Adaptive tracking of nonlinear systems with non-symmetric dead-zone input

• Published in: Automatica (Oxford) Vol. 43; no. 3; pp. 522 - 530
• Main Authors: Ibrir, Salim, Xie, Wen Fang, Su, Chun-Yi
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.03.2007; Elsevier
• Subjects: Adaptative systems; Adaptive control; Applied sciences; Computer science; control theory; systems; Control theory. Systems; Dead-zone nonlinearities; Exact sciences and technology; Linear matrix inequalities (LMIs); Mechatronics; Nonlinear non-smooth systems; Stabilization; Mechatronics; Linear matrix inequalities (LMIs); Stabilization; Adaptive control; Nonlinear non-smooth systems; Dead-zone nonlinearities; Bounded control; Adaptive algorithm; Position control; Bounded error; Non linear control; Linear time; Tracking task; Dead zone; Dynamical system; Time varying system; Uncertain system; Nonsmooth analysis; Symmetric matrix; Linear matrix inequality; Tracking error; Motion control
• ISSN: 0005-1098; 1873-2836
• DOI: 10.1016/j.automatica.2006.09.022

Quite successfully adaptive control strategies have been applied to uncertain dynamical systems subject to dead-zone nonlinearities. However, adaptive tracking of systems with non-symmetric dead-zone characteristics has not been fully discussed with minimal knowledge of the dead-zone parameters. It is shown that the controlled system preceded by a non-symmetric dead-zone input can be represented as an uncertain nonlinear system subject to a linear input with time-varying input coefficient. To cope with this problem, a new adaptive compensation algorithm is employed without constructing the dead-zone inverse. The proposed adaptive scheme requires only the information of bounds of the dead-zone slopes and treats the time-varying input coefficient as a system uncertainty. The new control scheme ensures bounded-error trajectory tracking and assures the boundedness of all the signals in the adaptive closed loop. By appropriate selections of the controller parameters, we show that the smoothness of the controller does not affect the accuracy of trajectory tracking control. A numerical example is included to show the effectiveness of the theoretical results.