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In this paper, we derive set constraints for a reduced order model and augment them into a model predictive control (MPC) scheme to ensure safe operation of the large-scale ensemble system. For the control feedback, only the aggregated information of the whole system is required. For the constraint satisfaction, we consider an adaptive tube formulation to characterize the deviation between the reduced order model and the ensemble system. Employing the robust control invariant set, we ensure recursive feasibility and initial feasibility under an easily verifiable condition.
On Consistency Viability and Admissibility in Constrained Ensemble and Hierarchical Control Systems
(2023)
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.