Verifying stabilizing controllers via closed-loop noisy data: MIMO case

This article introduces novel tests which utilize a limited amount of experimental and possibly noisy data obtained from a stable closed-loop system, i.e. an interconnection of an existing known stabilizing controller and an unknown plant, to infer if the introduction of a prospective controller will stabilize the unknown plant. This extends our earlier results to include the MIMO systems.

[1]  R. Kuc,et al.  A direct relation between a signal time series and its unwrapped phase , 1982 .

[2]  Xavier Bombois,et al.  The role of experimental conditions in model validation for control , 1998, Robustness in Identification and Control.

[3]  Ruud J.P. Schrama,et al.  An iterative scheme for identification and control design based on coprime factorizations , 1992, 1992 American Control Conference.

[4]  A. Morse Supervisory control of families of linear set-point controllers Part I. Exact matching , 1996, IEEE Trans. Autom. Control..

[5]  L. C. Kammer Stability assessment for cautious iterative controller tuning , 2004 .

[6]  Ian Postlethwaite,et al.  Multivariable Feedback Control: Analysis and Design , 1996 .

[7]  Michel Gevers A Decade of Progress in Iterative Process Control Design: from Theory to Practice , 2000 .

[8]  Brian D. O. Anderson,et al.  Unfalsified adaptive control: A new controller implementation and some remarks , 2007, 2007 European Control Conference (ECC).

[9]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .

[10]  Håkan Hjalmarsson,et al.  On the frequency domain accuracy of closed-loop estimates , 2005, Autom..

[11]  Robert R. Bitmead,et al.  Direct iterative tuning via spectral analysis , 2000, Autom..

[12]  P. V. D. Hof,et al.  Suboptimal feedback control by a scheme of iterative identification and control design , 1997 .

[13]  Brian D. O. Anderson Two Decades of Adaptive Control Pitfalls , 2004 .

[14]  Michel Gevers A decade of progress in iterative process control design: from theory to practice , 2002 .

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

[16]  Brian D. O. Anderson,et al.  Fundamental Problems in Adaptive Control , 1998 .

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

[18]  Delabarra Ba,et al.  On Undershoot in SISO Systems , 1994 .

[19]  G. Vinnicombe Uncertainty and Feedback: 8 loop-shaping and the-gap metric , 2000 .

[20]  Sippe G. Douma,et al.  Relations between uncertainty structures in identification for robust control , 2005, Autom..

[21]  Brian D. O. Anderson,et al.  Checking if controllers are stabilizing using closed-loop data , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[22]  Brian D. O. Anderson,et al.  A two‐degree‐of‐freedom ℋ︁∞ control design method for robust model matching , 2006 .

[23]  Michel Gevers,et al.  Towards a Joint Design of Identification and Control , 1993 .

[24]  Brian D. O. Anderson,et al.  Failures of adaptive control theory and their resolution , 2005, Commun. Inf. Syst..

[25]  K. Lau,et al.  Undershoot and settling time tradeoffs for nonminimum phase systems , 2003, IEEE Trans. Autom. Control..

[26]  Michel Gevers,et al.  Asymptotic accuracy of iterative feedback tuning , 2005, IEEE Transactions on Automatic Control.

[27]  Ruud J. P. Schrama Accurate identification for control: the necessity of an iterative scheme , 1992 .

[28]  Brian D. O. Anderson,et al.  Model validation for control and controller validation in a prediction error identification framework - Part I: theory , 2003, Autom..

[29]  C. Desoer,et al.  Feedback Systems: Input-Output Properties , 1975 .

[30]  Håkan Hjalmarsson,et al.  On the frequency domain accuracy of closed loop estimates , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[31]  Robert R. Bitmead,et al.  Iterative Control Design Approaches 1 , 1993 .

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

[33]  Svante Gunnarsson,et al.  Iterative feedback tuning: theory and applications , 1998 .

[34]  Paul M. J. Van den Hof,et al.  Identification and control - Closed-loop issues , 1995, Autom..

[35]  A. Paul,et al.  Cost-detectability and Stability of Adaptive Control Systems , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.