Mathematics for Economists

Optimal control

DeÖnition

The expression

H(t,x,u,p)=f(t,x,u)+p
g(t,x,u)

is called the Hamiltonian. The variablepis called the adjoint or co-state

variable. In some problems

H(t,x,u,p)=p 0 
f(t,x,u)+p
g(t,x,u)

and it is possible thatp 0 = 0.