Optimal control
Aspis continuous there is a pointt 2 ( 0 , 1 )wherep(t)= 0.
p(t)>0 on( 0 ,t)hence on this intervalu=1 so asx( 0 )= 0x(t)=t.On the interval(t, (^1) )p(t)<0 sou= 1 and
x(t)= t+Con this interval. Asxis continuous
x(t )=t= t+C=x(t+), 2 t=C
Asx( 1 )= 0
C t= 2 t t= 2 t 1 = 0 , t= 1 / 2.
Hencex(t)= 1 tift 1 / 2.
x(t)=
t if t< 1 / 2
1 t if t 1 / 2