Le 26 novembre 2018

Advances in Kalman-Type Filtering for Discrete Dynamic Systems

Nelson Eduardo Castaño et Giraldo Jose Perea Arango *

* Doctorants au LAREMA en co-tutelle avec l'Université de Medellin en Colombie, encadrés par Piotr Graczyk (LAREMA) et Vadim Azhmyakov (Université de Medellin)

Abstract:

In our talk we deal with a nonspecific robust Kalman Filter (KF) applied to a class of discrete stochastic dynamic processes. We consider the conventional-type estimation (identification) problem as well as the parametrized version of the dynamic system, namely, the controlled stochastic model. The robustness concept is understood here with respect to a family of probability distributions under consideration. This approach constitutes a natural generalization of the conventional Gaussian normality hypothesis. Moreover, we also incorporate a realistic “bounded resources” assumption into the KF modelling approach. The last one is mathematically expressed as a specific restricted norm optimization problem.

The above two formal generalizations, namely, the proposed robustification (consideration of a specific family of probability distributions) and additional (practically motivated) restrictions in the main KF optimization problem involve an absolutely new form of a resulting estimation algorithm. In our talk we give a rigorous presentation of the necessary theoretical facts and also discuss some initial (conceptual) numerical aspects.

Finally we hope to develop an implementable computational scheme for a “worst case” robust process estimation and the corresponding KF based control. The question of effectiveness of the proposed algorithm constitutes applicable parts of the both PhD projects we present. The newly elaborated KF approach will next be applied to a LQ-type discrete Optimal Control Problem (the first PhD title presented above) and also to an optimal price marketing strategy (see the second PhD title).