Numerical sensitivity of the backstepping adaptive tuning functions control design

The backstepping-based adaptive tuning functions design is a control scheme for uncertain systems that ensures reasonably good stability and performance properties of the closed loop. The complexity of the controller makes inevitable the use of digital computers to perform the calculation of the control signal. This paper addresses the issue of the numerical sensitivity of the adaptive tuning functions via computer algebra systems. It is shown that while the increase of the design parameters may be desirable to achieve a good transient performance, it harms the control signal as this increase introduces large high-frequency components due to the numerical errors. Our results suggest that it is necessary a certain compromise between the choice of the design parameters and the numeric precision of the tools involved in the control design.