Convergence properties of a Continuous-Time Multiple-Model Adaptive Estimator

We present and study a Continuous-Time Multiple-Model Adaptive Estimator (CT-MMAE) for state-affine multiple-input-multiple output (MIMO) systems with parametric uncertainty. The CT-MMAE is composed by a bank of local observers (typically Kalman filters) where each observer uses one element of a finite discrete parameter set in its implementation. The state estimate is given by a weighted sum of the estimates produced by the bank of observers. We show, for the case where the unknown noise and disturbance are L₂ signals, and under appropriate observability assumptions, that if the actual plant parameter is identical to one of its discrete values, the state estimate converges globally asymptotically to the true value and the plant model is correctly identified. If the actual plant parameter vector does not belong to the finite discrete parameter set, we provide upper bounds to state and parameter estimation errors. Some deterministic and stochastic simulation results are presented and discussed.