Use the minimum principle to find the input voltage u(t) that charges the capacitor, in Figure…

Use the minimum principle to find the input voltage u(t) that charges the capacitor, in Figure 5.31, from x(0) = 2 V at t = 0 to x(10) = 12 V while minimizing the energy dissipated in the resistor. There are no constraints on u(t). Note that, by Kirchhoff’s voltage law,

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where and the energy dissipated is