Administrative workflows in public services, such as university enrolment are increasingly recognized as complex systems characterized by nonlinear dynamics, interdependencies, and variable operational constraints. These characteristics often lead to inefficiencies in resource allocation and compromise process sustainability. This study develops a novel control-theoretic optimization framework that integrates feedback, adaptive, and predictive control strategies with the P-graph methodology to address these challenges. The proposed approach models enrollment workflows using system dynamics and P-graph-based network optimization, enabling structured representation, real-time control, and scenario-based decision-making. To assess sustainability and efficiency, the model simulates varying scenarios of student demand, digital transformation levels, and administrative capacity. Key performance indicators (KPIs) such as resource utilization, delay reduction, and process flexibility are used to evaluate the comparative effectiveness of Model Predictive Control (MPC), discrete-event control, and feedback control strategies. Results show that optimized scenarios achieved a 50 % reduction in CO2 emissions and over 2 h reduction in average processing time, significantly improving sustainability. This research uniquely applies control-theoretic methods to public administration and extends the P-graph methodology beyond industrial domains. The outcome is a scalable decision-support framework for policymakers aiming to enhance the resilience and sustainability of administrative service processes under dynamic conditions.