Algorithm for the Gradient Method

Transform the optimal control problem from the variable time interval [0,tf] to the fixed cr-interval, [0,1] 

Integrate state equations forward using the initial conditions and the control function values. Save the values of state variables at each grid point. 

Evaluate the objective functional using the values of control functions and state variables. Save the objective functional value. 

Improve u and tf using the gradient of the objective functional as follows. Change u by —eHu at each discrete point and tf by —eJtj where e is a positive real number, which causes maximum reduction in the objective functional. 

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Following Kelley (1962), modify the algorithm for the gradient method on p. 191 to determine the final time t using the following conditions for the... 

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