and 1 = 0 serves as the terminal constraint. The optimal control problem is to determine a piecewise, continuous function u(t), te(t0, such that the system is brought from the initial state to the final state with minimum cost. Because of the nonlinear nature of this problem, the optimal solution for a given initial time and state will best be obtained through a numerical algorithm. One of the well known methods used is the gradient technique. To focus discussion, the algorithm developed in Ref. 4 is adopted here. A flow diagram that outlines the computational procedure for our specific problem is shown in Fig. 6. Basically, this is an iterative computation, that starts with a guessed nominal control function u*(t) and integrates the state Eq. 30 from t0 to tf. Except for the first iteration, check the linerization errors, decrease control perturbation step-size, evaluate certain functions, integrate the adjoint equations, and then use the adjoint
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