Immersion-based model predictive control of constrained nonlinear systems: Polyflow approximation

Wang, Zheming;Jungers, Raphaël
(2022) 2021 European Control Conference (ECC) — Location: Delft, Netherlands (29.June.2021)

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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.
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Wang, Z., & Jungers, R. (2022). Immersion-based model predictive control of constrained nonlinear systems: Polyflow approximation. Published. 2021 European Control Conference (ECC), Delft, Netherlands. https://doi.org/10.23919/ecc54610.2021.9655233