Abstract
This paper deals with a design method for an adaptive scheme which would identify the parameters and observe the state of any unknown single-input single-output discrete time linear system using only input-output data.
Now, any traditional adaptive observer based on the stability theory guarantees the global asymptotic stability but does not guarantee a speedy parameter adjusting procedure.
In this paper, it is shown that the approach which uses the same canonical form for an adaptive observer as Lüders' one, can be reduced to the identification problem of the transformation matrix for an observer.
Then, it is shown that if any information with regard to the system parameters is not given, it is very difficult to determine adequately arbitrary parameters concerning the speed of the convergence in the Lüders' method.
This paper presents a clue to solve the optimal parameter adjusting procedure as the optimall control problem, letting the adjusting procedure correspond to the control problem of a linear system which has estimate error vectors as its state variables.
