Optimal control
Example
Study the problem
Z 2
0u^2 xdt!max, x=u,x( 0 )= 0 , 0 u 1.The Hamiltonian isH(t,x,u,p)=u^2 x+pu.One cannot use the
Mangasarian theorem asu^2 is convex and not concave.
dp
dt = H0
x=^1. )p(t)=t+C.Asx( 2 )is freep( 2 )=0 that is 2+C=0 soC= 2 ,p(t)=t 2.