Optimization in Function Spaces by Sasane Amol;

Author:Sasane, Amol; [Amol Sasane]
Language: eng
Format: epub
Publisher: Dover Publications
Published: 2016-02-29T16:00:00+00:00

(Here p is the profit per unit harvest, so that p multiplied by the actual harvest x(t)u(t)dt gives the profit at time t, and c is the cost per unit effort, so that c times the harvesting effort u(t)dt gives the cost incurred at time t. The factor e–rt is a discounting factor.) The problem of deciding how to harvest so that the above profit is maximized now arises: Which u maximizes f? This is an optimal control problem:

So we see that optimal control problems arise naturally in applications.◊

3.4.1. Linear control systems. Let A ∈ nxn, B ∈ nxm. A linear control system9 is an equation of the form

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