Solve the following LQR problem, which slightly changes Example 1 in Section 10.8. min fug Ju 1 2 y1T 5 2 1

Solve the following LQR problem, which slightly changes Example 1 in Section 10.8. min fug JðuÞ ¼ 1 2 ½y1ðTÞ  5 2 þ 1 2 ½y2ðTÞ  2 2 þ 1 2 Z2 0 1 2 u2 ðtÞdt s:t: yð0Þ ¼ 0 and yð2Þ free y_ 1ðtÞ ¼ y2ðtÞ y_ 2ðtÞ¼  y2ðtÞ þ uðtÞ: Set up in Excel the system of differential equations from the Hamiltonian Maximum Principle conditions, and also define the required transversality conditions at T.