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Discrete and Continuous Systems Optimisation

Objectives

At the end of this module, the student will have understood and be able to explain (main concepts):
* different approaches to analyse, evaluate the performance of discrete-event
systems through different models (deterministic or stochastic, graphs) and to optimise
them (linear programming)
* the optimisation methods for continuous systems:
- static (first -and second-order conditions)
- dynamic (dynamic programming)
- their applications to optimal or model-predictive control mainly for linear systems
The student will be able to:
- to analyse, model and solve an optimisation problem of discrete systems using linear
programming or a graph, by applying relevant algorithms (simplex or usual graphs
and networks algorithms)
- to model and to characterize stationary Markovian processes in discrete state
space (chains), in continuous or discrete time, queuing systems and their
transient and stationary behaviour, to evaluate their performance
- to model and analyse discrete event systems with Petri nets
- to formalise and solve an optimisation problem based on a non-linear, quadratic criterion,
without or with constraints, in the case of systems with real variables
-to develop and design an optimal control law (LQG) or a model predictive controller
for a linear or linearised process.

Needed prerequisite

Linear algebra - Probabilities - Dynamic systems (state concept). Basic elements in
logic systems and Petri nets.

Form of assessment

The evaluation of outcome prior learning is made as a continuous training during the semester. According ot the teaching, the assessment will be different: as a written exam, an oral exam, a record, a written report, peers review...