for my stochastic systems class

29'. Consider a linear timeinvariant Gaussian system: n+1 = An. + Bug. + Grok, where {mm 1|qu1 w]. . . .} are independent1 In N NEED. ED} and nut ~ NEEQ}. 1 Let P E [l' and T :5- U be symmetric matrices. Assume that [31,3] is reachable. and consider the discounted innite horizon cost criterion E E ts1PM + niTnk}. k= Determine the form of the optimal control law and the equations to be satised by it1 by solving the dynamic programming equation. You need not address the problem of whether the equation you get for 5 below exists or has an unique solution. [ [I-Ent: Consider VEI} = ITSI +5 in the discounted dynamic programming equation]