Asymptotic performance guarantees in adaptive control

In this paper we address the problem of improving the asymptotic performance guarantees of a class of model reference adaptive controllers under insufficient excitation and in the presence of perturbations such as non-parametric uncertainty and bounded disturbances. We show that for a class of perturbations whose normalized effect is bounded by an a priori known function of time an estimate of the parametric uncertainty set can be obtained on-line via a set membership estimator. Furthermore, by incorporating this estimate as an additional constraint in the adaptive law generating the controller parameters, we show that the resulting adaptive controller offers dead-zone-like performance guarantees in the lim-sup sense while preserving the desirable root-mean-square performance guarantees of gradient-based algorithms.

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

[2]  D. Bertsekas,et al.  Recursive state estimation for a set-membership description of uncertainty , 1971 .

[3]  E. Fogel.  System identification via membership set constraints with energy constrained noise , 1979 .

[4]  Brian D. O. Anderson,et al.  Stability of adaptive systems: passivity and averaging analysis , 1986 .

[5]  Gustavo Belforte,et al.  Parameter estimation algorithms for a set-membership description of uncertainty , 1990, Autom..

[6]  K. Narendra,et al.  Stable model reference adaptive control in the presence of bounded disturbances , 1982 .

[7]  Rogelio Lozano,et al.  Reformulation of the parameter identification problem for systems with bounded disturbances , 1987, Autom..

[8]  D. Mayne,et al.  Adaptive control of ARMA plants using worst-case design by semi-infinite optimization , 1987 .

[9]  T. T. Tay,et al.  A robust adaptive performance enhancement controller using set membership identification , 1992 .

[10]  R. Kosut.  Adaptive control via parameter set estimation , 1988 .

[11]  Petros A. Ioannou,et al.  A robust direct adaptive controller , 1986 .

[12]  K. Tsakalis.  Robustness of model reference adaptive controllers: an input-output approach , 1992 .

[13]  F. Schweppe.  Recursive state estimation: Unknown but bounded errors and system inputs , 1967 .

[14]  M. Vidyasagar.  Input-Output Analysis of Large-Scale Interconnected Systems: Decomposition, Well-Posedness, and Stability , 1981 .

[15]  B. Ydstie.  Bifurcations and complex dynamics in adaptive control systems , 1986, 1986 25th IEEE Conference on Decision and Control.

[16]  Brian D. O. Anderson,et al.  Adaptive systems, lack of persistency of excitation and bursting phenomena , 1985, Autom..

[17]  J. Deller.  Set membership identification in digital signal processing , 1989, IEEE ASSP Magazine.

[18]  Petros A. Ioannou,et al.  Theory and design of robust direct and indirect adaptive-control schemes , 1988 .

[19]  Y. F. Huang,et al.  On the value of information in system identification - Bounded noise case , 1982, Autom..

[20]  B. Anderson,et al.  Robust model reference adaptive control , 1986 .

[21]  Peter J. Gawthrop,et al.  Continuous-time self-tuning control , 1987 .

[22]  W. Rudin.  Principles of mathematical analysis , 1964 .

[23]  Mathukumalli Vidyasagar,et al.  Input-Output Analysis of Large-Scale Interconnected Systems , 1981 .

[24]  Iven M. Y. Mareels,et al.  Non-linear dynamics in adaptive control: Chaotic and periodic stabilization , 1986, Autom..

[25]  Robert R. Bitmead,et al.  Nonlinear Interactions between Signals and Parameters in Robust Adaptive Control , 1990, 1990 American Control Conference.

[26]  Gang Tao,et al.  Dominant richness and improvement of performance of robust adaptive control , 1989, Autom..