On Consistency, Viability, and Admissibility in Constrained Ensemble and Hierarchical Control Systems

Several control architectures, such as decentralized, distributed, and hierarchical control, have been elaborated over the past decades for controlling systems composed of a set of subsystems. However, computational complexity and constraint satisfaction are still challenging tasks. We present an approach to control an ensemble of similar heterogeneous systems with input and state constraints via an identical control input. This control input is globally admissible and computed based on an aggregated system that reflects the overall behavior of the ensemble. To limit the computational complexity of the control task, the aggregated system is designed such that its dimension is independent of the number of subsystems. To guarantee viability, i.e., state constraint satisfaction for all times, appropriate consistency conditions are derived based on invariant set theory. The presented approach is illustrated with a numerical example.