# Exploiting Term Sparsity in Moment-SOS hierarchy for Dynamical Systems

arXiv: https://arxiv.org/abs/2111.08347 · HTML: https://mlsanity.com/paper/2111.08347/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Nov 2021.

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

- [Tractable hierarchies of convex relaxations for polynomial optimization on the nonnegative orthant](https://mlsanity.com/paper/2209.06175/) (2022)

## Abstract (arXiv)

In this paper, we develop a dynamical system counterpart to the term sparsity sum-of-squares (TSSOS) algorithm proposed for static polynomial optimization. This allows for computational savings and improved scalability while preserving convergence guarantees when sum-of-squares methods are applied to problems from dynamical systems, including the problems of approximating region of attraction, the maximum positively invariant set, and the global attractor. At its core, the method exploits the algebraic structure of the data, thereby complementing existing methods that exploit causality relations among the states of the dynamical system. The procedure encompasses sign symmetries of the dynamical system as was already revealed for polynomial optimization. Numerical examples demonstrate the efficiency of the approach in the presence of this type of sparsity.