A data-driven Koopman model predictive control framework for nonlinear flows

摘要: The Koopman operator theory is an increasingly popular formalism of dynamical systems which enables analysis and prediction the nonlinear dynamics from measurement data. Building on recent development model predictive control framework (Korda Mezic 2016), we propose a methodology for closed-loop feedback flows in fully data-driven model-free manner. In first step, compute Koopman-linear representation system using variation extended dynamic mode decomposition algorithm then apply to constructed linear model. Our handles both full-state sparse measurement; latter case, it incorporates delay-embedding available data into identification processes. We illustrate application this periodic Burgers' equation boundary cavity flow governed by two-dimensional incompressible Navier-Stokes equations. examples proposed successful accomplishing tasks with sub-millisecond computation time required evaluation input closed-loop, thereby allowing real-time deployment.