Optimal singular adaptive observation of discrete stationary systems with initial state vector estimation

A direct algorithmic synthesis method is developed for designing new generation adaptive observers, including optimal estimators for the initial state vector, parameter identifiers, and optimal singular (complete and degenerate) observers of the current state vector. Input for the algorithm a's generated as special (Toeplitz and Hankel) matrices in order to widen the field of application of the method. The elements of the initial state vector do not yield to estimation by the algorithms generated by the Luenberger observations and the Kalman optimal filter with inherent consequences. The optimal, singular, and robust properties of the new class of adaptive observers are described. Synthesis may fail for certain poles, and additional difficulties arise in studying the Luenberger observations. Since the synthesized algorithm admits large-block representation and parallelism properties, ii can be implemented even on transputers.