Find the optimal control for the system: y_ 1t ayt ut to minimize: Ju

Find the optimal control for the system: y_ 1ðtÞ ¼ ayðtÞ þ uðtÞ to minimize: JðuÞ ¼ 1 2 Hy2 ðTÞ þ ZT 0 1 4 u2 ðtÞdt

a. Solve the problem with H ¼ 5, T ¼ 15, a ¼  0.2, and y(0) ¼ 5.0.

b. Solve the problem with H ¼ 5, T ¼ 15, a ¼ þ 0.2, and y(0) ¼ 5.0.