Activity report - Free University of Bozen · Bolzano

2. Variable structure control: theory and applications
Technical background
Variable Structure Systems are systems characterised
by the presence of switching manifolds: these
define regions of the state space where the system
dynamics evolve according to different nonlinear
differential equations. When the boundaries of
these regions are reached, the system switches
from one structure to the other. By exploiting this
feature is thus possible to design systems whose
trajectories are created by piecewise pasting those
of different systems and belonging to none of them.
In control theory these ideas have been exploited
to create the so-called 'sliding mode controls': the
aim is to deliberately create a variable structure
by using a discontinuous controller in order to
constrain in finite-time the motion on a prescribed
sliding manifold. This surface has to be defined in
order to fulfil the given control goal. This method
has two main advantages: 1) once in sliding (i.e.
when evolving on the manifold), the system is of
reduced order and 2) the evolution is independent
of matched external disturbances.
Aims
To provide a sound mathematical background for
the application of VSC techniques to both finite and
infinite dimensional systems. The use of discontinuous
controllers poses in fact several problems
from the point of view of the well-posedness of the
closed loop system.
To explore the possibility and potential advantages
of extending SMC methods outside the classical
areas of application. These techniques are in fact
relatively simple to implement, while being very
robust with respect to unmodeled dynamics and
external disturbances, an appealing feature for
their application to complex systems.
Main reference people
Laura Levaggi
3. Biostatistics and bioinformatics
Technical background
The physical appearance of living beings, i.e. the phenotype, is shaped by the genotype and the environment,
including nutrition. Depending on the phenotypic trait, the contributions of these two sources can
vary enormously. There is significant interest in many scientific fields to quantify precisely the impact of
the genotype on the one hand and of the environment on the other hand. In the medical and pharmaceutical
sciences, for example, it is of importance to know if, and if yes, to what extent, an unfavourable phenotpye
can be improved by a medical treatment or by a change in the environment. Another example is
the agricultural sciences. Knowing the genetic basis of a trait of interest, e.g. milk quality or yield, would
mean to apply more efficient breeding schemes. The exact biological mechanisms as to how a genotype
affects a phenotype are typically unknown, but biotechnologically high throughput methods have been
developed during the past two decades that make a better understanding of the genotype-phenotype relationship
tangible. The most influential of these methods include genome-wide association studies (GWAS)
and next generation sequencing (NGS).
Aims
The output that is generated by the aforementioned high throughput techniques consists of a tremendous
amount of data stored in flat files. The interpretation of these raw data constitutes a major challenge to
the “life scientist”. A serious of successive steps is necessary to achieve manageable lists of biological entities,
for instance genes or polymorphisms. The aim is to extract the essential features of such data and
at the same time to control the reliability of this analysis procedure. Furthermore, various public databases
have been set up that permit to extract the information that is necessary to understand the impact
of polymorphisms, like single nucleotide polymorphisms or genomic insertions or deletions.
Main reference people
Armin Schmitt