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
Contents
where the right-hand side is the vector of partial derivatives of the negative of the Hamiltonian with respect to the state variables.
Interpretation
The costate variables
Solution
The state equation is subject to an initial condition and are solved forwards in time. The costate equation must satisfy a terminal condition and are solved backwards in time, from the final time towards the beginning. For more details see Pontryagin's maximum principle.