Port-Hamiltonian theory is an established way to describe nonlinear physical
systems widely used in various fields such as robotics, energy management, and
mechanical engineering. This has led to considerable research interest in the
control of Port-Hamiltonian systems, resulting in numerous model-based control
techniques. However, the performance and stability of the closed-loop typically
depend on the quality of the PH model, which is often difficult to obtain using
first principles. We propose a Gaussian Processes (GP) based control approach
for Port-Hamiltonian systems (GPC-PHS) by leveraging gathered data. The
Bayesian characteristics of GPs enable the creation of a distribution
encompassing all potential Hamiltonians instead of providing a singular point
estimate. Using this uncertainty quantification, the proposed approach takes
advantage of passivity-based robust control with interconnection and damping
assignment to establish probabilistic stability guarantees