Let us consider an optimal control problem, where the final time is a free parameter. The objective function to minimize is J1. Since the final time is a free variable, the optimal control solution can be obtained in a fixed final time, optimal control framework by considering the final time as a design parameter.
Now, can we choose a different cost function J2 and select the final time (design parameter)
such that the final time will minimize J2?
Dear Avijit,
The cost function can integrate not only the state but also the input and the output plus the constraint; it is the case of an optimal control by generalized tracking with constraint.
In other hand you can design optimal dynamic control approach in a multiobjective.
For more details and information about this subject, i suggest you to see attached file on topic.
Best regards
Dear Avijit,
I think the answer depends on the application of the problem. In many applications, the final time has to be chosen by actual constraints and physical conditions. So, the designer is not free to choose it according to the cost function minimization.
But in other applications, cost reduction is a top priority. Therefor you can increase the end time to further reduction of the cost function. In this case, you can select the final time as design parameter based on amount of cost function .
Best regards
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