Course objectives:
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The aim of the course is to deepen the students ability to integrate various methods of mathematical modeling in specific simulations of complex, hybrid systems. The course focuses on a specific case and addresses the discrete and stochastic aspects of the modeling and simulation problem.
Main topics of the course organized into weekly blocks:
- Introduction to modeling and simulation of complex systems
- Fundamentals of discrete event-driven systems
- Algorithmic composition of finite automata
- Admissible languages and their compositions
- Supervisor theory and design algorithms
- Basics of Markov chains
- Calculation of expected values and methods of conditioning
- Statistical simulation and the Monte Carlo method
- Extension to Markov Chain Monte Carlo
- Statistical validation methods
- Advanced validation methods
- Presentation of simulation results
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Requirements on student
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Credit: project processed within semester and final report
Exam: Adequate knowledge of delivered and practiced course content (results achieved within semester can affect final evaluation)
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Content
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Main topics of the course organized into weekly blocks:
- Introduction to modeling and simulation of complex systems
- Fundamentals of discrete event-driven systems
- Algorithmic composition of finite automata
- Admissible languages and their compositions
- Supervisor theory and design algorithms
- Basics of Markov chains
- Calculation of expected values and methods of conditioning
- Statistical simulation and the Monte Carlo method
- Extension to Markov Chain Monte Carlo
- Statistical validation methods
- Advanced validation methods
- Presentation of simulation results
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Activities
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Fields of study
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Guarantors and lecturers
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Literature
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Recommended:
C. G. Cassandras. Introduction to Discrete Event Systems. Kluwer Academic Publishers, 1999.
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On-line library catalogues
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Time requirements
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All forms of study
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Activities
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Time requirements for activity [h]
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Contact hours
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39
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Presentation preparation (report) (1-10)
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10
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Practical training (number of hours)
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26
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Preparation for comprehensive test (10-40)
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35
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Preparation for an examination (30-60)
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50
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Total
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160
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Prerequisites
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Knowledge - students are expected to possess the following knowledge before the course commences to finish it successfully: |
Students are expected to have elementary knowledge in system theory, algorithm development and programming, all on level of basic university courses. |
Skills - students are expected to possess the following skills before the course commences to finish it successfully: |
student has basic programming knowledge in Matlab |
Competences - students are expected to possess the following competences before the course commences to finish it successfully: |
N/A |
N/A |
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Learning outcomes
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Knowledge - knowledge resulting from the course: |
understand systems analysis methods and their application to the analysis of cybernetic systems |
understand and apply the general principles of systems analysis |
analyze systems using systematic methods |
analyze systems using object-oriented methods |
effective use of computing systems |
Skills - skills resulting from the course: |
the student is able to translate the discrete behavior of the system into the generated language |
the student is able to schematically describe the language using a finite state machine |
the student is able to use automated tools to verify the correctness of the finite state machine |
the student is able to create compositions of finite automata |
the student is able to propose admissible rules of a finite state machine to verify their feasibility |
the student is able to design supervisory machines |
the student is able to design a simulation according to the Monte Carlo method |
the student is able to design and implement a simulation using the Markov Chain Monte Carlo method |
the student is able to validate the simulation program |
the student is able to validate the simulation results against the measured values |
Competences - competences resulting from the course: |
N/A |
N/A |
N/A |
N/A |
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Assessment methods
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Knowledge - knowledge achieved by taking this course are verified by the following means: |
Combined exam |
Individual presentation at a seminar |
Skills - skills achieved by taking this course are verified by the following means: |
Project |
Individual presentation at a seminar |
Written exam |
Competences - competence achieved by taking this course are verified by the following means: |
Skills demonstration during practicum |
Individual presentation at a seminar |
Seminar work |
Written exam |
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Teaching methods
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Knowledge - the following training methods are used to achieve the required knowledge: |
Lecture supplemented with a discussion |
Practicum |
Self-study of literature |
One-to-One tutorial |
Interactive lecture |
Skills - the following training methods are used to achieve the required skills: |
Lecture |
Practicum |
Multimedia supported teaching |
Textual studies |
Collaborative instruction |
Self-study of literature |
One-to-One tutorial |
Discussion |
Competences - the following training methods are used to achieve the required competences: |
Lecture |
Practicum |
Multimedia supported teaching |
Textual studies |
Collaborative instruction |
Self-study of literature |
One-to-One tutorial |
Discussion |
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