J010 Control and System Theory of Rational Systems

Fakulta informatiky
podzim 2018
Rozsah
1/1/1. 3 kr. (plus ukončení). Doporučované ukončení: zk. Jiná možná ukončení: k.
Vyučující
Dr. Jana Němcová (přednášející)
doc. RNDr. David Šafránek, Ph.D. (přednášející)
Prof. Jan H. van Schuppen (přednášející)
Garance
doc. RNDr. David Šafránek, Ph.D.
Katedra strojového učení a zpracování dat – Fakulta informatiky
Rozvrh
Čt 20. 9. 13:00–15:45 C525, Út 25. 9. 14:00–15:55 B411, Čt 27. 9. 13:00–15:45 C525, Čt 4. 10. 13:00–15:45 C525, Út 9. 10. 14:00–15:55 B411, Čt 11. 10. 13:00–15:45 C525, Čt 18. 10. 13:00–15:45 C525, Út 23. 10. 14:00–15:55 B411, Čt 25. 10. 13:00–15:45 C525, Čt 1. 11. 13:00–15:45 C525, Čt 8. 11. 13:00–15:45 C525, Čt 15. 11. 13:00–15:45 C525
Předpoklady
Knowledge of ordinary differential equations and of linear algebra at the level of a first-year master student in bioinformatics or of a comparable educational program.
Omezení zápisu do předmětu
Předmět je otevřen studentům libovolného oboru.
Předmět si smí zapsat nejvýše 15 stud.
Momentální stav registrace a zápisu: zapsáno: 0/15, pouze zareg.: 0/15, pouze zareg. s předností (mateřské obory): 0/15
Cíle předmětu
The aim of the course is to provide to master level or post-graduate students an introduction to mathematical modeling, analysis, system identification, and control of biochemical reaction systems and of rational systems of engineering phenomena. The course will be of interest to students in: bioinformatics, biomathematics, biology, mathematics, and engineering, all at the master or post-graduate level.
Výstupy z učení
The student will obtain theoretical and practical knowledge at the basic level in the following topics: modelling of biochemical reaction systems and of physiological systems; advantages, use and analysis of polynomial and rational systems;
The student will grasp the notions of stability, realization, identification, observers, and control and the elementary level.
Osnova
  • Biochemical reaction systems and rational systems of other areas of the sciences.
  • Rational systems.
  • Stability of linear, polynomial, and of rational systems.
  • Realization of linear and of rational systems.
  • System identification of rational systems.
  • Control and observers of rational systems.
Výukové metody
lectures, class discussion, weekly exercises
Metody hodnocení
exam: oral exam, evaluated weekly exercises
colloquium: evaluated weekly exercises only
Vyučovací jazyk
Angličtina
Informace učitele
http://bioinformatika.fi.muni.cz/predmety/dblok1

In the first two days of the course presentations it will be shown how to model the behavior of part of the biochemistry of a cell by a nonlinear differential equation. Also it may be shown how the behavior of an engineering system can be modeled by a nonlinear differential equation. The types of differential equations used are polynomial, for mass-action kinetics for example, or rational, which refers to a differential equation described by terms with quotients of polynomials. This covers most of the types of differential equations used in biochemistry.
In the subsequent lectures the rational systems are described in more detail and are mathematically in- vestigated. Background information will be provided on polynomial algebra. Stability is the study of the behavior of the state of a system if time goes to infinity. It also includes an analysis of periodic trajectories. Presented will be conclusions on the stability of a subset of biochemical reaction systems of polynomial type; possibly also for rational systems.
Realization theory describes the set of rational systems representations which represent the considered observed behavior of such a system. The concepts of observability and of controllability are defined. The results covered include: (1) an equivalent condition for the existence of a realization in the form of a rational system for a response map; (2) minimality of the realization; and (3) equivalences of minimal realizations. The results of realization theory are used in system identification and in control theory described below. System identification is the problem of how to go from the numerical values of an observed time series to a rational system in which the numerical values of the parameters of the system are determined. The rational system should be a realistic model of the observed time series. This rather difficult subject will be described for primarily polynomial systems. The students can learn a procedure to check whether or not the parametrization of a rational system is structurally identifiable. This means that one can in principle uniquely determine the values of the parameters from the observed time series. In addition, they will be shown how to estimate the values of the parameters from an observed time series. This will be useful to students of bioinformatics who can then assist biologists in obtaining realistic mathematical models using observed time series.
Control synthesis of a rational system is to determine a control law which determines the input to the considered rational system. The input can influence the behavior of the system so that a particular behavior occurs or so that unwanted behavior does not occur. A solution method may be based on the control canonical form of a rational system. Observers, which can estimate the state of a rational system from an observed output process, will be explained.
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