admissible control inputs and unmeasurable disturbances.

State observers for a class of bilinear descriptor systems subjected to unmeasurable disturbances

The class of singular bilinear systems (SBS) subjected to unmeasurable disturbances for which there exists an unknown input observer (UIO) with a linear observation error dynamics is characterised. Necessary and sufficient conditions for the existence of this UIO are given. It is shown that the design of such an UIO is equivalent to the design of an UIO for an appropriate singular linear system (SLS). Both full- and reduced-order UIOs are treated.