Optimal control

<p>Optimal control theory is a branch of <a href="/facts/Control_theory/aIuERpn6">control theory</a> that deals with finding a <a href="/facts/Control_(optimal_control_theory)/72TNmtRb">control</a> for a <a href="/facts/Dynamical_system/782gREl5">dynamical system</a> over a period of time such that an <a href="/facts/Objective_function/xv5ozuhl">objective function</a> is optimized. It has numerous applications in science, engineering and operations research. For example, the dynamical system might be a <a href="/facts/Spacecraft/YQqQaUw0">spacecraft</a> with controls corresponding to rocket thrusters, and the objective might be to reach the <a href="/facts/Moon/zKHqEMPb">Moon</a> with minimum fuel expenditure. Or the dynamical system could be a nation's <a href="/facts/Economy/okLWSsEY">economy</a>, with the objective to minimize <a href="/facts/Unemployment/qGzDQbWt">unemployment</a>; the controls in this case could be <a href="/facts/Fiscal_policy/ekVzP0xo">fiscal</a> and <a href="/facts/Monetary_policy/LXehzvG0">monetary policy</a>. A dynamical system may also be introduced to embed <a href="/facts/Operations_research/H5yJkV5n">operations research problems</a> within the framework of optimal control theory.
</p><p>Optimal control is an extension of the <a href="/facts/Calculus_of_variations/Ya5Lsma3">calculus of variations</a>, and is a mathematical optimization method for deriving <a href="/facts/Control_theory/aIuERpn6">control policies</a>. The method is largely due to the work of <a href="/facts/Lev_Pontryagin/fDdDv9rA">Lev Pontryagin</a> and <a href="/facts/Richard_Bellman/xButmP2X">Richard Bellman</a> in the 1950s, after contributions to calculus of variations by <a href="/facts/Edward_J._McShane/3BWdVkJu">Edward J. McShane</a>. Optimal control can be seen as a <a href="/facts/Control_strategy/aIuERpn6">control strategy</a> in <a href="/facts/Control_theory/aIuERpn6">control theory</a>.
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Optimal control open-in-new

Optimal control