Optimal singular low-order adaptive observation of a class of discrete systems (Q1881860)

Linear, finite-dimensional discrete-time control systems with constant coefficients are considered. First, the problem of discrete optimal low-order singular adaptive observation is formulated and discussed. Next, using algebraic methods and the theory of discrete-time difference equations, an algorithm for the synthesis of the observer is proposed. This algorithm contains several parts, i.e. optimal estimation of the initial state of the control system, parameter identification and, finally, design of an adaptive observer of the current state vector. Moreover, results of a computational experiment are also presented. The paper contains several remarks and comments concerning adaptive observers and discrete-time control systems. Finally, it should be pointed out that similar problems have been considered in the following papers: [\textit{L. N. Sotirov}, ``An algorithm for synthesis of optimal singular adaptive observers with direct estimation of the initial state vector'', Int. J. Syst. Sci. 28, No. 6, 559--562 (1997; Zbl 0886.93007)] and [\textit{Y.-C. Hong}, \textit{J.-H. Kim} and \textit{K.-K. Choi}, ``Discrete adaptive observer with exponential weighting properties'', IEEE Trans. Autom. Control 34, No. 2, 229--231 (1989; Zbl 0664.93047)].