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

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.