Welcome to Verification of Dymanical and Hybrid System


In the first part of the course we will briefly recall modeling of dynamical systems including stochastic differential equations and hybrid systems. Specifically, we will focus on piecewise deterministic Markov processes. For these systems, we will introduce conditions for stability and safety verification. We will show that the study of safety and stability boils down to determining if there is a certain function that is positive in a domain of interest. We shall call such a function a certificate. To illustrate, Lyapunov function is such a certificate of positivity used for studying stability, and barrier function is such a certificate for examining safety. On the other hand, certification of positivity can be reduced to finding functions that are sum of squares of polynomials. Our ambition is to show how to find certificates of positivity by means of numerical methods. We consider examples of electrical and mechanical systems, where the methods can be applied, and show how current numerical tools such as SOSTOOLS, YALMIP, and GloptiPoly can be applied on the examples.


A basic knowledge of mathematics as obtained through undergraduate engineering studies.

Organizer: Professor Rafael Wisniewski, e-mail: raf@es.aau.dk

Lecturers: Dr. Manuela Bujorianu, Professor Rafael Wisniewski & Assistant Professor Christoffer Sloth

ECTS: 3.0

Time: September 26-30, 2016

Place: Aalborg University

Zip code:


Number of seats: 30

Deadline: September 5, 2016

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 5,000 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 three 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.