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.

As institutions seek to reduce their environmental impact, administrative processes must be optimized for energy and resource efficiency. This study integrates control theory with P-graph methodology to develop a structured framework for sustainable administrative workflows, focusing on university enrollment systems. P-graph-based optimization identifies minimum-energy pathways and optimal resource configurations, while Model Predictive Control (MPC) and nonlinear control enable real-time process adaptation under dynamic conditions. A Life Cycle Analysis (LCA) compares the carbon footprint of digital and paper-based workflows, evaluating IT infrastructure energy use versus traditional operations. Simulated control strategies support energy-efficient decision-making, highlighting best practices for emission reduction and operational flexibility. The result is a decision-support framework that embeds P-graph into a dynamic control context, guiding control strategy selection to minimize energy use and emissions. This scalable approach supports sustainability-oriented process management across public service domains.