-5. The approximating difference equation representation for a continuously operating system is x(k + 1) = 0.75x(k) + u(k). It is desired to bring the system state to the target set S defined by 0.0 < x(2) <2.0 with minimum expenditure of control effort; i.e., minimize J- u(0) + u?(1). The allowable state and control values are constrained by 0.0 < x(k) < 6.0 -1.0 su(k) < 1.0.

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