Control (optimal control theory): Difference between revisions

Revision as of 21:01, 1 January 2021

Revision as of 21:01, 1 January 2021

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In [[optimal control theory]], a '''control''' is a variable chosen by the controller or [[Agent (economics)|agent]] to manipulate [[state variables]], similar to an actual [[control valve]]. Unlike the state variablesvariable, it does not have a predetermined [[equation of motion]].<ref>{{cite book |first=Brian S. |last=Ferguson |first2=G. C. |last2=Lim |title=Introduction to Dynamic Economic Problems |___location=Manchester |publisher=Manchester University Press |year=1998 |isbn=0-7190-4996-2 |page=162 }}</ref> The goal of optimal control theory is to find some [[sequence]] of controls (within an admissible set) to achieve an optimal path for the state variables (with respect to a [[loss function]]).

A control given as a function of time only is referred to as an ''open-loop control''. In contrast, a control that gives optimal solution during some remainder period as a function of the state variable at the beginning of the period is called a ''closed-loop control''.<ref>{{cite book |first=Daniel |last=Léonard |first2=Ngo Van |last2=Long |title=Optimal Control Theory and Static Optimization in Economics |___location=New York |publisher=Cambridge University Press |year=1992 |isbn=0-521-33158-7 |page=181 |url=https://www.google.com/books/edition/Optimal_Control_Theory_and_Static_Optimi/gSHxK5Cq4BgC?hl=en&gbpv=1&pg=PA181 }}</ref>