A Generalized-Moment Method for Control-Affine Ensemble Systems

Controlling dynamic ensemble systems is an essential yet challenging step to enable diverse applications in science and engineering. In this paper, we present a generalized moment method that gives rise to a moment representation of the control-affine ensemble system. The induced moment system is equipped with a banded structure that is beneficial to conducting systems-theoretic analysis and control design for ensemble systems. In addition, we introduce a Lie algebraic technique for exact bilinearization of nonlinear ensemble systems. This transformation provides a unified paradigm for studying highly intricate nonlinear ensemble systems through the associated bilinear moment systems. To demonstrate the applicability of the proposed method, we present numerical examples involving the control of nonlinear ensemble systems.