Multiple Model Adaptive Estimation and model identification usign a Minimum Energy criterion

Abstract

This paper addresses the problem of Multiple Model Adaptive Estimation (MMAE) for discrete-time, linear, time-invariant MIMO plants with parameter uncertainty and unmodeled dynamics. Model identification is analyzed in a deterministic setting by adopting a Minimum Energy selection criterion. The MMAE system relies on a finite number of local observers, each designed using a selected model (SM) from the original set of possibly infinite plant models. Results akin to those previously obtained in a stochastic setting are derived in a far simpler manner, in a deterministic framework. We show, under suitable distinguishability conditions, that the SM identified is the one that corresponds to the observer with smallest output prediction error energy. We also develop a procedure to analyze the behavior of MMAE when the true plant is not one of the SMs. This leads to an algorithm that computes, for each SM, the set of equivalently identified plants, that is, the set of plants that will be identified as that particular SM. The impact of unmodeled dynamics on model identification is discussed. Simulation results with a model of a motor coupled to a load via an elastic shaft illustrate the performance of the methodology derived.

Extending the Kalman filter for structured identification of linear and nonlinear systems

“…The EKF is naturally adapted to estimation of states and parameters of nonlinear models, and several authors have already used it for parameter or combined state and parameter estimation of structured nonlinear models (Kallapur et al, 2008;Hassani et al, 2009). The new IEKF is consequently also well-suited to identification of nonlinear models in the form of equations (1) and (2), and this can be achieved quite generally; for any smooth functions f, h, it can operate using the same set of equations (4), (11) to (14).…”

“…Examples include (Kallapur et al, 2008;Hassani et al, 2009;Best, 2007;Best et al, 2000). In this paper, we re-visit the Kalman filter, but address many of the concerns above, identifying a MIMO model of unknown structure and minimum parameter set using an iterative time-domain approach.…”

Adaptive Wave Filtering for Dynamic Positioning of Marine Vessels using Maximum Likelihood Identification: Theory and Experiments

“…Assuming that the distinguishablity condition in Hassani et al (2009a) and Hassani et al (2013a) are satisfied, the parameter estimateθ(t) in (23) and (26) coincide. Moreover, the parameter estimateθ(t) in (25) converges to the one in (23) and (26) asymptotically.…”

“…Before proving the lemma, let us introduce the Baram index (see Baram and Sandell (1978)) and summarize the main results in Hassani et al (2009a) and Hassani et al (2013a). It is shown in Hassani et al (2009a) and Hassani et al (2013a) that under some distinguishingly conditions, as t → ∞, one of the posterior probabilities governed by (24) (the a posterior probability associated with the KF designed based on the closet model to the true plant in a well defined sense), say p j , converges to 1 and the rest converge to 0.…”

“…It is shown in Hassani et al (2009a) and Hassani et al (2013a) that under some distinguishingly conditions, as t → ∞, one of the posterior probabilities governed by (24) (the a posterior probability associated with the KF designed based on the closet model to the true plant in a well defined sense), say p j , converges to 1 and the rest converge to 0. Moreover, it is shown that…”