Grant: GF20-22230L
from 01/01/2020
to 31/12/2022
Grantor: Austrian Science Foundation (FWF) - Czech Science Foudation
Banach spaces of continuous and Lipschitz functions
Objectives:
The supreme goal of this project is to study Banach spaces of continuous and Lipschitz functions over compact spaces from the points of view of various branches of mathematics. Since every Banach space can be isometrically embedded into a Banach space of continuous functions on a compact space, such spaces constitute one of the most important classes of Banach spaces and thus their better understanding will lead to sourcing broader knowledge and comprehension of all Banach spaces in general. We propose to apply mathematical techniques and methods originating from different areas of modern analysis, geometry, topology, and logic. Such a universal approach will allow us to obtain more profound insight into the structure of Banach spaces and related objects, aiming at solving several open problems in this area. Expected results will offer new tools for studying and classifying the topology and geometry of spaces of continuous and Lipschitz functions, as well as the corresponding compact and metric spaces.
Grant: 8J20AT022
from 01/01/2020
to 31/12/2021
Grantor: Ministerstvo školstv? mládeže a tělovýchovy
Hysteresis in hypo-plastic models
The findings of the project will be disseminated. All scientific results of the joint research will be presented in lectures and seminars at the Universities involved and also discussed with colleagues on international conferences. The important scientific aspects will be published in peer reviewed scientific journals, like for instance: Acta Mechanica, Acta Geotechnica, International Journal for Numerical and Analytical Methods in Geomechanics, etc.
Grant: LTAUSA19098
from 01/01/2020
to 31/12/2022
Grantor: Ministerstvo školstv? mládeže a tělovýchovy
Verification and Control of Networked Discrete-Event-Systems
Objectives:
The aim of this project is to extend current diagnosis, verification, and supervisory control approaches for modular discrete-event systems to networked discrete-event systems to cope with delays and losses in communications channels. In the standard supervisory control framework, it is assumed that communications between supervisors and the plant in both control and observation parts of the feedback loop are reliable and instantaneous. In a networked control system, the feedback loops are closed via a real-time communication network, which is shared with other nodes inside or outside the control system. The communication carried out over a shared network then induces delays and losses. We will investigate modular synthesis of supervisors that will be robust to these delays and losses. We will further apply the investigated approaches to the verification and control of guidepath-based transport systems that find applications in material handling systems, robotics and many other fields.
Grant: 8J20FR007
from 01/01/2020
to 31/12/2021
Grantor: Ministerstvo školstv? mládeže a tělovýchovy
Mathematics of diffuse interface models
The aim of the project is qualitative study of complex compressible fluid models with difuse interfaces, subject to stochastic external forces. In particular, the following will be addressed:
Existence of a suitable class of weak solutions
Relative (weak-strong) uniqueness
Singular limits
Desing, implementation and analysis of numerical schemes
Grant: GC19-06175J
from 01/01/2019
to 31/12/2021
Grantor: Czech Science Foundation
Compositional Methods for the Control of Concurrent Timed Discrete-Event Systems
Objectives:
Current approaches for control of timed discrete-event systems (DES) with dense real time only deal with monolithic plants, which means that their control suffers from high complexity and even decidability issues (non existence of finite state controllers). In order to face these issues, it is important to develop computationally efficient compositional approaches, such as modular control. We will investigate modular and coordination control of timed DES modeled by timed Petri nets or by (max,+)-automata.