Question: Consider the following scalar discrete-time control sys- tem x(k +1) = -3x(k) + u(k) where x E R, u ER and x(0) = -1.

Consider the following scalar discrete-time control sys- tem x(k +1) = -3x(k)

Consider the following scalar discrete-time control sys- tem x(k +1) = -3x(k) + u(k) where x E R, u ER and x(0) = -1. Let N > 1 be some integer. (a) Consider the following cost function N J =Eu(k). k=0 Find the optimal control law and the minimal cost. (b) Consider the following cost function N J = E x(k). k=0 Find the optimal control law and the minimal cost.

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