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
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.
The costateequation is related to the state equation used in optimal control. It is also referred to as auxiliary, adjoint, influence, or multiplier...
{\vec {c}}} in the adjoint equation, whereas the diffusion term remains self-adjoint. Adjoint state method Costateequations Jameson, Antony (1988). "Aerodynamic...
f(x)}{\partial x}}} which after replacing the appropriate terms recovers the costateequation − λ ˙ ( t ) = ∂ I ∂ x + λ ( t ) ∂ f ( x ) ∂ x ⏟ = ∂ H ∂ x {\displaystyle...
constrained trajectory. In control theory this is formulated instead as costateequations. Moreover, by the envelope theorem the optimal value of a Lagrange...
principle — infinite-dimensional version of Lagrange multipliers Costateequations — equation for the "Lagrange multipliers" in Pontryagin's minimum principle...
optimal control theory, the concept of shadow price is reformulated as costateequations, and one solves the problem by minimization of the associated Hamiltonian...
the term "primer vector" to refer to the adjoint variables in the costateequation associated with the velocity vector, pointing out their fundamental...
problems is to solve for the costate (sometimes called the shadow price) λ ( t ) {\displaystyle \lambda (t)} . The costate summarizes in one number the...
x/\partial \theta } the control. As usual in optimal control the costate evolution equation must satisfy ∂ ν ∂ θ = − ∂ H ∂ x = − ( ∂ V ∂ x ( x , θ ) − 1 −...
substituted for equation 4, while in equation 4, f 2 {\displaystyle f_{2}} can be replaced by f 3 {\displaystyle f_{3}} due to equation 3, which can then...
1793–6. doi:10.1109/9.467672. Fahroo, Fariba; Ross, I. Michael (2001). "Costate Estimation by a Legendre Pseudospectral Method". Journal of Guidance, Control...
Camila C. Francolin, David A. Benson, William W. Hager, Anil V. Rao. "Costate Estimation in Optimal Control Using Integral Gaussian Quadrature Orthogonal...
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