Consider the following discrete lincar time-invariant system: Ek = Apa + Buk, (0.1) where Is ER" is the system state at

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Consider The Following Discrete Lincar Time Invariant System Ek Apa Buk 0 1 Where Is Er Is The System State At 1 (87.04 KiB) Viewed 20 times

Consider the following discrete lincar time-invariant system: Ek = Apa + Buk, (0.1) where Is ER" is the system state at time k, uk R" is the control input at time k, and Y4 € {0,1} is the decision variable at the controller whether it sends us to the system or not. Consider any initial condition 20 € R" which is known to the controller (hence all future state Ink > 1 are known to the controller). Assume the controller can communicate with the system for d (de N and d<T) times, which is equivalent to say that TI Σγκ = d. (0.2) k=0 A schedule 6 at the controller consists of a sequence of binary-valued variables (74) : k = 0,...,T – 1}. For a given schedule 0, define J() as T! J(@) 4 min (369xx + (@)u' Rus) +27Qur. Find a closed-form expression of J(@) as well as the optimal control ux's.