Fuller's initial value problem
|Fuller's initial value problem|
|Discrete control functions:||1|
|Interior point equalities:||2|
This site describes a Fuller's problem variant with no terminal constraints and additional Mayer term for penalizing deviation from given reference values.
For almost everywhere the mixed-integer optimal control problem is given by
We use and .
If the problem is relaxed, i.e., we demand that be in the continuous interval instead of the binary choice , the optimal solution can be determined by means of direct optimal control.
The optimal objective value of the relaxed problem with is . The objective value of the binary controls obtained by Combinatorial Integral Approimation (CIA) is .