PhD in Fair Distributed Optimization and Control of Large-Scale Networked Systems

Can thousands of autonomous agents, each with only local information, reach decisions that are optimal, stable and provably fair? In this PhD you will build the distributed optimization and control theory that answers this question. You will design scalable multi-agent algorithms with fairness built in, handle uncertainty with stochastic and robust methods, and prove convergence, stability and fairness guarantees. Your testbed will be one of the largest and most demanding networked systems there is: the electricity distribution grid, where thousands of solar panels, heat pumps and electric vehicles compete for limited network capacity. If you enjoy turning hard real-world problems into elegant mathematics, this position is for you.

Note to applicants: No background in energy systems is required; you will pick up the domain knowledge during the project, together with our energy experts. We are looking for candidates with a strong background in control systems, optimization or applied mathematics.

Information
At its core, this project tackles a fundamental problem in networked control: how to allocate a scarce shared resource among many agents in a way that is efficient, scalable and fair, using only local computation and limited communication. The motivating application is congestion management in electricity distribution networks. As rooftop photovoltaics, heat pumps and electric vehicles spread, local networks increasingly hit their capacity limits, and operators must decide how much power each prosumer may inject or consume. The core idea is to embed clear and interpretable notions of fairness directly into distributed control and optimization algorithms, as constraints or objectives with provable guarantees.

The project advances fundamental science at the intersection of distributed optimization, control theory, multi-agent systems and machine learning. It seeks to redefine how societal objectives such as fairness are formalized mathematically and enforced in intelligent control systems.

You will be embedded in the Control Systems group at TU/e, contributing to its research program on intelligent and responsible control of networked systems.

You will work closely with experts in distributed control, responsible AI and power systems across departments, who provide the domain knowledge and real-world data to test your methods.

Beyond the theory, your algorithms will help distribution system operators manage congestion transparently and equitably, speeding up the integration of renewable energy and strengthening public trust in the energy transition.

As a PhD candidate, you will:

• Formulate fair resource allocation problems: Cast congestion management as a large-scale, constrained multi-agent optimization problem, and formalize interpretable fairness notions (e.g., proportional, max-min or probabilistic fairness) as mathematical constraints or objectives.
• Design distributed optimization algorithms: Develop and analyze consensus-based, primal-dual, ADMM-type and game-theoretic algorithms that coordinate thousands of agents using only local information and limited communication.
• Develop fairness-aware feedback controllers: Design distributed controllers (e.g., distributed MPC, online feedback optimization) that enforce fairness while guaranteeing scalability, stability and constraint satisfaction.
• Analyze probabilistic allocation policies: Study randomized and weighted allocation schemes, such as raffle-based curtailment, and characterize their fairness and efficiency over time.
• Handle uncertainty: Incorporate stochastic models of generation and demand using tools from stochastic, robust and learning-based control.
• Prove theoretical guarantees: Establish convergence, stability, robustness and fairness guarantees, including under forecasting errors, model mismatch and communication delays.
• Validate on realistic large-scale networks: Test your algorithms in simulations of realistic distribution networks and on real-world data from Dutch distribution system operators.
• Publish and collaborate: Publish in leading control and optimization venues (e.g., IEEE TAC, Automatica, CDC) and work with colleagues in control, AI and electrical engineering.

This PhD position is part of the project "Responsible AI for Fair and Efficient Control of Energy Systems (RAICES)“ (https://www.tue.nl/en/research/institutes/eindhoven-artificial-intelligence-systems-institute/ai-research/eaisi-emdair-program)