Find the optimal control of the plant

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Reference no: EM13971719

Problem: Find the optimal control u*(t) of the plant

x^.₁(t) = x₂(t); x₁(0) = 3, x₁(2) = 0

x^.₂(t) = -2x₁(t) + 5u(t); x₂(0) =5, x₂(2) = 0

which minimize the performance index

J = 1/2 ₀∫²[x₁²(t) + u²(t)]dt.

Reference no: EM13971719

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