Each module contains 3 ECTS. You choose a total of 10 modules/30 ECTS in the following module categories:

- 12-15 ECTS in technical scientific modules (TSM)

TSM modules teach profile-specific specialist skills and supplement the decentralised specialisation modules. - 9-12 ECTS in fundamental theoretical principles modules (FTP)

FTP modules deal with theoretical fundamentals such as higher mathematics, physics, information theory, chemistry, etc. They will teach more detailed, abstract scientific knowledge and help you to bridge the gap between abstraction and application that is so important for innovation. - 6-9 ECTS in context modules (CM)

CM modules will impart additional skills in areas such as technology management, business administration, communication, project management, patent law, contract law, etc.

In the module description (download pdf) you find the entire language information per module divided into the following categories:

- instruction
- documentation
- examination

Modelling, simulation and optimization are fundamental to solving problems in a number of fields of science, technology and life. Students will learn to design, implement, simulate, and optimize a model of dynamic system. Simulation, the exploration of the dynamic behavior of the model in time and space, is discussed for both continuous and discrete-event systems. Simulating a model allows the evaluation of indicators of the performance of the modelled system, improving our understanding of its behavior and dynamic complexity.

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### Prerequisites

Basic knowledge of

- Calculus (differential and difference equations)
- Linear Algebra (vectors, matrices, change of basis, matrix inversion, computation of eigenvalues)

### Learning Objectives

The main aim of the course is to understand the pervasive feedback principles that rule the world we live in. Thanks to the acquired competencies, the successful student is expected to be able to tackle problems where temporal dynamics plays a major role. The student will learn about alternative and complementary modelling paradigms: from difference and differential equations for continuous time modelling to queuing systems and discrete event systems for discrete event modelling. The student will be then able to formalise the problem thanks to a dynamical model formulation, implement a simulation of the model, and explore the space of alternative behaviours of the system in order to synthesise a possibly optimal management and control strategy.

### Contents of Module

- Tools for systems thinking: introduction to modelling with causal loop diagrams and stock and flows diagrams
- Models of feedback dynamics in dynamic systems: growth and collapse, delays and oscillations
- Elements of systems theory from linear and regular systems to non linear systems: analysis of equilibrium and stability
- Optimisation and control of continuous state and time systems: concept of feedback control, state estimation with the Kalman filter and Optimal Control
- Modelling with discrete event systems: elements of queuing systems.
- Building discrete event systems: modelling input data and analysing output of simulations
- Simulation as an optimisation design tool: design of experiments, metamodelling and the response surface methodology

### Teaching and Learning Methods

Frontal lectures (3h/week) during which the students also perform hands-on exercises with modelling and simulation tools in order to acquire the key applications of the presented theory.

### Literature

Business Dynamics - Systems Thinking and Modeling for a Complex World, John D Sterman, McGraw-Hill, 2000. ISBN: 007238915X Introduction to Dynamic Systems, David G. Luenberger, John Wiley & Sons, 1979. ISBN: 0471025941 Introduction to Discrete Event Systems - 2nd Edition. C.G. Cassandras and S. Lafortune.Springer 2008. ISBN 978-0-387-33332-8Simulation Modeling and Analysis 3rd Edition, Averill M Law and W David Kelton, McGraw-Hill, 2000. ISBN 0-07-116537-1

*Simio and Simulation - Modeling, Analysis and Applications*, W.David Kelton, Jeffrey S. Smith, David T. Sturrock, Alexander Verbraeck. McGraw-Hill. 2010. ISBN 0-07-340888-3 Simulation with ARENA - 4th Edition, W. David Kelton and Randall P. Sadowski and David T. Sturrock, McGraw-Hill International Edition 2007. ISBN 0-07-110685-5

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