“Investigation of dynamics of control systems with delays using Lambert function”

Author, institution: Irma Ivanovienė, Kaunas University of Technology

Science area, field: Physical Sciences, Informatics

The Doctoral Dissertation is available at the library of Kaunas University of Technology (K. Donelaičio St. 20, Kaunas).

Scientific supervisor:

Prof. Dr. Jonas RIMAS (Kaunas University of Technology, Physical Sciences, Informatics – 09P).

Scientific consultant:

Prof. Dr. Habil. Henrikas PRANEVIČIUS (Kaunas University of Technology, Physical Sciences, Informatics – 09P).

Dissertation Defence Board of Informatics Science Field:

Prof. Dr. Habil. Rimantas BARAUSKAS (Kaunas University of Technology, Physical Sciences, Informatics – 09P) – Chairman;

Prof. Dr. Habil. Romas BARONAS (Vilnius University, Physical Sciences, Informatics – 09P),

Prof. Dr. Habil. Vytautas KAMINSKAS (Vytautas Magnus University, Physical Sciences, Informatics – 09 P),

Prof. Dr. Gintaras PALUBECKIS (Kaunas University of Technology, Physical Sciences, Informatics – 09P),

Prof. Dr. Habil. Rimvydas SIMUTIS (Kaunas University of Technology, Physical Sciences, Informatics – 09P).

Opponents:

Prof. Dr. Habil. Feliksas IVANAUSKAS (Vilnius University, Physical Sciences, Informatics – 09P),

Prof. Dr. Habil. Minvydas RAGULSKIS (Kaunas University of Technology, Physical Sciences, Informatics – 09P).

Annotation:

Automatic control systems are widely used in the up-to-date industrial technologies, cosmic technological devices, aviation, military industry, domestic electric appliances.  When managing technological processes the signal delay, which influences system’s dynamic features, is often encountered. Multidimensional control systems with delays are not fully investigated in the control theory.
There are widely used diverse numerical methods for control systems’ investigations. In the case when approximated results, obtained applying numerical methods do not meet the requirements, there are used different means that would give an exact or close to exact results. Such results it is possible to achieve applying consequent integration method, which gives an exact solution in any finite interval by finite sum of functions and a method, based on application of Lambert’s W function that gives an exact result in the shape of infinite functional series.
In doctoral dissertation control systems with delays are described by a linear matrix differential equation with delayed argument and non-commuting coefficient matrices. These systems are investigated using a method offered in the dissertation work. The main points of this method are following: an original procedure of finding of an auxiliary matrix which enables to investigate systems having non- commuting coefficient matrices; a new method for finding the solution, applicable in the case when Lambert W function’s argument has zero eigenvalues.
There were analyzed diverse multidimensional control systems with delays applying  the method offered  in the dissertation work. The investigation of some control systems using known Lambert function method was impossible.