PhD in Control Theory for Learned Operators in Dynamical Systems

Introduction

Are you fascinated by the intersection of control theory and scientific machine learning? Join us in developing the mathematical foundations needed to make deep operators reliable, robust, and applicable for control of complex engineering systems. In this PhD project, you will investigate how operator-learning models can represent dynamical systems, how their stability and robustness can be characterized, and how controllers can be designed for them. Your work will combine rigorous theory, numerical methods, and applications in high-tech, medical, and energy systems.

Job Description

Modern engineering increasingly relies on data-driven models to describe complex dynamical systems. Scientific machine learning is now enabling a new class of models that learn operators mapping system inputs and initial conditions directly to system responses. These learned operators offer exciting opportunities for efficient simulation, digital twins, optimization, and control.

In this PhD project, you will develop a new systems and control theory for learned operators, bridging modern scientific machine learning with classical control theory. Rather than focusing on a single machine-learning architecture, you will establish mathematical principles that apply across a broad class of operator-learning methods, including current and future deep operator models.

Your research will investigate fundamental questions such as: when does a learned operator admit an equivalent state-space representation? How can stability, contraction, dissipativity, robustness, and other system-theoretic properties be defined and guaranteed directly in the operator domain? And how can feedforward, feedback, and predictive controllers be designed for systems represented by learned operators? You will combine analytical theory with numerical implementation and validate the developed methods on industrially relevant applications in the high-tech, medical, and energy sectors.

You will become part of the Dynamics and Control group at the Department of Mechanical Engineering at Eindhoven University of Technology, under the supervision of dr.ir. Fahim Shakib and prof.dr.ir. Nathan van de Wouw. You will contribute to research at the intersection of systems and control theory, scientific machine learning, operator theory, optimization, and applied mathematics. You will work in an interdisciplinary environment with opportunities to collaborate with academic and industrial partners. You will be part of a vibrant and socially interactive group of approximately 35 researchers in the field of dynamical systems and control.

Job Requirements

• A master’s degree (or an equivalent university degree) in Systems and Control, Mechanical Engineering, Electrical Engineering, Applied Mathematics, or a closely related field. A research-oriented attitude.
• Experience with and a strong interest in machine learning and artificial intelligence, and enthusiasm for combining these methods with systems and control theory.
• Excellent analytical and mathematical skills, with an interest in developing new theoretical results.
• An enthusiasm for combining theoretical research with numerical implementation.
• A research-oriented attitude and a strong curiosity for fundamental research.
• The ability to work independently while contributing effectively to an interdisciplinary research team and with industrial partners.
• Motivated to develop your teaching skills and coach students.
• Fluent in spoken and written English (C1 level).

Conditions of Employment

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. At TU/e we challenge you to take charge of your own learning process .
• 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!

About us

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.

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 .

Information

Do you recognize yourself in this profile and would you like to know more? Please contact the hiring manager Fahim Shakib, Assistant Professor, m.f.shakib@tue.nl .

Visit our website for more information about the application process . You can also contact Fahim Shakib, Assistant Professor, m.f.shakib@tue.nl .

Curious to hear more about what it’s like as a PhD candidate at TU/e? Please view the video .

Are you inspired and would like to know more about working at TU/e? Please visit our career page.

We invite you to submit a complete application by using the apply button. The application should include a:

• Cover letter in which you describe your motivation and qualifications for the position.
• Curriculum vitae, including a list of your publications and the contact information of three references. Kindly note that we may reach out to references at any stage of the recruitment process. We recommend notifying your references upon submitting your application.

Ensure that you submit all the requested application documents. We give priority to complete applications.

We look forward to receiving your application and will screen it as soon as possible. The vacancy will remain open until the position is filled.

Please note

• You can apply online. We will not process applications sent by email and/or post.
• A pre-employment screening (e.g. knowledge security check) can be part of the selection procedure. For more information on the knowledge security check, please consult the National Knowledge Security Guidelines .
• Please do not contact us for unsolicited services.