Question: Consider the discrete-time system described by the state-space model x[k + 1] = Ax[k] + Bu[k] y[k] = Cx[k] where -2 [1] 0 -2

Consider the discrete-time system described by the state-space model x[k + 1]

Consider the discrete-time system described by the state-space model x[k + 1] = Ax[k] + Bu[k] y[k] = Cx[k] where -2 [1] 0 -2 A H and x = [] is the state vector, and u = = [u1 Consider also the finite horizon cost functional given by J = 2_o (2x [k] + 4x [k] + u [k]) + x [3] + x [3]. If the initial system state is given by x [0] = 2 [3] 9 9 B - C = [10], u] is the input vector. and a control sequence that is optimal with respect to minimising the cost J is applied to the system, what is the corresponding control u[2] at the sample time k = 2?

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