Uncertain variables in decision and control problems for uncertain cascade systems

• Authors: Z. Bubnicki
• Venue: MIC'06 Proceedings of the 25th IASTED international conference on Modeling, indentification, and control
• Year: 2006

The uncertain variables have been introduced and developed as a tool for analysis and decision making in a class of uncertain systems described by traditional mathematical models or by relational knowledge representations with unknown parameters characterized by an expert. The purpose of this paper is to show how the uncertain variables may be applied to decision making in a class of uncertain systems with the cascade structure consisting of parts (elements) with different descriptions of the uncertainty. The different cases have been considered: the random and uncertain parameters in the different parts of the system and the random parameter in the certainty distribution. The first part of the paper presents a general approach to decision making in the complex system consisting of elements with random parameters and elements with uncertain parameters treated as values of uncertain variables characterized by certainty distributions given by an expert. The second part is devoted to a special case: the system with a cascade structure containing random and uncertain parts. The first subsystem is described by probability distribution and the second subsystem is characterized by an expert. Simple numerical examples illustrate the presented problem and results. The description of he simulations and possibilities of practical applications for control of complex production systems are included.