Emerging applications in robotics, aerospace and autonomous driving necessitate control systems capable of autonomously performing complex tasks. These control systems need to learn and adapt to unforeseen circumstances. In this PhD project, the focus lies on developing the missing theory to enable the formal verification of such autonomous control systems.   

Autonomous driving is a key application area in which theory needs to be developed to improve the verifiability and safety of autonomous control systems. Safe driving maneuvers can be expressed as dynamic constraints using temporal logics. These temporal logic specifications combine logical operations with temporal modalities based on constraints over control system's states and outputs and can be automatically verified using formal methods. However, while driving a car, inherent uncertainty is encountered that necessitates the inclusion of learning and estimation strategies. Verifying and designing such learning controllers is an open research problem for complex driving maneuvers or control tasks.

This project aims to build a framework for the safe and verifiable design of controllers for systems with state and model uncertainty. The objective of the PhD research is to exploit advanced system identification and filtering techniques (Kalman filtering, Bayesian estimation, machine learning) together with control techniques (approximate dynamic programming, Lyapunov stability, temporal logics) to improve the resilience of verifiable design methodologies to uncertainty. The research also involves some laboratory work in terms of implementation and validation on small-scale vehicles.

Main research directions

• Investigate data-driven modelling and uncertainty quantification using system identification for Linear Time Invariant (LTI) models and Linear Parameter Varying (LPV) models.
• Develop design methods for verifiable output-based controllers that are robust to model uncertainty.
• Integrate abstraction techniques and model checking tools for temporal logic specification with data-driven estimation and modelling techniques.
• Implement and apply the developed theory on suitable case studies and/or laboratory setups.

Control Systems group

The CS group research activities span all facets of systems and control theory, such as linear, nonlinear and hybrid systems theory, model predictive control, distributed control, networked systems, machine learning for control, modelling and identification, and formal methods in control. The CS group has a strong interconnection with industry via national and European funded projects in various application areas like high-precision mechatronics, power electronics, and sustainable energy (mobility, transport, smart grids). The CS group owns an Autonomous Motion Control (AMC) laboratory and hosts several high-tech setups. The PhD student will join the group and interact with the other CS group members (around 40 researchers), where he/she will participate in a mix of academic and industrial research activities. Research within the CS Group is characterized by personal supervision. The PhD student will have access to the advanced courses offered by the Dutch Institute for Systems and Control and will attend the yearly Benelux Meeting on Systems and Control.

You are a talented and enthusiastic young researcher who wants to pursue an academic career. Furthermore, as a good candidate, you have

• A strong background in control preferably in combination with knowledge of computer science, machine learning, probability theory and a wish to gain knowledge on the other area(s)
• Consistently performed well in your studies
• A Master's degree in, e.g., Control engineering, Mathematics, Computer Science, Electrical Engineering, Mechanical Engineering or a related engineering discipline,
• A research-oriented and proactive attitude,
• A team-player mentality with excellent communication and cooperation skills in a multi-disciplinary project environment,
• Good written and oral communication skills in English.

• A meaningful job in a dynamic and ambitious university with the possibility to present your work at international conferences.
• A full-time employment for four years, with an intermediate evaluation (go/no-go) after nine months.
• To develop your teaching skills, you will spend 10% of your employment on teaching tasks.
• To support you during your PhD and to prepare you for the rest of your career, you will make a Training and Supervision plan and you will have free access to a personal development program for PhD students (PROOF program).
• A gross monthly salary and benefits (such as a pension scheme, pregnancy and maternity leave, partially paid parental leave) in accordance with the Collective Labor Agreement for Dutch Universities.
• Additionally, an annual holiday allowance of 8% of the yearly salary, plus a year-end allowance of 8.3% of the annual salary.
• Should you come from abroad and comply with certain conditions, you can make use of the so-called '30% facility', which permits you not to pay tax on 30% of your salary.
• A broad package of fringe benefits, including an excellent technical infrastructure, moving expenses, and savings schemes.
• Family-friendly initiatives are in place, such as an international spouse program, and excellent on-campus children day care and sports facilities.