Input-delay compensation in a robust adaptive control framework

A modification to the ℒ₁ control framework for uncertain systems with actuator delays is presented. Specifically, a time delay is introduced in the control input of the state predictor to compensate for the destabilising effect of an input delay in the plant. For this modified framework, the analysis shows that the output of the adaptive system closely follows the behaviour of a suitably defined, non-adaptive, stable reference system provided that a delay-dependent stability condition is satisfied and the adaptive gain is chosen sufficiently large. The set of combinations of input delay and compensation delay for which the stability condition is satisfied contains an open set of pairs of positive values provided that a filter bandwidth is chosen sufficiently large. The efficacy of the delay compensation is illustrated by a simple example. A numerical continuation is also performed to explore the stability region for a case where this can be approximated a priori.