Adaptive Observer with Exponential Rate of Convergence for Multi-Input Multi-Output Systems

Abstract An adaptive observer for multi-input multi-output systems is designed in this paper. The observer estimates inaccessible state variables and identifies unknown parameters with desired rate of exponential convergence. The adaptive law of the observer is derived from the law developed by authors for single-input single-output systems. Its adjusting speed is specified by the parameters of the observer under the condition of sufficient richness of signals. A sufficient condition on the richness is obtained. The observer structure is based on a form extended for multi-output systems from the Kreisselmeier's parametrised representation. The extended form includes filtered signals which are augmented by measured outputs to represent the interactions between outputs. The adaptive law for single-output systems car. be applied to the extended form for the general multi-output systems without augmenting the order of the unknown systems. An example is given to show the effect of the rate of convergence.

[1]  R. Carroll,et al.  An adaptive observer for single-input single-output linear systems , 1973 .

[2]  Design and application of reduced-order adaptive observer with exponential rate of convergence for single-input single-output linear systems , 1984 .

[4]  D. Luenberger.  Canonical forms for linear multivariable systems , 1967, IEEE Transactions on Automatic Control.

[5]  S. Nuyan,et al.  Minimal order arbitrarily fast adaptive observers and identifiers , 1979 .

[6]  Ioan Doré Landau,et al.  On the recursive identification of multi-input, multi-output systems , 1978, Autom..

[7]  W. Wonham,et al.  Probing signals for model reference identification , 1977 .

[8]  K. Narendra,et al.  Synthesis of an adaptive observer using Lyapunov's direct method , 1973 .

[9]  W. Wolovich,et al.  Parameter adaptive identification and control , 1978 .

[10]  K. Narendra,et al.  Stable adaptive schemes for state estimation and identification of linear systems , 1974 .

[11]  G. Kreisselmeier.  Adaptive observers with exponential rate of convergence , 1977 .

[12]  Jürgen Ackermann,et al.  On the synthesis of linear control systems with specified characteristics , 1975, Autom..

[13]  Hidekatsu Tokumaru,et al.  Finite Time Setting Adaptive Observer for Multi-Input Multi-Output Systems , 1983 .

[14]  Kimio Kanai,et al.  A Design of an Adaptive Observer for a Multi-Input Multi-Output System , 1982 .

[15]  R. Guidorzi.  Canonical structures in the identification of multivariable systems , 1975, Autom..