Development of local dynamic mode decomposition with control: Application to model predictive control of hydraulic fracturing

- Development of a new local model reduction method (local DMDc).
- Temporal clustering of the snapshot data via an MINLP algorithm for capturing local dynamics.
- Computation of dynamically relevant spatial structures for accurate approximation.
- Application of local DMDc to design a feedback controller of hydraulic fracturing.

Dynamic mode decomposition with control (DMDc) is a modal decomposition method that extracts dynamically relevant spatial structures disambiguating between the underlying dynamics and the effects of actuation. In this work, we extend the concepts of DMDc to better capture the local dynamics associated with highly nonlinear processes and develop temporally local reduced-order models that accurately describe the fully-resolved data. In this context, we first partition the data into clusters using a Mixed Integer Nonlinear Programming based optimization algorithm, the Global Optimum Search, which incorporates an added feature of predicting the optimal number of clusters. Next, we compute the reduced-order models tailored to each cluster by applying DMDc within each cluster. The developed models are subsequently used to compute approximate solutions to the original high-dimensional system and to design a feedback control system of hydraulic fracturing processes for the computation of optimal pumping schedules.