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Optimal Control - APM4809

Honours Year module NQF level: 8 Credits: 12
Module presented in English Module presented online
Purpose: Systems that evolve in time occur naturally in various fields such as dynamics, economics, medicine and ecology, and modelling the behaviour of such systems provides an important application of mathematics. These systems can be completely deterministic, but often it may be possible to control their behaviour through the application of external controls. The theory of optimal control is concerned with finding the controls which, at minimum cost, either direct the system along a given trajectory or enable it to reach a desired target state. This module introduces some of the basic tools of optimal control. Many applications from various fields are also included, to show how the various 'maximum principles' help us find the optimal controls in practice. Contents: Terminology and classifications of optimal control problems. Controllability and reachability. Linear time optimal problem. The Time Optimal Principle. The Pontryagin Maximum Principle. Linear equations with quadratic costs.