Isostable Reduction and Boundary Feedback Control for Nonlinear Convective Flows

• Published in: Proceedings of the IEEE Conference on Decision & Control pp. 2138 - 2143
• Main Authors: Wilson, Dan, Djouadi, Seddik
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01.12.2019
• ISSN: 2576-2370
• DOI: 10.1109/CDC40024.2019.9029951

A model reduction strategy using isostable coordinates is developed and applied to a prototype nonlinear convective flow past an obstacle. The flow is governed by the two-dimensional Burgers' equation subject to Dirichlet boundary controls. The Burgers' equation is used as a surrogate to the Navier-Stokes equations. The isostable coordinates are fully nonlinear and based on the infinite time convergence of transient behavior to a stationary solution. Linearization yields a model reduction strategy that explicitly accounts for the temporal dynamics of the underlying nonlinear flow and a strategy is developed for fitting observed data to the isostable reduced model. Open loop simulations of the isostable reduction outperform a previously validated nonlinear reduction strategy based on proper orthogonal decomposition. Additionally, the resulting isostable reduced framework is amenable for feedback control as demonstrated by solving a linear quadratic regulator problem in an isostable reduced coordinate system and applying the result to the full order system. To our knowledge, the use of isostable coordinates for reduced order modeling of fluid flows is novel.