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Concept# Optimal control

Summary

Optimal control theory is a branch of mathematical optimization that deals with finding a control for a dynamical system over a period of time such that an objective function is optimized. It has numerous applications in science, engineering and operations research. For example, the dynamical system might be a spacecraft with controls corresponding to rocket thrusters, and the objective might be to reach the moon with minimum fuel expenditure. Or the dynamical system could be a nation's economy, with the objective to minimize unemployment; the controls in this case could be fiscal and monetary policy. A dynamical system may also be introduced to embed operations research problems within the framework of optimal control theory.
Optimal control is an extension of the calculus of variations, and is a mathematical optimization method for deriving control policies. The method is largely due to the work of Lev Pontryagin and Richard Bellman in the 1950s, after contributions to calculus of

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This doctoral course provides an introduction to optimal control covering fundamental theory, numerical implementation and problem formulation for applications.

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The goal of the project is to study an optimal control problem for the Cahn-Hilliard equation. To this end, we proceed in three steps: we first introduce the Cahn-Hilliard equation and how it is derived, and describe some of its applications; then, we approximate it with the finite element method and solve it with FreeFem++. Finally, we formulate the optimal control problem and solve it with FreeFem++.

2015The goal of this project would be to study the thermochemical production of hydrogen by using woody biomass as a raw material. The thermo-economic performance of the process will be evaluated and an optimisation will be performed to define the optimal system.

2009