Robust redesign of adaptive control

Effects of unmodeled high frequency dynamics on stability and performance of adaptive control schemes are analyzed. In the regulation problem global stability properties are no longer guaranteed, but a region of attraction exists for exact adaptive regulation. The dependence of the region of attraction on unmodeled parasitics is examined first. Then the general case of model reference adaptive control is considered in which parasitics can destroy stability and boundedness properties. A modified adaptive law is proposed guaranteeing the existence of a region of attraction from which all signals converge to a residual set which contains the equilibrium for exact tracking. The size of this set depends on design parameters, the frequency range of parasitics, and the reference input signal characteristics.

[1]  Hassan K. Khalil,et al.  ON THE ROBUSTNESS OF OUTPUT FEEDBACK CONTROL METHODS TO MODELING ERRORS. , 1981 .

[2]  I. D. Landau,et al.  A survey of model reference adaptive techniques - Theory and applications , 1973, Autom..

[3]  A. Morse,et al.  Adaptive control of single-input, single-output linear systems , 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.

[4]  I. Landau,et al.  A stability theorem with applications to adaptive control , 1978, 1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes.

[5]  P. Ramadge,et al.  Discrete-time multivariable adaptive control , 1979 .

[6]  M. Athans,et al.  Convergence studies of adaptive control algorithms part I: Analysis , 1980, 1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[7]  G. Kreisselmeier.  Adaptive control via adaptive observation and asymptotic feedback matrix synthesis , 1980 .

[8]  Reduced order adaptive controller studies , 1980 .

[9]  K. Narendra,et al.  Stable adaptive controller design, part II: Proof of stability , 1980 .

[10]  Petros A. Ioannou.  Robustness of absolute stability , 1981 .

[11]  P. Kokotovic,et al.  Robustness redesign of continuous-time adaptive schemes , 1981, 1981 20th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[12]  Michael Athans,et al.  Analytical verification of undesirable properties of direct model reference adaptive control algorithms , 1981, 1981 20th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[13]  B. Anderson,et al.  On reduced-order adaptive output error identification and adaptive IIR filtering , 1982 .

[14]  G. Kreisselmeier.  On adaptive state regulation , 1982 .

[15]  Petros A. Ioannou,et al.  An asymptotic error analysis of identifiers and adaptive observers in the presence of parasitics , 1982 .