Exact and Positive Controllability of Boundary Control Systems

TL;DR

This paper characterizes the space of exactly reachable states in boundary control systems using semigroup theory and explores conditions for positive controllability, with applications to network flows.

Contribution

It provides a comprehensive characterization of reachable states and analyzes positive controllability in boundary control systems, extending to network flow applications.

Findings

Characterization of all exactly reachable states.

Conditions for positive controllability established.

Applications to network flow systems demonstrated.

Abstract

Using the semigroup approach to abstract boundary control problems we characterize the space of all exactly reachable states. Moreover, we study the situation when the controls of the system are required to be positive. The abstract results are applied to flows in networks with static as well as dynamic boundary conditions.