Re-entry predictive guidance based on linear matrix inequalities optimal constraints for sub-orbit vehicles

Significant challenges with re-entry G&C include dynamics with significant nonlinearities, states and trajectory constraints, limit on control authority, and parametric uncertainty. A designing new method based on linear matrix inequalities (LMIs) constraints is presented for the longitudinal guidance law. First, the nonlinear longitudinal dynamic equations are linearized about the nominal trajectory. Then the guidance law is designed by solving LMI convex optimal. In each control period the feedback control law and control increment is obtained. The control increment plus the nominal one is used to guide the actual reentry trajectory, and closed-loop systems stability is proved. Simulation results show the proposed guidance law is robust to deviations from reentry initial states.