### Abstract

A new method is investigated to reconfigure smart structures using the technique of polynomial series to approximate a true heteroclinic connection between unstable equilibria in a smart structure model. We explore the use of polynomials of varying order to first approximate the heteroclinic connection between two equal-energy, unstable equilibrium points, and then develop an inverse method to control the dynamics of the system to track the reference polynomial trajectory. It is found that high-order polynomials can provide a good approximation to heteroclinic connections and provide an efficient means of generating such trajectories. The method is used first in a simple smart structure model to illustrate the method and is then extended to a more complex model where the numerical generation of true heteroclinic connections is difficult. It is envisaged that being computationally efficient, the method could form the basis for real-time reconfiguration of smart structures using heteroclinic connections between equal-energy, unstable configurations.

Language | English |
---|---|

Article number | 105034 |

Number of pages | 16 |

Journal | Smart Materials and Structures |

Volume | 24 |

Issue number | 10 |

DOIs | |

Publication status | Published - 23 Sep 2015 |

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### Keywords

- feedback linearization
- heteroclinic connection
- inverse method
- polynomial series
- reconfiguring smart structures

### Cite this

*Smart Materials and Structures*,

*24*(10), [105034]. https://doi.org/10.1088/0964-1726/24/10/105034

}

*Smart Materials and Structures*, vol. 24, no. 10, 105034. https://doi.org/10.1088/0964-1726/24/10/105034

**Reconfiguring smart structures using approximate heteroclinic connections.** / Zhang, Jiaying; McInnes, Colin R.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Reconfiguring smart structures using approximate heteroclinic connections

AU - Zhang, Jiaying

AU - McInnes, Colin R

PY - 2015/9/23

Y1 - 2015/9/23

N2 - A new method is investigated to reconfigure smart structures using the technique of polynomial series to approximate a true heteroclinic connection between unstable equilibria in a smart structure model. We explore the use of polynomials of varying order to first approximate the heteroclinic connection between two equal-energy, unstable equilibrium points, and then develop an inverse method to control the dynamics of the system to track the reference polynomial trajectory. It is found that high-order polynomials can provide a good approximation to heteroclinic connections and provide an efficient means of generating such trajectories. The method is used first in a simple smart structure model to illustrate the method and is then extended to a more complex model where the numerical generation of true heteroclinic connections is difficult. It is envisaged that being computationally efficient, the method could form the basis for real-time reconfiguration of smart structures using heteroclinic connections between equal-energy, unstable configurations.

AB - A new method is investigated to reconfigure smart structures using the technique of polynomial series to approximate a true heteroclinic connection between unstable equilibria in a smart structure model. We explore the use of polynomials of varying order to first approximate the heteroclinic connection between two equal-energy, unstable equilibrium points, and then develop an inverse method to control the dynamics of the system to track the reference polynomial trajectory. It is found that high-order polynomials can provide a good approximation to heteroclinic connections and provide an efficient means of generating such trajectories. The method is used first in a simple smart structure model to illustrate the method and is then extended to a more complex model where the numerical generation of true heteroclinic connections is difficult. It is envisaged that being computationally efficient, the method could form the basis for real-time reconfiguration of smart structures using heteroclinic connections between equal-energy, unstable configurations.

KW - feedback linearization

KW - heteroclinic connection

KW - inverse method

KW - polynomial series

KW - reconfiguring smart structures

UR - http://www.scopus.com/inward/record.url?scp=84942884241&partnerID=8YFLogxK

UR - http://iopscience.iop.org/0964-1726

U2 - 10.1088/0964-1726/24/10/105034

DO - 10.1088/0964-1726/24/10/105034

M3 - Article

VL - 24

JO - Smart Materials and Structures

T2 - Smart Materials and Structures

JF - Smart Materials and Structures

SN - 0964-1726

IS - 10

M1 - 105034

ER -