Resolvent-based approach for H2-optimal estimation and control: an application to the cylinder flow

TL;DR

This paper introduces a resolvent-based iterative algorithm for designing efficient, low-rank optimal estimators and controllers for cylinder flow at low Reynolds numbers, avoiding model reduction.

Contribution

It develops a novel resolvent analysis approach to design optimal flow estimation and control with limited sensors and actuators, leveraging low-rank flow characteristics.

Findings

Algorithms converge to true global optima

Flow estimation and control are effective with limited sensors and actuators

Method avoids the need for model-order reduction

Abstract

We consider estimation and control of the cylinder wake at low Reynolds numbers. A particular focus is on the development of efficient numerical algorithms to design optimal linear feedback controllers when there are many inputs (disturbances applied everywhere) and many outputs (perturbations measured everywhere). We propose a resolvent-based iterative algorithm to perform i) optimal estimation of the flow using a limited number of sensors; and ii) optimal control of the flow when the entire flow is known but only a limited number of actuators are available for control. The method uses resolvent analysis to take advantage of the low-rank characteristics of the cylinder wake and solutions are obtained without any model-order reduction. Optimal feedback controllers are also obtained by combining the solutions of the estimation and control problems. We show that the performance of the estimators and controllers converges to the true global optima, indicating that the important physical mechanisms for estimation and control are of low rank.