Smooth controller design for non-linear systems using multiple fixed models

Multiple model adaptive control (MMAC) with second-level adaptation is a recently proposed methodology for dealing with systems where the parametric uncertainty is large. Compared with the multiple model switching scheme, the new scheme can lead to significant improvements in performance. Some research has been conducted using the new scheme, but all of the results concern linear systems with an adaptive identification model set. In this study, MMAC with second-level adaptation scheme is extended to non-linear systems in strict feedback form, and the fixed identification model set is under consideration. This is motivated by the fact that a smooth controller can lead to smooth performance and the fixed identification model set gains potential advantages over the adaptive identification model set, especially for the case that the parameters of the system change over the time. Design details are presented and the stability of MMAC with second-level adaptation using a fixed identification model set for non-linear systems is given, which has not been discussed before. Finally, two simulations are performed to show that this scheme performs much better than conventional schemes, including adaptive control and multiple-model switching schemes, in terms of convergence speed and transient performance.

[1]  Thomas S. Brinsmead,et al.  Multiple model adaptive control. Part 2: switching , 2001 .

[2]  B. Anderson,et al.  Multiple model adaptive control. Part 1: Finite controller coverings , 2000 .

[3]  Kumpati S. Narendra,et al.  Adaptive control using multiple models , 1997, IEEE Trans. Autom. Control..

[4]  Antonio M. Pascoal,et al.  Issues, progress and new results in robust adaptive control , 2006 .

[5]  Kumpati S. Narendra,et al.  Improving transient response of adaptive control systems using multiple models and switching , 1994 .

[6]  Liang Yan,et al.  High-Accuracy Tracking Control of Hydraulic Rotary Actuators With Modeling Uncertainties , 2014, IEEE/ASME Transactions on Mechatronics.

[7]  Jie Chen,et al.  Adaptive robust dynamic surface control with composite adaptation laws , 2010 .

[8]  Jovan D. Boskovic,et al.  Stable multiple model adaptive flight control for accommodation of a large class of control effector failures , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

[9]  Thomas S. Brinsmead,et al.  Multiple model adaptive control with safe switching , 2001 .

[10]  Zhuo Han,et al.  Location of models in multiple-model based adaptive control for improved performance , 2010, Proceedings of the 2010 American Control Conference.

[11]  Zongxia Jiao,et al.  A Practical Nonlinear Adaptive Control of Hydraulic Servomechanisms With Periodic-Like Disturbances , 2015, IEEE/ASME Transactions on Mechatronics.

[12]  Debasish Chatterjee,et al.  Input-to-state stability of switched systems and switching adaptive control , 2007, Autom..

[13]  Kumpati S. Narendra,et al.  The changing face of adaptive control: The use of multiple models , 2011, Annu. Rev. Control..

[14]  A. Pascoal,et al.  RMMAC: a novel robust adaptive control scheme. Part I. Architecture , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[15]  Jian Sun,et al.  Adaptive control of a class of nonlinear systems using multiple models with smooth controller , 2015 .

[16]  Michael Athans,et al.  The stochastic control of the F-8C aircraft using a multiple model adaptive control (MMAC) method--Part I: Equilibrium flight , 1977 .

[17]  João Pedro Hespanha,et al.  Postprints from CCDC Title Hysteresis-based switching algorithms for supervisory control of uncertain systems Permalink , 2002 .

[18]  Robert Shorten,et al.  Stability Criteria for Switched and Hybrid Systems , 2007, SIAM Rev..

[19]  Qingling Zhang,et al.  Simplified filtering-based adaptive fuzzy dynamic surface control approach for non-linear strict-feedback systems , 2016 .

[20]  Brian D. O. Anderson,et al.  Challenges of adaptive control-past, permanent and future , 2008, Annu. Rev. Control..

[21]  Kumpati S. Narendra,et al.  New Concepts in Adaptive Control Using Multiple Models , 2012, IEEE Transactions on Automatic Control.

[22]  Bin Yao,et al.  A globally stable saturated desired compensation adaptive robust control for linear motor systems with comparative experiments , 2006, American Control Conference.

[23]  L. Jiao,et al.  Brief Paper: Output-feedback adaptive dynamic surface control of stochastic non-linear systems using neural network , 2010 .

[24]  Wei Chen,et al.  The Rationale for Second Level Adaptation , 2015, ArXiv.