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# hw7 - EE364b Prof S Boyd EE364b Homework 7 1 MPC for output...

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Unformatted text preview: EE364b Prof. S. Boyd EE364b Homework 7 1. MPC for output tracking. We consider the linear dynamical system x ( t + 1) = Ax ( t ) + Bu ( t ) , y ( t ) = Cx ( t ) , t = 0 ,...,T − 1 , with state x ( t ) ∈ R n , input u ( t ) ∈ R m , and output y ( t ) ∈ R p . The matrices A and B are known, and x (0) = 0. The goal is to choose the input sequence u (0) ,...,u ( T − 1) to minimize the output tracking cost J = T summationdisplay t =1 bardbl y ( t ) − y des ( t ) bardbl 2 2 , subject to bardbl u ( t ) bardbl ∞ ≤ U max , t = 0 ,...,T − 1. In the remainder of this problem, we will work with the specific problem instance with data A = 1 1 0 0 1 1 0 0 1 , B = . 5 1 , C = bracketleftBig − 1 0 1 bracketrightBig , T = 100, and U max = 0 . 1. The desired output trajectory is given by y des ( t ) = t < 30 , 10 30 ≤ t < 70 , t ≥ 70 ....
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hw7 - EE364b Prof S Boyd EE364b Homework 7 1 MPC for output...

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