Consider a temperature control model described by: x + x + U *= 13x + 2x0,...

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Consider a temperature control model described by: ₁x₁ + x₂ + U *₂= 13x₂ + 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* [(C1₁²₁ + 0₂x₂)² + k²u²]dr, (2) where C₁, C₂, and k are positive constants. Consider a temperature control model described by: ₁x₁ + x₂ + U *₂= 13x₂ + 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* [(C1₁²₁ + 0₂x₂)² + k²u²]dr, (2) where C₁, C₂, and k are positive constants.

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