Proximal Gradient-based Low Rank Tensor Decomposition for State Dependent Riccati Equation

TL;DR

This paper introduces a tensor decomposition method based on proximal gradients to efficiently reduce large control systems derived from PDEs, enabling faster solutions to reduced state-dependent Riccati equations.

Contribution

It proposes a novel approach combining sparse optimization and hybrid methods for low rank CP tensor basis extraction in control system reduction.

Findings

Efficient reduction of large control systems from PDEs.

Reduced Riccati equations are solvable more efficiently.

Tensor-based dimensionality reduction improves computational performance.

Abstract

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.