Differential inclusions are generalization of differential equations having multivalued right-hand
sides. They model systems with (bounded, non-stochastic) uncertainties or inputs. They arise
directly from control systems, equations with time-varying inputs, discontinuous right-hand side,
or from model-order reduction. Numerical methods are needed to reliably analyze the behavior,
notable safety, under uncertainty. Designing numerical algorithms for computing solutions of
differential inclusions, both efficiently and with high precision, remains a point of current
research. Different techniques and various types of numerical methods have been proposed as
approximations to the solution set of a differential inclusion such as Lohner-type algorithms,
grid-based methods, comparison theorems, interval enclosures, Taylor Models, conservative
linearization, etc. Mini-course will start with introduction to the theory of differential inclusions
including presentation of different types of set-valued maps, selection theorems, existence
theorems, properties of reachable sets, relaxation theorem, and fixed-point theorem for
differential inclusions. An overview of various numerical methods proposed for computation of
the solution set of differential inclusions over the last two decades will follow. In-depth analysis
of several efficient algorithms will be demonstrated concluded by deliberation on accuracy vs.
efficiency of these algorithms.
The lectures in Advanced numerical analisys II are suspended in this week.
Speaker: Sanja Zivanovic Gonzalez [webpage
Mo 13/05 10:30-12:30 Aula H
Tu 14/05 8:30-10:30 Aula L
We 15/05 14:30-15:30 Aula F
Thr 16/0514:30-15:40 Aula C
Fr 17/05 8:30-10:30 Aula Alfa