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

Eindhoven University of Technology (TU/e); Eindhoven; Vor Ort; EUR 36.000 - 45.000; Vollzeit

Benefits dieser Stelle

ABP pension scheme

8% holiday allowance and 8.3% year-end

Generous leave options

Zusammenfassung

Eindhoven University of Technology (TU/e) in Eindhoven is seeking a PhD candidate to design scalable distributed optimization and control methods for large energy networks. You will tackle fair resource allocation among thousands of agents in electrical grids with local information and limited communication.

You will join TU/e’s Control Systems group and collaborate with energy experts to prove guarantees on convergence, stability and fairness, while testing on realistic distribution networks

Qualifikationen

• A master’s degree (or equivalent) in Systems and Control, Electrical Engineering, Mechanical Engineering, Applied Mathematics, Operations Research or a related field.
• Strong background in control theory and/or optimization (convex or distributed optimization, multi-agent systems, MPC, game theory).
• Solid mathematical skills and enjoyment of rigorous analysis and proofs.
• Programming experience (Python, MATLAB or Julia).
• Fluent in English (C1 level).

Aufgaben

• Formulate fair resource allocation problems for congestion management as a large-scale multi-agent optimization problem.
• Design distributed optimization algorithms (consensus-based, primal-dual, ADMM-type, game-theoretic).
• Develop fairness-aware feedback controllers (distributed MPC, online feedback optimization).
• Analyze probabilistic allocation policies and their fairness over time.
• Handle uncertainty with stochastic/robust/learning-based control approaches.
• Prove theoretical guarantees: convergence, stability, robustness, fairness.
• Validate methods on simulations of realistic networks and real-world data.
• Publish in leading control and optimization venues and collaborate across departments.

Kenntnisse

Control theory

Optimization

Distributed control

Multi-agent systems

Python

MATLAB/Julia

Ausbildung

Master's degree in Systems and Control or related field

Tools

Python

MATLAB

Julia

Jobbeschreibung

Job description

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.

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.

Requirements

• A master’s degree (or an equivalent university degree) in Systems and Control, Electrical Engineering, Mechanical Engineering, Applied Mathematics, Operations Research or a related field.
• In case you are still doing your MSc in the field listed above, please indicate your expected graduation date in the cover letter.
• A strong background in control theory and/or optimization (e.g., convex or distributed optimization, multi-agent systems, model predictive control, game theory).
• Solid mathematical skills and enjoyment of rigorous analysis and proofs.
• Programming experience (e.g., Python, MATLAB or Julia).
• A research-oriented attitude with curiosity.
• Ability to work in an interdisciplinary team.
• Motivated to develop your teaching skills and coach students.
• Fluent in spoken and written English (C1 level).
• Prior knowledge of power or energy systems is not required.

Conditions of employment

Fixed-term contract: 4 years. A meaningful job in a dynamic and ambitious university, in an interdisciplinary setting and within an international network. You will work on a beautiful, green campus within walking distance of the central train station.

In addition, we offer you:

• Full-time employment for four years, with an intermediate assessment after nine months.
• You will spend a minimum of 10% of your four-year employment on teaching tasks, with a maximum of 15% per year of your employment.
• Salary and benefits (such as a pension scheme, paid pregnancy and maternity leave, partially paid parental leave) in accordance with the Collective Labour Agreement for Dutch Universities, scale P (min. € 3,204 - max. € 4,051 gross base salary per month (full-time)).
• In addition to your base salary, you will receive an 8% holiday allowance and an 8.3% year-end bonus, both calculated based on your annual gross base salary.
• Generous leave options: a standard 29 days (based on a 38 hour working week) per year that you can increase to 41 days by working two hours more per week (flexible working hours). This is prorated if you work part-time.
• As a TU/e employee, you participate in the ABP pension scheme, providing retirement pension and pension benefits for surviving dependents and occupational disability. TU/e pays 70% of the pension premium, while employees contribute the remaining 30%.
• High-quality training programs and other support to grow into a self-aware, autonomous scientific researcher.
• An excellent technical infrastructure, and on-campus children's day care.
• Unlimited access to the modern on‑campus TU/e Student Sports Center at an exceptionally affordable rate.
• We support your wellbeing with free 24/7 access to OpenUp, providing you and your family with mental health support, expert guidance, and online training.
• An allowance for commuting, working from home and internet costs.
• A Staff Immigration Team and a tax compensation scheme (the Expat Scheme) for international candidates.

On our website you can discover even more information about our conditions of employment. Build on your career at TU/e!

Employer

Employer TU/e We are a leading international university where scientific curiosity meets a hands‑on mindset. We work in an open and collaborative way with high‑tech industries to tackle complex societal challenges. Our responsible and respectful approach ensures impact — today and in the future. TU/e is home to over 13,000 students and more than 7,000 staff, forming a diverse and vibrant academic community. Discover what Light Up means to TU/e in our short company video. Our university is located in Brainport Eindhoven — a world‑leading tech region with more than 7,000 high‑tech companies and strong R&D activity. Known for breakthroughs in AI, photonics, semiconductors and advanced manufacturing, Brainport is a place where technology serves people and society. Learn more about the Brainport region here. The mission of the Department of Electrical Engineering is to acquire, share and transfer knowledge and understanding in the whole field of Electrical Engineering through education, research and valorization. We work towards a ‘Smart Sustainable Society’, a ‘Connected World’, and a healthy humanity (‘Care & Cure’). Activities share an application‑oriented character, a high degree of complexity and a large synergy between multiple facets of the field. Research is carried out into the applications of electromagnetic phenomena in all forms of energy conversion, telecommunication and electrical signal processing. Existing and new electrical components and systems are analyzed, designed and built. The Electrical Engineering department takes its inspiration from contacts with high‑tech industry in the direct surrounding region and beyond. The department is innovative and has international ambitions and