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Master Thesis - Verification of vehicle control using subset simulation 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 subsets simulation approach for verification. With this approach, the model of the plant and the controller are wrapped within a probabilistic envelope describing all the disturbances and the modelling errors. Then, Monte Carlo simulations are carried out in order to assess the requirement satisfaction of the closed loop system. In order to obtain results that are statistically valid, this verification method has to satisfy two main requirements: high number of simulations and good coverage of scenarios leading to possible harmful situation. Thus, the main tasks of the projects are:

  • Modelling of the disturbances and understanding of the scenarios leading to harmful situations;
  • Analysis of the practical feasibility of the method for the vehicle control problem;
  • Study of the complexity of the method, based on the dimension of the random variables describing the disturbances and the dimension of the system dynamics;
  • Building simulation examples showing the effectiveness of the method.

Sub-tasks will be related to the analysis of big experimental data, and the improvement of the existing models via estimation/identification methods.


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

  • creative mindset;
  • a strong background in mathematics, system theory (linear algebra, linear systems, non-linear systems, feedback control, linear programming), and statistics and probability;
  • 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: Giuseppe Giordano, giuseppe.giordano@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.


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