In the prediction and control of physical systems, combining records from different experiments and operations is expected to supply information that no single experiment provides on its own. Time-series foundation models, which learn a shared predictor from diverse time series, offer a framework for treating such records as a common training resource. Moreover, query-based prediction models, which switch between known and target signals within the same time series, make it possible to handle response prediction and control-input generation in a unified manner. However, in control-experiment data, the connections between signals change with the experimental stage, such as system identification, filtering, and feedback control, which calls for a formulation that handles signal values and connection structures dynamically and in a unified way. We formulate a control foundation model that defines a data space of dynamic graphs containing connections, signal values, and missing values, together with an operation on this space that specifies the known signals and the prediction targets. This allows response prediction and control-input generation to be described as a common masked prediction problem, even for experimental data with different connections and recorded signals. The Block Diagram Transformer (BDT), which implements this formulation, combines attention along the time axis with a graph neural network that follows the block-diagram connections, and can be initialized with the pretrained parameters of existing time-series foundation models. Trained on control-experiment data that mix multiple experimental settings, the proposed model stabilized an unstable system through feedback control, which is difficult to achieve by fine-tuning existing time-series foundation models. Ongoing work applying this approach to a wide range of target systems is also yielding promising results.

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