The costate equation is related to the state equation used in optimal control. It is also referred to as auxiliary, adjoint, influence, or multiplier equation. It is stated as a vector of first order differential equations

${\displaystyle {\dot {\lambda }}^{\mathsf {T}}(t)=-{\frac {\partial H}{\partial x}}}$

where the right-hand side is the vector of partial derivatives of the negative of the Hamiltonian with respect to the state variables.