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.
This course covers methods for the analysis and control of systems with multiple inputs and outputs, which are ubiquitous in modern technology and industry. Special emphasis will be given to discrete-time systems, due to their relevance for digital and embedded control architectures.
This course focuses on dynamic models of random phenomena, and in particular, the most popular classes of such models: Markov chains and Markov decision processes. We will also study applications in queuing theory, finance, project management, etc.
Mathematical optimization (alternatively spelled optimisation) or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternative
Control theory is a field of control engineering and applied mathematics that deals with the control of dynamical systems in engineered processes and machines. The objective is to develop a model or a
A Bellman equation, named after Richard E. Bellman, is a necessary condition for optimality associated with the mathematical optimization method known as dynamic programming. It writes the "value" of
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++.
The 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.