Three Tank multimode problem
|Three Tank multimode problem|
|Discrete control functions:||3|
|Interior point equalities:||2|
This site describes a Double tank problem variant with three binary controls instead of only one control and three tanks, i.e., three differential states representing different compartments.
The mixed-integer optimal control problem is given by
These fixed values are used within the model.
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 and the CIA decomposition. We denote the relaxed control values with .
The optimal objective value of the relaxed problem with is . The objective value of the binary controls obtained by Combinatorial Integral Approimation (CIA) is .
Model description is available in (using pycombina for solving the (CIA) rounding problem step):