Stability analysis of weighted multiple model adaptive control of a linear time-invariant discrete-time system

The paper is concerned with the long-standing problem of the stability of weighted multiple model adaptive control (MMAC). Based on virtual equivalent system (VES) concept and methodology, a positive answer to the problem is presented under a unified framework which is independent of specific `local' control strategy and specific algorithm for weight calculation. The obtained results indicate that the stability of a weighted MMAC system depends mainly on the convergence of posterior probability weights, i.e., the posterior probability corresponding to the model closest to the true plant converges to 1, and others converge to 0.

[1]  D. Magill.  Optimal adaptive estimation of sampled stochastic processes , 1965 .

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

[3]  D. Lainiotis,et al.  Partitioning: A unifying framework for adaptive systems, I: Estimation , 1976, Proceedings of the IEEE.

[4]  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 .

[5]  Y. Baram,et al.  An information theoretic approach to dynamical systems modeling and identification , 1977, 1977 IEEE Conference on Decision and Control including the 16th Symposium on Adaptive Processes and A Special Symposium on Fuzzy Set Theory and Applications.

[6]  Yoram Baram,et al.  Information, consistent estimation and dynamic system identification , 1977 .

[7]  Y. Baram,et al.  Consistent estimation on finite parameter sets with application to linear systems identification , 1978 .

[8]  R. Moose,et al.  Modeling and Estimation for Tracking Maneuvering Targets , 1979, IEEE Transactions on Aerospace and Electronic Systems.

[9]  A. Kehagias.  Convergence properties of the Lainiotis partition algorithm , 1991 .

[10]  H. Kaufman,et al.  Multiple-model adaptive predictive control of mean arterial pressure and cardiac output , 1992, IEEE Transactions on Biomedical Engineering.

[11]  Yaakov Bar-Shalom,et al.  Design of an interacting multiple model algorithm for air traffic control tracking , 1993, IEEE Trans. Control. Syst. Technol..

[12]  P.S. Maybeck,et al.  Multiple model adaptive estimation applied to the LAMBDA URV for failure detection and identification , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[13]  Kumpati S. Narendra,et al.  Adaptive control of discrete-time systems using multiple models , 2000, IEEE Trans. Autom. Control..

[14]  Michael Athans,et al.  ISSUES ON ROBUST ADAPTIVE FEEDBACK CONTROL , 2005 .

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

[16]  J. Choi,et al.  A Unified Analysis of Switching Multiple Model Adaptive Control - Virtual Equivalent System Approach , 2008 .

[17]  Weicun Zhang,et al.  The convergence of parameter estimates is not necessary for a general self-tuning control system- stochastic plant , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[18]  Weicun Zhang,et al.  On the stability and convergence of self-tuning control–virtual equivalent system approach , 2010, Int. J. Control.

[19]  H. Momeni,et al.  Robust multiple model adaptive control: Modified using ν‐gap metric , 2011 .

[20]  Aaas News,et al.  Book Reviews , 1893, Buffalo Medical and Surgical Journal.