# Three Tank multimode problem

Three Tank multimode problem | |
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State dimension: | 1 |

Differential states: | 3 |

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.

## Mathematical formulation

The mixed-integer optimal control problem is given by

## Parameters

These fixed values are used within the model.

## Reference Solutions

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 .

## Source Code

Model description is available in (using pycombina for solving the (CIA) rounding problem step):