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{{Main article|Optimal control|Dynamic programming|Linear-quadratic regulator}}
In [[engineering]] and [[economics]], many problems involve multiple objectives which are not describable as the-more-the-better or the-less-the-better; instead, there is an ideal target value for each objective, and the desire is to get as close as possible to the desired value of each objective. For example, energy systems typically have a trade-off between performance and cost<ref>{{Cite journal|last1=Shirazi|first1=Ali|last2=Najafi|first2=Behzad|last3=Aminyavari|first3=Mehdi|last4=Rinaldi|first4=Fabio|last5=Taylor|first5=Robert A.|date=2014-05-01|title=Thermal–economic–environmental analysis and multi-objective optimization of an ice thermal energy storage system for gas turbine cycle inlet air cooling|journal=Energy|volume=69|pages=212–226|doi=10.1016/j.energy.2014.02.071|hdl=11311/845828 |doi-access=free}}</ref><ref>{{cite journal|last1=Najafi|first1=Behzad|last2=Shirazi|first2=Ali|last3=Aminyavari|first3=Mehdi|last4=Rinaldi|first4=Fabio|last5=Taylor|first5=Robert A.|date=2014-02-03|title=Exergetic, economic and environmental analyses and multi-objective optimization of an SOFC-gas turbine hybrid cycle coupled with an MSF desalination system|journal=Desalination|volume=334|issue=1|pages=46–59|doi=10.1016/j.desal.2013.11.039|hdl=11311/764704 |doi-access=free}}</ref> or one might want to adjust a rocket's fuel usage and orientation so that it arrives both at a specified place and at a specified time; or one might want to conduct [[open market operations]] so that both the [[inflation rate]] and the [[unemployment rate]] are as close as possible to their desired values.
Often such problems are subject to linear equality constraints that prevent all objectives from being simultaneously perfectly met, especially when the number of controllable variables is less than the number of objectives and when the presence of random shocks generates uncertainty. Commonly a multi-objective [[quadratic function#Bivariate (two variable) quadratic function|quadratic objective function]] is used, with the cost associated with an objective rising quadratically with the distance of the objective from its ideal value. Since these problems typically involve adjusting the controlled variables at various points in time and/or evaluating the objectives at various points in time, [[intertemporal optimization]] techniques are employed.<ref>{{cite book |doi=10.1109/IECON.2009.5415056 |isbn=978-1-4244-4648-3 |chapter=Chaos rejection and optimal dynamic response for boost converter using SPEA multi-objective optimization approach |title=2009 35th Annual Conference of IEEE Industrial Electronics |pages=3315–3322 |year=2009 |last1=Rafiei |first1=S. M. R. |last2=Amirahmadi |first2=A. |last3=Griva |first3=G.|s2cid=2539380 }}</ref>
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