Adaptive Data‐Driven Models in Port‐Hamiltonian Form for Control Design

<jats:title>Abstract</jats:title><jats:p>Control engineering applications usually require a model that accurately represents the dynamics of the system. In addition to classical physical modeling, powerful data‐driven approaches are gaining popularity. However, the resulting models may not be ideal for control design due to their black‐box structure, which inherently limits interpretability. Formulating the system dynamics in port‐Hamiltonian form is highly beneficial, as its valuable property of passivity enables the straightforward design of globally stable controllers while ensuring physical interpretability. In a recently published article, we presented a method for data‐driven inference of port‐Hamiltonian models for complex mechatronic systems, requiring only fundamental physical prior knowledge. The resulting models accurately represent the nonlinear dynamics of the considered systems and are physically interpretable. In this contribution, we advance our previous work by including two key elements. Firstly, we demonstrate the application of the above described data‐driven PCHD models for controller design. Preserving the port‐Hamiltonian form in the closed loop not only guarantees global stability and robustness but also ensures desired speed and damping characteristics. Since control systems based on output measurements, which are continuously measured during operation due to the feedback structure, we secondly aim to use this data. Thus, we augment the existing modeling strategy with an intelligent adaptation approach to address uncertainties and (un)predictable system changes in mechatronic systems throughout their lifecycle, such as the installation of new components, wear, or temperature fluctuations during operation. Our proposed algorithm for recursively calculated data‐driven port‐Hamiltonian models utilizes a least‐squares approach with extensions such as automatically adjusting the forgetting factor and controlling the covariance matrix trace. We demonstrate the results through model‐based application on an academic example and experimental validation on a test bench.</jats:p>