Costate equation

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.