Computational Moment Control of Ensemble Systems

Finely manipulation of a large population of structurally identical dynamical systems exhibiting different dynamics, referred to as an ensemble system, is a crucial task arising from various emerging applications across diverse disciplines. A significant challenge in controlling this class of systems is the inherent scalability issue, involving computational complexity and efficiency, due to the massive size. To overcome this bottleneck, in this paper, we introduce a moment transform that maps ensemble systems defined on the space of continuous functions to their associated moment systems defined on the space of moment sequences. This transformation enables the approximation of the dynamics of an ensemble system in terms of a finite-dimensional truncated moment system. We leverage this reduction to facilitate control design for ensemble systems by developing an iterative computational optimal control algorithm with convergence guarantees. The efficiency and performance of the proposed algorithm are further demonstrated through its application to practical ensemble control problems encountered in physics and robotics.