Economists use optimal control both in microeconomics and in macroeconomics.
Your question is about economic policy in particular, but policy decisions can be guided both by micro and macro models.
Central banks do use both simple feedback loops (think Taylor rule) and optimal control analysis to guide decisions. There is this Federal Reserve note from 2014 with introductory information and some references. It describes FRB/US model, which helps find the optimal path for the federal funds rate to minimize a given loss function.
Microeconomic models can also guide policy decisions, for example, there is an active literature on oligopoly from optimal control theory perspective, which historically focused on advertising (e.g. this survey from 1977). These can be used to predict behavior of agents on micro level and motivate policy decisions as well.
Microeconomics even contains a nice extension of optimal control to a setting with multiple decision-makers called differential game theory, which I will attempt to loosely describe as non-cooperative optimal control.
These models are further from policy making, but more of "exact science" type. Searching this stackexchange for "optimal control" brings up some relevant results too.
Speaking of Taylor rule, John Taylor and John Williams in this 2010 paper argue against complex rules in favor of simpler ones. They mention the more obvious problems of measurement error and unobservables, which we have to make assumptions about: expectations, learning etc. However, they also state that simpler rules have advantage of working in a wider set of settings in practice:
"One potential shortcoming of the optimal control approach is that it
ignores uncertainty about the specification of the model. Although in
principle one can incorporate various types of uncertainty to the
analysis of optimal policy, in practice computational feasibility
limits what can be done. As a result, existing optimal control policy
analysis is typically done using a single reference model, which is
assumed to be true." (page 29)
The paper has other references and history of the topic.
In the same note by Federal reserve there is also a warning:
"These models are by necessity an abstraction of a much more complex
economic reality, and hence the actual strategies followed by the
Federal Reserve and other central banks necessarily retain an
important judgmental component."