Consider a linear time-invariant Gaussian system: n+1 = Amk + Bu;c + ka, where {$0,w0,w1, . . } are independent, $0 N N(E0, 20) and wk N N(0,Q). Let P 2 0 and T > 0 be symmetric matrices. Assume that (A, B) is reachable, and consider the discounted innite horizon cost criterion E Z ngxk + ufTuk). k=0 Determine the form of the optimal control law and the equations to be satised by it, by solving the dynamic programming equation. You need not address the problem of whether the equation you get for 5' below exists or has an unique solution. [ [Hintz Consider V(:.c) = mTS$+ s in the discounted dynamic programming equation]