Data-Driven Boundary Control of Distributed Port-Hamiltonian Systems
This addresses the problem of model uncertainty in physical system control for engineers, but it is incremental as it builds on existing dPHS and GP methods.
The paper tackled the challenge of controlling distributed Port-Hamiltonian systems with unknown dynamics by combining Gaussian Process learning with boundary control, resulting in probabilistic bounds for closed-loop stability demonstrated on a simulated shallow water system.
Distributed Port-Hamiltonian (dPHS) theory provides a powerful framework for modeling physical systems governed by partial differential equations and has enabled a broad class of boundary control methodologies. Their effectiveness, however, relies heavily on the availability of accurate system models, which may be difficult to obtain in the presence of nonlinear and partially unknown dynamics. To address this challenge, we combine Gaussian Process distributed Port-Hamiltonian system (GP-dPHS) learning with boundary control by interconnection. The GP-dPHS model is used to infer the unknown Hamiltonian structure from data, while its posterior uncertainty is incorporated into an energy-based robustness analysis. This yields probabilistic conditions under which the closed-loop trajectories remain bounded despite model mismatch. The method is illustrated on a simulated shallow water system.