Hamiltonian of an optimal-control problem
= Hamiltonian of an optimal-control problem
{c}
{title2=$H(t,x,u,p)=L(t,x,u)+p\cdot f(t,x,u)$}
In a normal minimization convention for <optimal control>, the running cost $L$ and dynamics $\dot x=f$ define $H=L+p\cdot f$. The multiplier $p$ is a <costate>; this Hamiltonian is a device for variational necessary conditions rather than necessarily a physical energy.