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Master Thesis - Verification of vehicle control using a set based approach


An automatic control system is always designed and tuned in order to meet specific requirements, e.g. the tracking requirement. In this case, the variable of interest describing some state of the system to be controlled (the plant), e.g. velocity of the vehicle, has to follow a predefined (required) profile. For some systems, the tracking problem is a safety requirement problem: a too big tracking error might lead to hazardous situations that might harm humans and/or damage goods. Thus, it is necessary to derive a verification strategy showing that the tracking requirement is always met, even when internal and external disturbances affects the system under control. To achieve this, three complementary methods are considered:

  • Set-based approach that relies on linear system theory, optimization, and worst case assumptions for the correlation between internal and external disturbances;
  • Subset simulation approach that relies on stochastic modelling and Monte Carlo methods;
  • High fidelity simulation for a limited number predefined test case with a detailed nonlinear model of the vehicle dynamics, actuator limitations and electronic stability control system.

Project Description 

In this master thesis project, we aim at deploying the set-based verification strategy and analyzing its properties. The set-based method implements a backward propagation of plant and controller dynamics, starting from the set described by the requirements. The propagation takes into account the internal and external disturbances by considering the worst-case scenarios. The result of the backward propagation is a safe set for which the requirements are fulfilled. For more information you can read about the Robust Invariance Theory.

By modelling the disturbances via worst-case descriptions, the computed safe set might be too conservative. Thus, the main research tasks for this master thesis are:

  • Understand which disturbances need to be modeled in details in order to allow this simple approach to provide useful results;
  • Analyse the conservativeness and the practical feasibility of the method;
  • Write scripts for deploying the method to simulations studies on Zenuity's clusters;
  • Write scripts for analyzing big data and for visualizing high dimensional safe set.


We are looking for (one or two) students with the following skills:

  • creative mindset;
  • a strong background in mathematics and system theory (linear algebra, linear systems, non-linear systems, feedback control, linear programming);
  • Solid programming kills (Matlab, Python, C++);
  • a passion for data analysis and programming.

Further information 

Final application date: November, 30th, 2019.

Please send in individual applications with CV, motivational letter and grade transcripts. If you wish to partner with someone, simply note that in your application.

Planned start: February 1st, 2020, with some flexibility.

Duration: 30 ECTS

For questions regarding the project, please Contact: Lars Johannesson Mårdh Technical Specialist Vehicle Motion Control, lars.johannesson.mardh@zenuity.com 

Or, know someone who would be a perfect fit? Let them know!

Gothenburg, Sweden

Lindholmspiren 2
417 56 Göteborg Directions

Making safe and intelligent mobility real.

At Zenuity, we lead the global movement of crafting tomorrow's mobility with the software platform of choice. Our mission is to “Make safe and intelligent mobility real, for everyone, everywhere”. This statement marks our conviction and dedication to bring autonomous driving out on the streets for real and is at the center of everything we do.

We could not dream of achieving this without our great teams of very talented people. We are on this journey together and our agile way of working is reflected throughout our entire organization; it is part of our culture and how we work, develop and grow together.


Applicant tracking system by Teamtailor