  In the framework of Model Predictive Control (MPC), the control input is
typically computed by solving optimization problems repeatedly online. For
general nonlinear systems, the online optimization problems are non-convex and
computationally expensive or even intractable. In this paper, we propose to
circumvent this issue by computing a high-dimensional linear embedding of
discrete-time nonlinear systems. The computation relies on an algebraic
condition related to the immersibility property of nonlinear systems and can be
implemented offline. With the high-dimensional linear model, we then define and
solve a convex online MPC problem. We also provide an interpretation of our
approach under the Koopman operator framework.
