The Adaptive Integral Multi-Observer with Switched Moving Windows

W. Byrski and M. Pelc (Poland)


State Observers, Finite Time Observers, Deadbeat Observers, Kalman Filter.


In the paper the new results of application of optimal integral state observer are presented. The integral moving window observers based on finite time observation reconstruct the state exactly. This property is contrary to properties of differential observers like Kalman Filter and Luenberger type observer, which are only estimators and reconstruct the state asymptotically. The optimality of integral observers is connected with their minimal norm. If the measurement disturbances can be neglected (perfect input-output measurements) any finite time integral observer will reconstruct the state exactly. In real applications the measurements are often affected by disturbances. Hence, the choice from the set of many different exact observers that one with minimal norm guaranties the minimal state reconstruction error. The norm of the observer is function of two parameters: the input/output disturbance norm ratio and the width T of current observation window [ t-T, t]. The new idea of the best integral observer application is based on off-line preparation of a few different optimal observer versions for a few chosen intervals Ti and then based on current level of noise adaptive choice of the best observer.

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