Framing control policies to mitigate the impact of invasive plants on indigenous biodiversity within the Sustainable Development Goals (SDG) framework is the primary objective of this work. Using reported ecological dynamics of the invasive species _Lantana camara_, we develop a minimal three-species network model, where each node follows generalized Lotka-Volterra (GLV) dynamical equations. Employing Lie algebra and network control theory, we establish the model’s controllability and accessibility criteria. Through nonlinear optimization programming, we derive sustainable policies for controlling abundances of _Lantana camara_. We also have used Shannon entropy as an indicator to assess the sustainability of these optimal policies. The analysis of the sensitivity measured using this technique reveals that the control strategy is critically dependent on the ratio of the intrinsic growth rates of the _Lantana camara_ and the control plant. Thus, we get a modular algorithmic decision support mechanism for designing control policies to manage _Lantana camara_ abundances. KEYWORDS: Lantana camara; Generalized Lotka-Volterra; Shannon entropy; Sustainable development goals; Sensitivity analysis.