Online parameter identification without Ricatti-type equations in a class of time-dependent partial differential equations: an extended state approach with potential to partial observations

This is the authors' abstract. We don't add key points for this paper.

Online parameter identification for dynamical systems is the task of estimating model parameters simultaneously to the time evolution of the physical state and plays a crucial role in adaptive control. The existing techniques for time-dependent partial differential equations exclude the case of partial state observations or require to solve online Ricatti-type operator evolution equations accompanied with high computational costs. In this paper we suggest and analyze an extended state approach to online parameter identification in a class of possibly nonlinear PDEs that avoids Ricatti-type equations but still has the potential to allow for partial state observations. Numerical examples underline the feasibility of our method.