PhD/Postdoc Position for Automatic Formal Verification of Cyber-Physical Systems Using Reachability Analysis

11.04.2025, Wissenschaftliches Personal

The research group Cyber-Physical Systems of Prof. Matthias Althoff at the Technical University of Munich offers a PhD/Postdoc position in the area of automatic formal verification of cyber-physical systems. The Technical University of Munich is one of the top research universities in Europe fostering a strong entrepreneurial spirit and international culture.

Expected Starting Date: 01 July-01 December 2025

Closing Date for Applicants: 15 June 2025

Duration: 3 years with a possible extension ( individual duration for Postdocs).

Project and Job Description

Formal verification of cyber-physical systems is an enabler of critical technologies that potentially cause fatalities (e.g. crash of an automated vehicle) or huge economic costs (e.g. blackout of a smart grid). While there has been tremendous progress in formal verification of cyber-physical systems, existing approaches still require expert knowledge. The main goal of this project is to develop essentially new methods to automatically verify cyber-physical systems.

Because none of the existing methods and tools for the formal verification of cyber-physical systems are fully automatic, these methods are currently stuck in academia and are not yet used regularly in industrial development processes. We believe that fully automating the verification process is a crucial step towards a broad acceptance of this technology. Our pre-studies have shown that full automation is possible in principle when formally verifying systems using reachability analysis. However, our pre-studies also showed that further research is needed to guarantee user-defined error bounds of reachable sets for nonlinear and hybrid systems. This project will exactly close this research gap: We will develop essentially new methods to ensure that algorithmic parameters are tuned so that the over-approximation of the computed reachable set is small enough to verify a given specification.

We will demonstrate our approach not only on ARCH benchmarks, but also on power systems in the CoSES lab at the Technical University of Munich.

Previous Work

Job Specifications

• For PhD applicants: Excellent Master’s degree (or equivalent) in computer science, engineering, or related disciplines (typically mathematics, physics).

• For Postdoc applicants: Excellent track record in computer science or engineering.

• Fluency in spoken and written English is required.

• Proficient in at least one programming language, e.g. MATLAB, C/C++, Python.

• Highly motivated and keen on working in an international and interdisciplinary team.

• Applicants with strong background in the following fields are preferred:

• Dynamical Systems

• Control Theory

• Formal Methods

• Reachability Analysis

• Computational Geometry

Context

The applicant will be directly advised by Prof. Matthias Althoff ( https://www.ce.cit.tum.de/cps/members/prof-dr-ing-matthias-althoff/ ). Besides excellent skills for conducting innovative science, the candidate should also be talented in implementing research results on a real robot and lead teams of students.

Our Offer

PhD remuneration will be in line with the current German collective pay agreement TV-L E13 (around 4500 Euros/month in the first year, 4900 Euros/month second year). The Technical University of Munich is an equal opportunity employer committed to excellence through diversity. We explicitly encourage women to apply and preference will be given to disabled applicants with equivalent qualifications.

Contact

International candidates are highly encouraged to apply. Please submit your complete application (in English or German) via our application form: https://wiki.tum.de/display/cpsforms/Ph.D.+Application . Fill out all mandatory fields (*) and kindly use "Verification of CPS” as the "Title of Position”. Please do not include a cover letter.

Further similar job offerings will be announced on https://www.ce.cit.tum.de/cps/open-positions/ .

Kontakt: hannah.markgraf@tum.de