Consider a temperature control model described by: x + x + U *= 13x + 2x0, *o = 0, (1) where 21, 2 are

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Consider a temperature control model described by: x + x + U *= 13x + 2x0, *o = 0, (1) where 21, 2 are internal temperatures, and to the outside temperature assumed constant. u is the control input (u > 0 means add heat, and u < 0 means remove heat). Find an optimal controller to minimize the cost J = = f* [(C1 + 0x) + ku]dr, (2) where C, C, and k are positive constants.