final time specified Optimal control theory please true solution Example 4.3-2. Find an extremal curve for the functional J(x) = 2** [x160 + 4x3(0) + 8,3(180) de (4.3-10) which satisfies the boundary conditions 2(0) [*] -6) and ()-[0] * The Euler equations, found from (4.3-6a), 2x100 - 2000) = 0 (4.3-11) 8x76) - 70 -0, (4.3-11b) are linear, time-invariant, and homogeneous. Solving these equations by classical methods (or Laplace transforms) gives *90) - € +66-34 + cos2t + sin 21, (4.3-12) where Cs. Cues, and are constants of integration. Differentiating *T() twice and substituting into Eq. (4.3-11b) gives *16) - 10,1 + 106-3 -- I cos 2t - Iso sin 2. (4.3-13) Putting i = 0 and + = 1/4 in (4.3-12) and (4.3-13), we obtain four equa- tions and four unknowns; that is, *f(0) = 0; *f(0) = 1; **(*) - 1; **(*) - 0. Solving these equations for the constants of integration yields -* +62 - EN/ C = -1; cs == 1 C