ΑΛΓΟΡΙΘΜΟΙ ΓΙΑ ΤΗΝ ΕΠΙΛΥΣΗ ΤΗΣ ΕΞΙΣΩΣΗΣ RICCATI

Abstract

RICCATI EQUATION PLAYS AN IMPORTANT ROLE IN MANY FIELDS OF COMPUTER SCIENCE, SUCH AS ESTIMATION THEORY, OPTIMAL CONTROL, COMMUNICATIONS, SIGNAL PROCESSING. THE AIM OF THIS THESIS IS THE DEVELOPMENT OF NEW ALGORITHMS WHICH SOLVE THE RICCATI EQUATION EMANATING FROM LINEAR DISCRETE TIME STATE SPACE MODELS. THE DEVELOPMENT OF THE NEW RECURSIVE ALGORITHMS IS BASED ON THE COMBINATION OF THE CLASSICAL PER STEP AND DOUBLING ALGORITHMS. THE SEQUENTIAL AS WELL AS THE PARALLEL IMPLEMENTATION OF THESE ALGORITHMS IS ANALYSED IN TERMS OF MEMORY MANAGEMENT AND CALCULATION TIME. THE ALGORITHMS CONVERGENCE AND STABILITYIS THEORETICALLY PROVEN AND CONFIRMED THROUGH SIMULATION RESULTS. THE COMPARISON OF THE CALCULATION TIME OF THE ALGORITHMS LEEDS TO THE CONCLUSION THAT THE PER CENT GAIN RESULTING WHEN APPLYING THE NEW ALGORITHMS INSTEAD OF APPLYING THE CLASSICAL ONES IS OF THE ORDER OF 40% MOREOVER, THE APPLICATION OF THE PROPOSED ALGORITHMS IS INVESTIGATED IN THE CASE WHERE THE PLANT COVARIANCE MATRIX IS NONSIGULAR AND IN THE PERIODIC MODELS CASE. FINALLY, A NEW STEADY STATE ESTIMATOR IS PROPOSED, THE CALCULATION TIME NEEDED FOR THE SEQUENTIAL IMPLEMENTATION OF WHICH IS AN ORDER OF MAGNITUDE LESS THAN THE CALCULATION TIME NEEDED FOR THE SEQUENTIAL IMPLEMENTATION OF THE CLASSICAL ONE. A LOW HARDWARE COST AND HIGH SPEEDUP PARALLEL IMPLEMENTATION OF THE PROPOSED ESTIMATOR IS DEVELOPED.