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Séminaire du département Automatique du 24/11/2017 à 14h00

 

Operator-theoretic methods for prediction and control of nonlinear dynamical systems

Intervenant : Milan KORDA, University of California at Santa Barbara

Lieu : B208 Gipsa-lab

 

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This talk presents a framework for prediction and control of non-linear dynamical systems based on the so-called Koopman operator, which is an infinite-dimensional linear operator providing an equivalent description of the underlying nonlinear dynamical system. We extend the Koopman operator framework to systems with control inputs and show that truncation of this operator in a certain way results in a linear predictor whose state evolves on a higher-dimensional (lifted or embedded) state-space. This allows one to design controllers for the nonlinear dynamical system using linear control design methods; in particular, we show that standard linear model predictive control can be designed with computational complexity of the underlying optimization problem independent of the dimension of the lifted state-space, thereby allowing for deployment of the controller even under tight computation time constraints. The operator truncation procedure works directly with observed trajectories of the dynamical system and hence the entire scheme is purely data-driven. The approach will be demonstrated on several numerical examples, including power grid and PDE control, and its theoretical properties will be discussed.


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