An analytical comparison of the weighted LQ performance of a robust and an adaptive backstepping design

A robust and an adaptive backstepping design for an uncertain strict feedback system are compared with respect to a quadratic cost which is exponentially weighted in time. The cost penalises both the output transient and the control effort. It is shown that the adaptive design outperforms the robust design when the actual uncertainty level is sufficiently high and the a-priori known uncertainty level is sufficiently conservative.