Question: Consider the control system given by with initial state x(0) =1. Find the optimal control feedback law to minimize the performance index x(k+1)=0.5x(k) + u(k)

Consider the control system given by

x(k+1)=0.5x(k) + u(k)

with initial state x(0) =1.
Find the optimal control feedback law to minimize the performance index

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x(k+1)=0.5x(k) + u(k)

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