Proximal Gradient-based Low Rank Tensor Decomposition for State Dependent Riccati Equation
For researchers working on optimal control of large-scale PDE systems, this method offers a way to obtain reduced-order models via tensor decomposition, though the novelty is incremental.
This paper proposes a proximal gradient-based low-rank tensor decomposition method to reduce the dimensionality of optimal control problems for large-scale PDE systems, enabling efficient solution of reduced state-dependent Riccati equations.
We address the optimal control problems arising from partial differential equations with large discrete dimensional control systems. To obtain reduced order models, we find basis elements from the canonical polyadic (CP) decomposition. Tensor datasets are from snapshots of the large models. Our method to reduce the control system is to use dimensionality reduction approaches through sparse optimization and flexible hybrid methods is to obtain low rank CP tensor basis elements. The reduced optimal control problem leads to reduced state-dependent Riccati Equations which can be solved efficiently.