Modeling and control of dynamical systems in bioengineering

Part 1 (Ph. Bogaerts, 18h): Introduction to parameter estimation, Mathematical model structures (taxinomy and properties), Parameter estimation (least squares, maximum likelihood), Mathematical modeling of biological networks, Case studies.

Part 1 (D. Gonze, 18h): Discrete and continuous models (ODE) in population dynamics: logistic equation, Ricker's and Nicholson-Bailey's discrete models, Gompertz model, Allee effect, Lotka-Volterra's models, chemostat, SIR models. Overview of some recent scientific articles.

Part 2 (Ph. Bogaerts, 24h): (Bio)chemical process control (Control of a CSTR : basic principles, Control of a batch exothermic reactor, Control of time delay and minimum phase processes, Feedforward control, Control of MIMO systems).

At the end of the course, the student will be able to

• choose, develop and analyze a dynamical model for describing a system in biology and/or in bioengineering;

• build a mathematical model of a process on the basis of experimental data;

• design control structures for processes of chemical and biotechnological industries.

Required and Corequired knowledge and skills

Generally: basics of linear algebra; function analysis; statistics and probability theory; linear system dynamics.

More specifically: vectors and matrices (product, inverse, trace, transpose, etc.); function minimization; Taylor series development; integration of first order ordinary differential equations; mathematical expectation, probability density function, mean, variance, stochastic processes, white noise, Gaussian distribution, uniform distribution; state equations and transfer functions for linear time-invariant dynamical systems.

Part 1: 3 ECTS of ex cathedra courses.

Part 2: 1 ECTS of ex cathedra courses and 1 ECTS of seminars (simulations on computer).

Course notes

• Podcast
• Syllabus
• Université virtuelle

Contacts

Philippe Bogaerts : École polytechnique de Bruxelles, 3BIO-BioControl (Biosystems Modeling and Control); email: philippe.bogaerts@ulb.be

Didier Gonze : Faculté des Sciences, Unit of Theoretical Chronobiology; email: didier.gonze@ulb.be

Campus

Solbosch

Method(s) of evaluation

• written examination
• Oral examination

written examination

Oral examination

1^st exam: written exam with Prof. D. Gonze

• subject: Part 1 taught by Prof. Gonze

2^nd exam: oral exam (without preparation) with Prof. Ph. Bogaerts

• subject of question 1: Part 1 taught by Prof. Bogaerts
• subject of question 2: Part 2

Mark calculation method (including weighting of intermediary marks)

• Written exam with Prof. Gonze: 30% (mark 1)
• Oral exam with Prof. Bogaerts (Part 1): 30% (mark 2)
• Oral exam with Prof. Bogaerts (Part 2): 40% (mark 3)

Final mark = 0,3 * mark 1 + 0,3 * mark 2 + 0,4 * mark 3

If one of these partial marks is greater than or equal to 10/20, it is then definitively acquired (from one session to another and/or from one academic year to another) and the corresponding exam may not be taken anymore.

An attendance note (NDP) may be obtained for 1, 2 or the 3 above-mentioned partial marks, hence leading to an attendance note (NDP) for the whole course. However, it remains possible to definitively acquire a mark greater than or equal to 10/20 for the partial mark(s) whose corresponding exams have been successfully presented.

If, upon deliberation, the course is not validated, then all the exams associated to a mark lower than 10/20 must be redone (from one session to another and from one academic year to another). 
 

Language(s) of evaluation

• english