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FI:IV120 Continuous and Hybrid Systems - Course Information

## IV120 Continuous and Hybrid Systems

**Faculty of Informatics**

Spring 2019

**Extent and Intensity**- 2/1. 3 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), z (credit).
**Teacher(s)**- RNDr. David Šafránek, Ph.D. (lecturer)

prof. RNDr. Jiří Barnat, Ph.D. (lecturer) **Guaranteed by**- doc. RNDr. Aleš Horák, Ph.D.

Department of Machine Learning and Data Processing - Faculty of Informatics

Supplier department: Department of Machine Learning and Data Processing - Faculty of Informatics **Timetable**- Thu 21. 2. to Thu 16. 5. Thu 9:00–11:50 C525
**Prerequisites***Elementary mathematical knowledge:*linear algebra (matrix, linear map, eigenspace), calculus (continuous function, multi-variable diferential calculus, first-order differential equations).

*Elementary knowledge of computer science:*finite automata, state-transition system, behavioral equivalence, bisimulation.

*General knowledge of modeling and simulation:*population model, feedback, simulation.**Course Enrolment Limitations**- The course is also offered to the students of the fields other than those the course is directly associated with.
**Fields of study the course is directly associated with**- Bioinformatics (programme FI, N-AP)

**Course objectives**- At the end of the course students should be able to:
understand elementary notions from the domain of continuous and hybrid systems;

orient themselves in methods for analysis of continuous and hybrid systems, system control and related problems;

characterize complexity of the given system;

apply computational methods to analyze dynamic properties of systems. **Syllabus**- Introduction to general systems theory. System, object, model. Boulding's hierarchy. Dynamical system, causality, state transition function. Dimensionality, state equations. Feedbacks, block diagram.
- Continuous, discrete, hybrid system. Trajectories, their existence, simulation. Examples of systems (electronics, economy, chemistry, biology).
- System presentation - system matrix and its meaning. Non-linear systems, classes of non-linearity, linearization. Stability, characterization of stability, Lyapunov theorems. Attractors and domains of attraction. Oscillation, multi-stability, chaos. Feinberg's classification of reaction kinetics systems.
- Reachability, reachability analysis for hybrid systems. Reachability in continuous systems - piece-wise linear systems, finite quotients.
- Controllability. Open-loop and closed-loop control, black-box control, model-based control, controller synthesis. System observability and identifiability.
- Parameterization, parameter uncertainty, sensitivity analysis. Tools for parameter estimation, system identification.
- Methods for system comparison: system equivalence, bisimulation and approximative bisimulation. Robustness analysis.
*Explained methods will be demonstrated in the form of practicals especially from the domain of computational systems biology. Tools from the following set will be employed: MATLAB/Octave, COPASI, GNA, SpaceEx/PHAVer, Ariadne.*

**Literature**- J.H. van Schuppen. Control and System Theory of Positive Systems, CWI Lecture notes, 2007.
- P. Tabuada.
*Verification and Control of Hybrid Systems: A Symbolic Approach.*Springer, 2009. xv, 202 p. ISBN 978-1-4419-0223-8. - VRIES, Gerda de.
*A course in mathematical biology : quantitative modeling with mathematical and computational methods*. Philadelphia, Pa.: Society for Industrial and Applied Mathematics, 2006. xii, 309. ISBN 0898716128. info - LYNCH, Stephen.
*Dynamical systems with applications using MATLAB*. Boston, Mass.: Birkhäuser, 2004. xv, 459. ISBN 3764343214. info - ŠTECHA, Jan and Vladimír HAVLENA.
*Teorie dynamických systémů : přednášky*. 2. vyd. Praha: Vydavatelství ČVUT, 2002. 247 s. ISBN 8001019713. info - ARROWSMITH, David K. and C. M. PLACE.
*An introduction to dynamical systems*. New York, N.Y.: Cambridge University Press, 1990. 423 s. ISBN 0521316502. info

*recommended literature***Teaching methods**- lectures, exercises
**Assessment methods**- 50% project, 50% written exam
**Language of instruction**- Czech
**Further Comments**- Study Materials

The course is taught once in two years.

- Enrolment Statistics (Spring 2019, recent)
- Permalink: https://is.muni.cz/course/fi/spring2019/IV120