Global dynamics and control of a nonlinear body equation with strong structural damping

A nonlinear hinged extensible elastic body equation with strong structural damping and Balakrishnan-Taylor damping of full exponent is studied as a general model for large space structures of higher dimensions. In this paper, the absorbing sets and flat inertial manifold are obtained for this nonlinear body equation. The control spillover problem associated with the stabilization of this equation is resolved by constructing a linear finite dimensional feedback, control based on the existence of inertial manifolds of the uncontrolled equation. Moreover, the results obtained are robust with respect to the uncertainty in structural parameters. Supported by the National Natural Science Foundation of China (No. 19701023)