Adaptive control of discrete-time systems using multiple models

The adaptive control of a linear time-invariant discrete-time system using multiple models is considered in this paper. Both the deterministic (noise free) case and the stochastic case when random disturbances are present are discussed. Based on the prediction errors of a finite number of fixed and adaptive identification models, a procedure is outlined for switching between a finite number of controllers to improve performance. The principal contributions of the paper are the proof of global stability of the overall system and the convergence of the tracking error signal to zero in the deterministic case and the proof of convergence of the minimum variance control problem. Computer simulation results are included to complement the theoretical results.

[1]  Michel Loève,et al.  Probability Theory I , 1977 .

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

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

[6]  K. Narendra,et al.  Stable discrete adaptive control , 1980 .

[7]  Graham C. Goodwin,et al.  Adaptive filtering prediction and control , 1984 .

[8]  B. Barmish,et al.  Adaptive stabilization of linear systems via switching control , 1986, 1986 25th IEEE Conference on Decision and Control.

[9]  D. Mayne,et al.  Design issues in adaptive control , 1988 .

[10]  A. Morse,et al.  Applications of hysteresis switching in parameter adaptive control , 1992 .

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

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

[13]  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.

[14]  G. Goodwin,et al.  Hysteresis switching adaptive control of linear multivariable systems , 1994, IEEE Trans. Autom. Control..

[15]  Kumpati S. Narendra,et al.  Adaptation and learning using multiple models, switching, and tuning , 1995 .

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

[17]  Roderick Murray-Smith,et al.  Multiple Model Approaches to Modelling and Control , 1997 .

[18]  A. Morse.  Supervisory control of families of linear set-point controllers. 2. Robustness , 1997, IEEE Trans. Autom. Control..

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