Reconfiguring Smart Structures using Approximate Heteroclinic Connections

A new method is investigated to reconfigure smart structures by the technique of polynomial series, used to approximate a true heteroclinic connection between unstable equilibria in a smart structure model. We explore the use of polynomials of varying order to firstly approximate the heteroclinic connection between two equalenergy 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 firstly 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.