Guaranteed Transient Performance with L1 Adaptive Controller for Systems with Unknown Time-varying Parameters and Bounded Disturbances: Part I

This paper presents a novel adaptive control methodology for uncertain systems with time-varying unknown parameters and time-varying bounded disturbances. The adaptive controller ensures uniformly bounded transient and asymptotic tracking for system's both signals, input and output, simultaneously. The performance bounds can be systematically improved by increasing the adaptation rate. Simulations of a robotic arm with time-varying friction verify the theoretical findings.

[1]  Chengyu Cao,et al.  Stability Margins of L1 Adaptive Controller: Part II , 2007, 2007 American Control Conference.

[2]  Petros A. Ioannou,et al.  Adaptive control of linear time-varying plants , 1987, Autom..

[3]  Ramon R. Costa.  Improving transient behavior of model-reference adaptive control , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

[4]  Kumpati S. Narendra,et al.  Improving transient response of adaptive control systems using multiple models and switching , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[5]  Riccardo Marino,et al.  An adaptive output feedback control for a class of nonlinear systems with time-varying parameters , 1999, IEEE Trans. Autom. Control..

[6]  Jing Sun.  A Modified Model Reference Adaptive Control Scheme for Improved Transient Performance , 1991, 1991 American Control Conference.

[7]  G. Goodwin,et al.  Adaptive control of time-varying linear systems , 1988 .

[8]  B. Ydstie.  Transient performance and robustness of direct adaptive control , 1992 .

[9]  Yu Tang,et al.  Adaptive control of robots with an improved transient performance , 2002, IEEE Trans. Autom. Control..

[10]  Petros A. Ioannou,et al.  Performance analysis and improvement in model reference adaptive control , 1994, IEEE Trans. Autom. Control..

[11]  Riccardo Marino,et al.  Adaptive tracking of linear systems with arbitrarily time-varying parameters , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[12]  R. Ortega.  On Morse's new adaptive controller: parameter convergence and transient performance , 1993, IEEE Trans. Autom. Control..

[13]  Daniel E. Miller,et al.  An adaptive controller which provides an arbitrarily good transient and steady-state response , 1991 .

[14]  Chengyu Cao,et al.  Design and Analysis of a Novel L1 Adaptive Controller, Part I: Control Signal and Asymptotic Stability , 2006, 2006 American Control Conference.

[15]  Aniruddha Datta,et al.  On modifying model reference adaptive control schemes for performance improvement , 1994 .

[16]  Naira Hovakimyan,et al.  Effect of non-zero initialization error on the performance bounds in ℒ 1 adaptive control architecture , 2007 .

[17]  Anuradha M. Annaswamy,et al.  Robust Adaptive Control , 1984, 1984 American Control Conference.

[18]  Riccardo Marino,et al.  Adaptive control of linear time-varying systems , 2003, Autom..

[19]  Chengyu Cao,et al.  Design and Analysis of a Novel L1 Adaptive Controller, Part II: Guaranteed Transient Performance , 2006, 2006 American Control Conference.

[20]  Dimitris C. Dracopoulos.  Adaptive Control Architecture , 1997 .

[21]  Petros A. Ioannou,et al.  Adaptive control of linear time varying systems , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[22]  Miroslav Krstic,et al.  Transient-performance improvement with a new class of adaptive controllers , 1993 .

[23]  Antonella Ferrara,et al.  Robustness and performance of an indirect adaptive control scheme in presence of bounded disturbances , 1999, IEEE Trans. Autom. Control..

[24]  R. Bitmead,et al.  Transient bounds for adaptive control systems , 1990, 29th IEEE Conference on Decision and Control.

[25]  J. Doyle,et al.  Essentials of Robust Control , 1997 .