Costate equation

Summary

The costate equation is the differential equation satisfied by the multipliers, or costates, of an optimal control problem along an optimal trajectory. It reads $p' = -\partial H / \partial x$, where $H$ is the Hamiltonian of the problem. Together with the state equation $x' = \partial H / \partial p$ it forms a Hamiltonian system in Pontryagin's maximum principle. It is affine in $p$, and its linear part is the adjoint of the linearized state equation.