Advantages of Bilinear Koopman Realizations for the Modeling and Control of Systems With Unknown Dynamics

Nonlinear dynamical systems can be made easier to control by lifting them into the space of observable functions, where their evolution is described linear Koopman operator. This letter describes how operator used generate approximate linear, bilinear, and nonlinear model realizations from data, argues in favor bilinear for characterizing with unknown dynamics. Necessary sufficient conditions a system have valid or realization over given set functions are presented show that every control-affine admits an infinite-dimensional realization, but does not necessarily admit one. Therefore, constructed generic sets basis tend improve as number increases, whereas may not. To demonstrate advantages control, simulated robot arm data. In trajectory following task, exceeds prediction accuracy computational efficiency when incorporated predictive framework.