Optimal control, explanation, interpretation
If(x(t),u(t))is optimal then they must be optimal at every moment of
time. If not change the path accordingly. (May be not true as sometimes
one must undertake some short term sacriÖces. There are local and global
criteria for optimality.) So if you are greedy then you must choosexas
∂
∂x
H(t,x,u,p)+xp^0
=Hx+p^0 = 0 )p^0 = Hx.
Observe that there are no constraints on the state variable. Now ifx(t)
and therefore its pricep(t)is already given thenx(t)p 0 (t)is also given
and one should directly maximizeHwith respect tou.(There are
constraints onuso we cannot simply calculate the stationary points.)
