An algorithm for synthesis of optimal singular adaptive observers with direct estimation of the initial state vector

An algorithmic synthesis is suggested of a new generation of adaptive observers, including optimal estimators of the initial state vector, identifiers of parameters and optimal singular (full and degenerated) observers of the current state vector, for SISO linear discrete systems. The estimation of the elements of the initial state vector is not typical for the algorithms, inherent to Luenberger's theory of observation with all due consequences. The important fact is emphasized of the dropping off of the procedure for the synthesis of systems with given poles, causing additional difficulties when Luenberger's theory of observation is used. The synthesized algorithm has features such as large-scale granularity and natural parallelism, which also allow its software and hardware interpretation on a transputer basis.