Linear Control of a Nonlinear Aerospace System via Extended Dynamic Mode Decomposition

The linear representation of nonlinear systems dynamics has a tremendous potential to enable the estimation, prediction, and control of nonlinear systems using standard and well-known methodologies available for linear systems. Numerical algorithms such as the Extended Dynamic Mode Decomposition (EDMD) has been recently proposed to identify, from experimental data, such nonlinear transformations. The key point of these methods is that the original state space variables are lifted, via a nonlinear transformation (Koopman transformation), in an augmented space where the evolution of the lifted variables is linear. This up-and-coming framework has been applied to the identification of linear prediction models that approximate the nonlinear dynamics of an aerospace system, specifically a CubeSat. Based on this linear representation, simple LQR controllers have been designed to control the dynamics of the nonlinear CubeSat.