A Robust Method for Dual Faceted Linearization

Abstract

The dynamics of nonlinear systems become linear systems when lifted to higher or infinite dimensional spaces. We call such linear system representations and approximations, ‘lifting linear’ representations. The lifting linear representations are linear system representations that are closer to the original systems than Taylor series approximations. Once we have such a linear system representation, we can apply linear control theory to the nonlinear systems. In Model Predictive Control (MPC), the computation time is reduced because the nonlinear optimization problem becomes a convex quadratic optimization problem. In this paper, we propose a method to make Dual Faceted Linearization (DFL) robust for uncertainties of the plants. It will be shown that the proposed method can yield a lifting linearization leading to better control results for MPC by numerical examples.