On weak ensemble controllability with applications to a chain of integrators

Simultaneous and robust manipulation of a large ensemble of structurally similar dynamical systems is an essential task for many cutting-edge applications in emerging scientific and engineering areas, and the ability to achieve this goal enables the full understanding of such ensemble systems. Controllability of ensembles has been extensively studied in recent years, which is concerned with the ability to manipulate the whole ensemble with a common control signal. In this paper, we develop a weaker notion of ensemble controllability, in which we consider the property of steering the entire ensemble from the same initial to the same target state. Specifically, we consider time-invariant linear ensemble systems, including an ensemble with linear parameter variation and a chain of integrators in the presence of uncertainty, and establish explicit weak ensemble controllability conditions.