Finite Alphabet Control of Logistic Networks with Discrete Uncertainty
For researchers in control theory, the paper offers theoretical conditions for robust invariance in discrete-valued logistic networks, but the results are incremental and domain-specific.
The paper derives necessary and sufficient conditions for robust control invariance in logistic networks with finite-alphabet control and disturbance inputs, and shows a stronger condition ensures robust global attractivity. It provides constructive proofs that yield control laws and demonstrates results with examples.
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.