Adaptive electrodeposition process control through Zakai filtering

• The deposition process is influenced by unmodelled side reactions and is given by a diffusion process model whose main parameters are unknown.
• The deposition process can be boundary controlled using feed-forward and feedback controls adapted with the parameters estimated by means of Zakai filtering.
• The consistency of estimates and the stabilising property of adaptive controls are validated numerically.

The stochastic evolutionary process inspired by the electrodeposition of metal ions on an electrode surface is considered in one dimension. The process is fixed on one boundary and is observed-controlled on the other boundary where the process is additionally influenced by unmodelled side reactions – their effect on the boundary is considered as a random process applied to the controls and measurements. The electrodeposition process is given by a diffusion process model, whose main parameters are unknown – the diffusivity of species and the thickness of the diffusion layer are unknown and no knowledge is available about the current losses in the plating bath or the throwing power of the electrolyte. Furthermore the side reactions have an unknown systematic component. Even so this paper verifies that the electrodeposition process can be boundary controlled using feed-forward and feedback controls adapted with the parameters estimated by Zakai filtering. The consistency of the estimates as well as the stabilising property of the adaptive controls is validated by simulations.