Tarek Raïssi

This article aims at investigating distributed interval estimation methods for continuous-time linear time-invariant (LTI) systems. By allying a robust observer design method and interval analysis techniques, we develop a novel two-step interval estimation method for LTI systems whose outputs are measured by a series of nodes connected via a given directed graph. First, a distributed observer formed by a group of local observers is designed via an $H_{\infty } $ approach to obtain an accurate point-valued estimation. This estimation is completed by a reliable interval-valued estimation achieved by a rigorous set-valued analysis of the estimation error dynamics. In order to further enhance the accuracy of the estimated intervals, an elimination by inconsistency technique is applied to characterize the smallest common interval containing the actual state vector of the system. Compared with the existing distributed interval observer approaches, the proposed method can effectively enhance the tightness of the estimated state intervals. Simulation results are shown to support the theoretical findings.

Control and state estimation procedures need to be robust against imprecisely known parameters, uncertainty in initial conditions, and external disturbances. Interval methods and other set-based techniques form the basis for the implementation of powerful approaches that can be used to identify parameters of dynamic system models in the presence of the aforementioned types of uncertainty. Moreover, they are applicable to a verified feasibility and stability analysis of controllers and state estimators. In addition to these approaches which are typically used offline for analysis of system models designed with classical floating point procedures, interval and set-based methods have also been developed in recent years, which allow to directly solve the associated design tasks and to implement reliable techniques that are applicable online, i.e., during system operation. The latter approaches include set-based model predictive control, online parameter adaptation techniques for nonlinear variable-structure and backstepping controllers, interval observers, and fault diagnosis techniques. This paper provides an overview of the methodological background and reviews numerous practical applications for which interval and other set-valued approaches have been employed successfully.

This article investigates interval estimation for continuous-time linear time-invariant systems with discrete measurements. To obtain a reliable interval estimation, a novel interval estimation method is proposed by combining a robust observer gain design approach with an interval analysis method. First, a robust observer synthesis approach is adopted to compute an observer gain to improve the accuracy of the pointwise estimation when the discrete measurements are available. In the case of aperiodic discrete-time measurements, a polytopic model with an additive norm-bounded term is proposed to characterize the uncertainties induced by the time-varying character of the intermeasurement interval times. Then, to cope with these uncertainties, a robust observer design method is introduced. Based on the obtained pointwise estimation, an interval estimation is achieved via an interval-based explicit reachability method. Compared with the existing results, the proposed method relies on nonrestrictive assumptions and provides high estimation performance. Simulation results are presented to illustrate the effectiveness and superiority of the proposed method.

This study deals with passive Fault Tolerant Control (FTC) based on Functional Interval Observers (FIO) for Linear Parameter‐Varying systems. First, positive systems theory is used to design an asymptotic FIO, giving the upper and lower bounds of the state variable function. Next, an norm‐based method is proposed to attenuate the effect of uncertainties and to improve the accuracy of the proposed observer. Then, a FIO‐based FTC law is designed to reduce the fault effect and stabilize the closed‐loop system based on an index. Stability conditions are expressed in terms of Linear Matrix Inequalities. Finally, a simulation example is given to verify the effectiveness of the proposed techniques.