Finite Alphabet Control of Logistic Networks with Discrete Uncertainty

TL;DR

This paper studies control of logistic networks with finite control and disturbance sets, providing conditions for invariant sets and control laws to ensure robustness and stability.

Contribution

It introduces necessary and sufficient conditions for invariant sets in finite alphabet logistic networks and constructs control laws ensuring robustness.

Findings

Derived a necessary and sufficient condition for invariant sets.

Showed a stronger condition guarantees global attractivity.

Provided constructive proofs enabling control law extraction.

Abstract

We consider logistic networks in which the control and disturbance inputs take values in finite sets. We derive a necessary and sufficient condition for the existence of robustly control invariant (hyperbox) sets. We show that a stronger version of this condition is sufficient to guarantee robust global attractivity, and we construct a counterexample demonstrating that it is not necessary. Being constructive, our proofs of sufficiency allow us to extract the corresponding robust control laws and to establish the invariance of certain sets. Finally, we highlight parallels between our results and existing results in the literature, and we conclude our study with two simple illustrative examples.