# Structured linear quadratic control computations over 2D grids

arXiv: https://arxiv.org/abs/2304.04980 · HTML: https://mlsanity.com/paper/2304.04980/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Apr 2023.

## Built on by (most cited first, 1 of 1)

- [Application of deep and reinforcement learning to boundary control problems](https://mlsanity.com/paper/2310.15191/) (2023)

## Abstract (arXiv)

In this paper, we present a structured solver based on the preconditioned conjugate gradient method (PCGM) for solving the linear quadratic (LQ) optimal control problem for K × N sub-systems connected in a two-dimensional (2D) grid structure. Our main contribution is the development of a structured preconditioner based on a fixed number of inner-outer iterations of the nested block Jacobi method. We establish that the proposed preconditioner is positive-definite. Moreover, the proposed approach retains structure in both spatial dimensions as well as in the temporal dimension of the problem. The arithmetic complexity of each PCGM step scales as O(KNT), where T is the length of the time horizon. The computations involved at each step of the proposed PCGM are decomposable and amenable to distributed implementation on parallel processors connected in a 2D grid structure with localized data exchange. We also provide results of numerical experiments performed on two example systems.