Costate equation

The costate equation is related to the state equation used in optimal control.^[1]^[2] It is also referred to as auxiliary, adjoint, influence, or multiplier equation. It is stated as a vector of first order differential equations

{\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.

^ Kamien, Morton I.; Schwartz, Nancy L. (1991). Dynamic Optimization (Second ed.). London: North-Holland. pp. 126–27. ISBN 0-444-01609-0.
^ Luenberger, David G. (1969). Optimization by Vector Space Methods. New York: John Wiley & Sons. p. 263. ISBN 9780471181170.

[1] Kamien, Morton I.; Schwartz, Nancy L. (1991). Dynamic Optimization (Second ed.). London: North-Holland. pp. 126–27. ISBN 0-444-01609-0.

[2] Luenberger, David G. (1969). Optimization by Vector Space Methods. New York: John Wiley & Sons. p. 263. ISBN 9780471181170.

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