A Multi-observer Approach for Parameter and State Estimation of Nonlinear Systems with Slowly Varying Parameters

Abstract

Abstract This manuscript addresses the parameter and state estimation problem for continuous time nonlinear systems with unknown slowly time-varying parameters, which are assumed to belong to a known compact set. The problem is tackled by using the multi-observer approach under the supervisory framework, which generates parameter and state estimates by using a finite number of sample points of the parameter set, a bank of observers, a set of monitoring signals and a selection criterion. This note proposes a novel dynamic sampling policy for the multi-observer technique and studies its convergence properties. We prove that the parameter and state estimation errors are ultimately bounded where the ultimate bounds can be made arbitrarily small if the parameter varies sufficiently slowly, and the number of samples is sufficiently large.