Minimum switching control for adaptive tracking

The switching control approach has attracted a lot of attention recently for solving adaptive control problems. This approach relies on the condition that there exist a finite (or countable) number of non-switching controllers such that at least one of them will be able to control a given family of unknown (uncertain) plants. In this paper, we consider a class of minimum-phase plants (MIMO) with some mild closedness assumptions. Given any polynomial reference input, we provide a switching control law which guarantees the exponentially stability of the closed-loop system with exponential tracking performance. The main contribution of the paper is that we give the minimum number of non-switching controllers required for switching. In particular, the number is equal to 2 for a single-input single-output plant (one for each sign of the high-frequency gain), and is equal to 2/sup m/ for an m-input m output plant. In particular, the number is independent of the degree and the relative degree of the plant.

[1]  B. Ross Barmish,et al.  An iterative design procedure for simultaneous stabilization of MIMO systems , 1987, Autom..

[2]  P. Ramadge,et al.  Controller switching based on output prediction errors , 1998, IEEE Trans. Autom. Control..

[3]  B. R. Barmish,et al.  Adaptive Stablization of Linear Systems with Singular Perturbations , 1988 .

[4]  S.R. Kulkarni,et al.  Supervised switched control based on output prediction errors , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

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

[6]  Kumpati S. Narendra,et al.  Intelligent control using fixed and adaptive models , 1995, Proceedings of 1995 American Control Conference - ACC'95.

[7]  Michael G. Safonov,et al.  A falsification perspective on model reference adaptive control , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[8]  B. R. Barmish,et al.  Adaptive stabilization of linear systems via switching control , 1986 .

[9]  M. Fu,et al.  Localization based switching adaptive controllers , 1997, 1997 European Control Conference (ECC).

[10]  Michael Athans,et al.  Robustness of continuous-time adaptive control algorithms in the presence of unmodeled dynamics , 1985 .

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

[12]  Kumpati S. Narendra,et al.  Intelligent control using fixed and adaptive models , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

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

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

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

[16]  A. Morse.  Supervisory control of families of linear set-point controllers. II. Robustness , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[17]  S. Sastry,et al.  Adaptive Control: Stability, Convergence and Robustness , 1989 .

[18]  Michael G. Safonov,et al.  The unfalsified control concept and learning , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

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

[20]  R. Nussbaum.  Some remarks on a conjecture in parameter adaptive control , 1983 .

[21]  A. Morse.  Supervisory control of families of linear set-point controllers , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[22]  Bengt Mårtensson,et al.  The order of any stabilizing regulator is sufficient a priori information for adaptive stabilization , 1985 .

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

[24]  Joao P. Hespanha,et al.  Logic-based switching algorithms in control , 1998 .

[25]  A. Morse,et al.  Applications of hysteresis switching in parameter adaptive control , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.