# Earthquake Hazard Mitigation for Uncertain Building Systems Based on Adaptive Synergetic Control

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## Abstract

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## 1. Introduction

- Forming an extended differential equation system that represents the various operations, such as optimizing, achieving fixed values, suppressing disturbances, observing coordinates, etc.;
- Synthesizing external controls that work to reduce the extra degree of freedom (DOF) of the extended dynamic system model relative to the final manifold;
- Synthesizing the internal controls, which can establish links or relations among the internal coordinates of the system. The control goal can be guaranteed and assured by these links.

- Developing classical and adaptive synergetic control algorithms to solve the vibration control problem in earthquaked buildings on the basis of MR dampers and Lyapunov stability analysis;
- Proving asymptotic stability for building systems controlled by classical and adaptive synergetic control schemes, such that all errors finally converge to their corresponding zero equilibrium points based on the Lyapunov theorem;
- Guaranteeing the boundedness of the estimated viscosity and stiffness coefficients of building systems;
- Conducting a comparison between the proposed classical and adaptive synergetic controllers in terms of vibration suppression capabilities.

## 2. Dynamic Model

## 3. Adaptive Synergetic Control Design

#### 3.1. Design of Classical Synergetic Control

#### 3.2. Adaptive Synergetic Control

**Assumption:**

## 4. Computer Simulation

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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Simulation Parameter | Value |
---|---|

${c}_{0a}$ | $21$ $\mathrm{N}\xb7\mathrm{s}/\mathrm{cm}$ |

${c}_{1a}$ | $283$ $\mathrm{N}\xb7\mathrm{s}/\mathrm{cm}$ |

${c}_{0b}$ | $3.5$ $\mathrm{N}\xb7\mathrm{s}/\mathrm{cm}$ |

${c}_{1b}$ | $2.95$ $\mathrm{N}\xb7\mathrm{s}/\mathrm{cm}$ |

$\gamma $ | $363{\mathrm{cm}}^{-2}$ |

$n$ | $2$ |

${x}_{o}$ | $14.3\mathrm{cm}$ |

$\beta $ | $363{\mathrm{cm}}^{-2}$ |

$A$ | $301$ |

${k}_{o}$ | $46.9$ $\mathrm{N}/\mathrm{cm}$ |

${k}_{1}$ | $5$ $\mathrm{N}/\mathrm{cm}$ |

$\eta $ | $190{\mathrm{s}}^{-1}$ |

${\alpha}_{a}$ | $140\mathrm{N}/\mathrm{cm}$ |

${\alpha}_{b}$ | $695\mathrm{N}/\mathrm{cm}$ |

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**MDPI and ACS Style**

Al-Dujaili, A.Q.; Humaidi, A.J.; Allawi, Z.T.; Sadiq, M.E.
Earthquake Hazard Mitigation for Uncertain Building Systems Based on Adaptive Synergetic Control. *Appl. Syst. Innov.* **2023**, *6*, 34.
https://doi.org/10.3390/asi6020034

**AMA Style**

Al-Dujaili AQ, Humaidi AJ, Allawi ZT, Sadiq ME.
Earthquake Hazard Mitigation for Uncertain Building Systems Based on Adaptive Synergetic Control. *Applied System Innovation*. 2023; 6(2):34.
https://doi.org/10.3390/asi6020034

**Chicago/Turabian Style**

Al-Dujaili, Ayad Q., Amjad J. Humaidi, Ziyad T. Allawi, and Musaab E. Sadiq.
2023. "Earthquake Hazard Mitigation for Uncertain Building Systems Based on Adaptive Synergetic Control" *Applied System Innovation* 6, no. 2: 34.
https://doi.org/10.3390/asi6020034