Optimal control problems free final time

We first consider optimal control problems in which the final time is free, i.e., not specified or fixed. Thus, in addition to finding optimal control functions, we need to determine the optimal final time as well in these problems. 

This is the optimal control problem of Section 5.2 (p. 126) in which both the final time and the final state are unspecified or free. Using vectors, the objective is to minimize the functional... 

Integral constraints could be equality or inequality constraints. We first consider integral equality constraints in an optimal control problem with free state and free final time. 

Table 7.1 lists the parameters used to solve the optimal control problem with the above algorithm. In this problem, the final time and final states are free. It is desired to find two controls, u t) and U2 t), and the final time tf that maximize the final product concentration 2/4(tf). 

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