Example 5.1 Consider the standard integrator .5: m a (with can E R} and let Menu} 2 Id + a" The corresponding HJB equation is 11(5, x} = mirth-4 + u.' + mean}. (5.15) :16 Since the expression inside the inmum is polynomial in u, we can easily nd the control that achieves the inmum: differentiating with respect to a, we have 4113 + It'x) = 0 which yields a 2 {%V=[t' In 133' Plugging this control into the HJB equation [5.15), we obtain - We =1\" s