Mathematical Problems in Engineering
Volume 2 (1996), Issue 2, Pages 131-142

Discrete-time adaptive control using a sliding mode

Tetsuo Semba and Katsuhisa Furuta

IBM Tokyo Research Laboratory, 1623-14, Shimo-tsuruma, Yamato-shi, Kanagawa 242 Japan Tokyo Institute of Technology, 2-12-1, Oh-Okayama, Meguro-Ku Tokyo 152, Japan

Received 5 April 1995

Copyright © 1996 Tetsuo Semba and Katsuhisa Furuta. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Adaptive control using a sliding mode in discrete time systems is proposed as a means of achieving robustness with respect to parameter variations, fast tracking to a desired trajectory, and fast parameter convergence, without increasing the chattering of the control inputs. We first prove the stability of a system in which the control inputs consist of equivalent control driven by the adaptive control law and bounded discontinuous control. The discontinuous control driven by the sliding control law is then obtained so that the output error quickly converges to zero. Finally, the performance improvements obtained by adding the sliding mode control input are shown through computer simulations.