Description: The course comprises three parts:
Background: In this part, we will discuss Markovian processes, both continuous and discrete (Markov chain). We will discuss the definition of conditional expectations and martingale theory to optional sampling theorems.
Safety and Control: In this part, we will first discuss safety. Stochastic safety deals with the computation of the probability that a system hits a forbidden state. This notion is related to fault detection, the detection of cyber-attacks, obstacle avoidance in robotics. To this end, we will use the idea of the occupation measure. That is the probability that a realization of a process belongs to a given set. We will show how to design a safe controller that reaches a target set with a “very low probability” of hitting a forbidden set.
Numerical Methods: The safety and control are translated into a problem of certificates of positivity. The task here is to find a polynomial that is positive in a given set. There are powerful tools available leaning upon sums of polynomials. The sum of squares can be solved by means of semi-positive programming, e.g., in Yalmip (Matlab).
Organizer: Rafael Wisniewski
Lecturers: Rafael Wisniewski (ES, AAU), Manuela L. Bujorianu, Maritime Safety Research Center, Department of Naval Architecture, University of Strathclyde, Scotland, UK
ECTS: 3.0
Time: 12-16 April 2021
Place: Aalborg University
Zip code: 9220
City: Aalborg
Number of seats: 20
Deadline: 22 March 2021
Important information concerning PhD courses: We have over some time experienced problems with no-show for both project and general courses. It has now reached a point where we are forced to take action. Therefore, the Doctoral School has decided to introduce a no-show fee of DKK 3.000 for each course where the student does not show up. Cancellations are accepted no later than 2 weeks before start of the course. Registered illness is of course an acceptable reason for not showing up on those days. Furthermore, all courses open for registration approximately four months before start. This can hopefully also provide new students a chance to register for courses during the year. We look forward to your registrations.
- Teacher: Rafal Wisniewski