Editing Costate equation (section)

{{Short description|Optimal control equation}}
The '''costate equation''' is related to the state equation used in [[optimal control]].<ref>{{cite book |first1=Morton I. |last1=Kamien |author-link1=Morton Kamien |first2=Nancy L. |last2=Schwartz |title=Dynamic Optimization |location=London |publisher=North-Holland |edition=Second |year=1991 |isbn=0-444-01609-0 |pages=126–27 |url=https://books.google.com/books?id=0IoGUn8wjDQC&pg=PA126 }}</ref><ref>{{cite book |first=David G. |last=Luenberger |author-link=David Luenberger |title=Optimization by Vector Space Methods |location=New York |publisher=John Wiley & Sons |year=1969 |isbn= 9780471181170|page=263 |url=https://books.google.com/books?id=lZU0CAH4RccC&pg=PA263 }}</ref> It is also referred to as '''auxiliary''', '''adjoint''', '''influence''', or '''multiplier equation'''. It is stated as a [[vector (geometry)|vector]] of first order [[differential equation]]s
:<math>
\dot{\lambda}^{\mathsf{T}}(t)=-\frac{\partial H}{\partial x}
</math>
where the right-hand side is the vector of [[partial derivative]]s of the negative of the [[Hamiltonian (control theory)|Hamiltonian]] with respect to the state variables.