Robust on-line parameter identification with general knowledge on level of information noise: continuous and discrete cases

A robust on-line parameter identification problem is posed and solved for systems with general knowledge of the level of the inherent information noise. Both continuous-time and discrete-time cases are considered in this paper. For the former case, the knowledge can be the bound on either the magnitude or the finite-time L^p norm, p∈[1, ∞), of the noise. Whereas for the latter case, it can be the bound on either the magnitude or the finite-index l^p norm, p∈[1, ∞), of the noise. Based on the knowledge, a switching type algorithm is proposed to estimate the parameters of the system from the available input-output data. In spite of the existence of the information noise, this on-line algorithm guarantees that the estimation error is monotonically decreasing, and the parameter estimate is convergent to a steady state value under a mild condition