Adaptive identification of distributed parameters in nonlinear PDE setting: Sine–Gordon case study

The primary concern of the work is to develop adaptive identification approach to uncertain dynamic systems governed by nonlinear partial differential equations. The well-known nonlinear sine-Gordon PDE model, which describes distributed wave dynamics (e.g., of continuum of interacting oscillators), serves as a testbed. It is shown that the sine-Gordon model with uncertain external force and viscous friction, which are distributed in space, is identifiable over the entire state measurement provided that it is excited by a specific nonzero input. Numerical simulations support the theory in the case where unknown plant parameters are spatially invariant.