Further results on plant parameter identification using continuous-time multiple-model adaptive estimators

This paper describes a deterministic approach to adaptive state and parameter estimation using a multiple model structure. In the set-up adopted, the plant of interest is described by a finite dimensional model with parametric uncertainty. To each choice of a finite number of parameter values there corresponds a finite set of multiple design models and a corresponding set of observers. Assuming the latter have been chosen, a dynamic weighting signal generator (DWSG) performs on-line adaptation of the weights given to the individual observer estimates based on the energy of the output error signals. In the present paper we develop a distance-like pseudo norm between the true plant and the identified model in a deterministic setting, based on the energy of the output error signals. Furthermore we show, under a distinguishability condition, that the model identified is the one that is closest to the true plant in the defined deterministic norm. We also prove that the convergence of the parameter estimate is exponentially fast. Performance and convergence of the CT-MMAE procedure are illustrated with Monte-Carlo simulation runs using the model of an inverted pendulum.