Simultaneous identification of time-varying parameters and estimation of system states using iterative learning observers

This article presents the design of an iterative learning observer (ILO) for the purpose of estimating system states while simultaneously identifying time-varying parameters. The proposed ILO uses a novel updating mechanism to identify time-varying parameters instead of using integrators which are commonly used in classical adaptive observers to identify constant parameters while estimating system states. The main idea behind the design of the ILO is the use of learning, i.e. previous information is combined into the ILO for identifying time-varying parameters in real time. Stability and convergence of state and parameter estimation errors are established and proven. An illustrative example exhibits the effectiveness of the proposed ILO.