# Annihilation of calcium oscillations with PLC activation inhibition

Annihilation of calcium oscillations with PLC activation inhibition | |
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State dimension: | 1 |

Differential states: | 4 |

Discrete control functions: | 2 |

Path constraints: | 1 |

Interior point equalities: | 4 |

This control problem is closely related to Annihilation of calcium oscillations. The only difference is an additional control function, the inhibition of PLC activation. We state only the differences in this article.

## Mathematical formulation

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

Note that we write instead of and have an additional control function . The regularization parameters are set to .

## Reference Solutions

A solution for this problem is described in [Lebiedz2005]**Author: ** *Lebiedz, D.; Sager, S.; Bock, H.G.; Lebiedz, P.***Journal: ** *Physical Review Letters***Pages: ** *108303***Title: ** *Annihilation of limit cycle oscillations by identification of critical phase resetting stimuli via mixed-integer optimal control methods***Volume: ** *95***Year: ** *2005*

. A local minimum that is actually slightly worse than the solution provided for only one control, is shown in the next plots.

## Variants

## References

[Lebiedz2005] | Lebiedz, D.; Sager, S.; Bock, H.G.; Lebiedz, P. (2005): Annihilation of limit cycle oscillations by identification of critical phase resetting stimuli via mixed-integer optimal control methods. Physical Review Letters, 95, 108303 |