# Low-order Linear Parameter Varying Approximations for Nonlinear Controller Design for Flows

arXiv: https://arxiv.org/abs/2311.05305 · HTML: https://mlsanity.com/paper/2311.05305/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Nov 2023.

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

- [Polytopic Autoencoders with Smooth Clustering for Reduced-order Modelling of Flows](https://mlsanity.com/paper/2401.10620/) (2024)

## Abstract (arXiv)

The control of nonlinear large-scale dynamical models such as the incompressible Navier-Stokes equations is a challenging task. The computational challenges in the controller design come from both the possibly large state space and the nonlinear dynamics. A general purpose approach certainly will resort to numerical linear algebra techniques which can handle large system sizes or to model order reduction. In this work we propose a two-folded model reduction approach tailored to nonlinear controller design for incompressible Navier-Stokes equations and similar PDE models that come with quadratic nonlinearities. Firstly, we approximate the nonlinear model within in the class of LPV systems with a very low dimension in the parametrization. Secondly, we reduce the system size to a moderate number of states. This way, standard robust LPV theory for nonlinear controller design becomes feasible. We illustrate the procedure and its potentials by numerical simulations.