Exact Controllability of Semi-linear Heterogeneous Networked Control Systems

This paper investigates the controllability of networked systems with heterogeneous node-specific semilinear control systems. The nonlinearities are assumed to be Hölder continuous with bounded growth. A compact Kronecker-based formulation is developed to represent the system dynamics, and algebraic conditions are derived to ensure controllability under structural and dynamical heterogeneity. The analysis leverages fixed point theorems to guaranty the existence and uniqueness of solutions. The proposed framework generalizes classical PBH-based controllability results to include nonlinear effects and nonuniform actuation. Three illustrative examples - a bidirectional 2-node network, a 3-node ring, and a 3-node star with partial actuation-demonstrate the effectiveness of the proposed controllability conditions. This work contributes a rigorous and flexible extension of controllability theory for realistic semilinear networked control systems.