# Fuller's initial value multimode problem

From mintOC

Fuller's initial value multimode problem | |
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State dimension: | 1 |

Differential states: | 2 |

Discrete control functions: | 4 |

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. Furthermore, this variant comprises four binary controls instead of only one control.

## Mathematical formulation

For almost everywhere the mixed-integer optimal control problem is given by

## Parameters

We use together with:

## 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.

The optimal objective value of the relaxed problem with is . The objective value of the binary controls obtained by Combinatorial Integral Approimation (CIA) is .