Application of Dirichlet Distribution for Polytopic Model Estimation

The polytopic model (PM) structure is often used in the areas of automatic control and fault detectionand isolation (FDI). It is an alternative to the multiple model approach which explicitly allowsfor interpolation among local models.This thesis proposes a novel approach to PM estimation by modeling the set of PM weights asa random vector with Dirichlet Distribution (DD). A new approximate (adaptive) PM estimator,referred to as a Quasi-Bayesian Adaptive Kalman Filter (QBAKF) is derived and implemented.The model weights and state estimation in the QBAKF is performed adaptively by a simple QBweights’ estimator and a single KF on the PM with the estimated weights. Since PM estimationproblem is nonlinear and non-Gaussian, a DD marginalized particle filter (DDMPF) is also developedand implemented similar to MPF. The simulation results show that the newly proposedalgorithms have better estimation accuracy, design simplicity, and computational requirements forPM estimation.