Identification and Convergence Analysis of a Class of Continuous-Time Multiple-Model Adaptive Estimators

Abstract

This paper discusses the identification and convergence, in a deterministic setting, of a class of Continuous-Time Multiple-Model Adaptive Estimators (CT-MMAE) for state-affine multiple-input-multiple-output systems with parametric uncertainty. The CT-MMAE is composed by a dynamic weighting signal generator and a bank of local continuous-time observers where each observer is designed using one element of a finite discrete model (parameter) set. The state estimate is generated by a weighted sum of the estimates produced by the bank of observers and the parameter estimate is selected to be the one that corresponds to the weighted signal with the largest value. We show that under suitable persistent of excitation like conditions the model identified is the one that exhibits less output error “power”. Furthermore, a distance-like metric between the true plant and the identified model is derived. We also provide conditions for convergence of the state estimation error and for ℒ2 and ℒ∞ input-to-state stability. These deterministic continuous time results complement existing knowledge for stochastic discrete-time MMAE designs.