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

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 takes advantage of the low-rank characteristics of the cylinder wake and provides full-dimensional solutions by implementing a terminal reduction technique based on resolvent analysis. 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.

Automated summary

This study focuses on the estimation and control of the cylinder wake at low Reynolds numbers, with an emphasis on developing efficient numerical algorithms for designing optimal linear feedback controllers. The proposed resolvent-based iterative algorithm allows for optimal estimation of the flow using a limited number of sensors and optimal control when only a limited number of actuators are available. The method takes advantage of the low-rank characteristics of the cylinder wake and provides full-dimensional solutions by implementing a terminal reduction technique based on resolvent analysis.