Decentralized Robust Control Invariance for a Network of Storage Devices

Robust control of networked storage devices is considered. Each storage device is modeled as a single-state, discrete-time integrator with bounded control input, and subject to additive disturbance. The values of the disturbance are unknown but are assumed to belong to bounded sets. Nodes exchange stored resource through links of limited capacity. Characterization of the maximal robust control invariant (RCI) set is provided and decentralization of the robust feasibility problem is considered. A notion of decentralized RCI set is introduced and a parametrization of a family of decentralized RCI sets is proposed. It is shown that the set of parameters for which the decentralized RCI sets are non-empty is a polyhedral set. The result offers a possibility to use convex optimization for selection of bounds on the admissible flow through the network which ensure feasibility of the proposed decentralized design.