These 3 PhD projects are part of the European ERC Advanced Grant project CLariNet – a novel control paradigm for large-scale hybrid networks. The goal of CLariNet is to create a completely new paradigm for control of large-scale networks with hybrid dynamics by bridging the gap between optimization-based control and learning-based control. The breakthrough idea is to bridge that gap by using piecewise affine models and to unite the optimality of optimization-based control with the on-line tractability of learning-based control.

The 3 projects all have a strong fundamental flavor. In addition, applications for the case studies include multi-modal transportation networks and smart multi-energy networks.

Topic 1: Multi-agent integrated optimization-based and learning-based control for large-scale networks with hybrid dynamics

In this PhD project we will develop integrated optimization-based and learning-based control methods for large-scale hybrid systems – in particular piecewise affine (PWA) systems. More specifically, the aim is to develop several innovative approaches to combine model predictive control (MPC) and reinforcement learning so as to merge the advantages of both approaches, and to embed them in a distributed/multi-agent control setting. The main challenge will be to determine efficient approaches to obtain coordination among the control agents.

Topic 2: Integrated optimization-based and learning-based control for constrained hybrid systems in the presence of uncertainty

In this PhD project we will develop integrated optimization-based and learning-based control methods for hybrid systems – in particular piecewise affine (PWA) systems, in the presence of (stochastic) uncertainty and subject to input, output, and state constraints. The idea is to integrate scenario-based chance-constrained model predictive control (MPC) with learning-based control approaches. This also includes methods to efficiently obtain sets of representative scenarios that are rich enough so that performance guarantees can be given, and that be extracted in an efficient way from the huge amount of historical data that is available.

Topic 3: Performance analysis of integrated optimization-based and learning-based control for constrained hybrid systems

In this PhD project we will analyze and prove formal properties of integrated optimization-based and learning-based control methods for piecewise affine (PWA) systems subject to input, output, and state constraints. We will consider issues such as stability, computational complexity, error bounds, formal or probabilistic performance guarantees, robustness, finite termination effects, safety, etc. We will also investigate and characterize the various trade-offs (e.g., between allowed computation time and control performance/constraint violations).

The department Delft Center for Systems and Control (DCSC) of the faculty Mechanical, Maritime and Materials Engineering, coordinates the education and research activities in systems and control at Delft University of Technology. The Centers' research mission is to conduct fundamental research in systems dynamics and control, involving dynamic modelling, advanced control theory, optimisation and signal analysis. The research is motivated by advanced technology development in physical imaging systems, renewable energy, robotics and transportation systems.

We are looking for a candidate with an MSc degree in systems and control, applied mathematics, computer science, electrical engineering, or a related field, and with a strong background or interest in

• distributed control, machine learning, and (distributed) optimization (for Topic 1);
• stochastic control and machine learning (for Topic 2);
• systems & control, machine learning, and formal analysis (for Topic 3).

The candidate is expected to work on the boundary of several research domains. A good command of the English language is required.

Doing a PhD at TU Delft requires English proficiency at a certain level to ensure that the candidate is able to communicate and interact well, participate in English-taught Doctoral Education courses, and write scientific articles and a final thesis. For more details please check the Graduate Schools Admission Requirements.

Doctoral candidates will be offered a 4-year period of employment in principle, but in the form of 2 employment contracts. An initial 1,5 year contract with an official go/no go progress assessment within 15 months. Followed by an additional contract for the remaining 2,5 years assuming everything goes well and performance requirements are met.

Salary and benefits are in accordance with the Collective Labour Agreement for Dutch Universities, increasing from € 2443 per month in the first year to € 3122 in the fourth year. As a PhD candidate you will be enrolled in the TU Delft Graduate School. The TU Delft Graduate School provides an inspiring research environment with an excellent team of supervisors, academic staff and a mentor. The Doctoral Education Programme is aimed at developing your transferable, discipline-related and research skills.

The TU Delft offers a customisable compensation package, discounts on health insurance and sport memberships, and a monthly work costs contribution. Flexible work schedules can be arranged. For international applicants we offer the Coming to Delft Service and Partner Career Advice to assist you with your relocation.

Delft University of Technology

Delft University of Technology is built on strong foundations. As creators of the world-famous Dutch waterworks and pioneers in biotech, TU Delft is a top international university combining science, engineering and design. It delivers world class results in education, research and innovation to address challenges in the areas of energy, climate, mobility, health and digital society. For generations, our engineers have proven to be entrepreneurial problem-solvers, both in business and in a social context. At TU Delft we embrace diversity and aim to be as inclusive as possible (see our Code of Conduct). Together, we imagine, invent and create solutions using technology to have a positive impact on a global scale.

Challenge. Change. Impact!

Faculty Mechanical, Maritime and Materials Engineering

The Faculty of 3mE carries out pioneering research, leading to new fundamental insights and challenging applications in the field of mechanical engineering. From large-scale energy storage, medical instruments, control technology and robotics to smart materials, nanoscale structures and autonomous ships. The foundations and results of this research are reflected in outstanding, contemporary education, inspiring students and PhD candidates to become socially engaged and responsible engineers and scientists. The faculty of 3mE is a dynamic and innovative faculty with an international scope and high-tech lab facilities. Research and education focus on the design, manufacture, application and modification of products, materials, processes and mechanical devices, contributing to the development and growth of a sustainable society, as well as prosperity and welfare.

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