On-line input identification and application to Active Noise Cancellation

We give an overview of a recent method we proposed for the solution of on-line deconvolution problems, which can be applied to Active Noise Cancellation (ANC). The method has been studied both for lumped parameter systems and for distributed systems in input–output and in state space form. Finally, we show that the identification algorithm can be extended to identify inputs to systems modelled by partial differential equations with infinite memory. Such class of equations are encountered in different applications: thermal processes with finite diffusion speed, viscoelasticity, nonfickian diffusion… So, this identification problem is of interest for example in thermodynamics, biology or pharmacology, when the immission of a solute – a drug for example – has to be detected. The analysis of this example will give a feeling of the methods of proof used in this kind of study.