Consider the system of two linear differential equations: y_ 1t y2t y_ 2t y2t

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Consider the system of two linear differential equations: y_ 1ðtÞ ¼ y2ðtÞ y_ 2ðtÞ¼  y2ðtÞ þ uðtÞ

which needs to be controlled to minimize: JðuÞ ¼ 1 2 ZT 0 y2 1ðtÞ þ y2 2ðtÞ þ u2 ðtÞ  dt: Solve the problem setting yð0Þ ¼½ 4 2 , T ¼ 2, and y(T) free.

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