This paper addresses the stability and performance of discretized adaptive control algorithms for robotic manipulator control, and the compensation of these algorithms for improved stability and tracking performance. The discretization of Slotine and Li's direct adaptive control algorithm results in a sampled-data system for which stability has not been guaranteed. By formulating the entire sampled-data system in continuous-time, Lyapunov's direct method is used to determine the stability and to derive a non-linear discrete-time compensating term. This compensator is added to a multi-rate discretization of Slotine and Li's adaptive algorithm, to stabilize the sampled-data system. For sufficiently high gain, globally stable performance and a known bound on the norm of the filtered error is proven. The effect of the compensator and validity of the error bound predictions are demonstrated through simulation and implementation of 2 degree-of-freedom manipulator control.

Proceedings of the 1994 American Control Conference. Part 1 (of 3)
Department of Systems and Computer Engineering

Warshaw, Gabriel D. (Gabriel D.), & Schwartz, H.M. (1994). Sampled-data robot adaptive control with stabilizing compensation. In Proceedings of the American Control Conference (pp. 602–608).