Learning processes and logic-algebraic method in knowledge-based control systems

Abstract

A great variety of definitions and approaches in the field of knowledge-based and learning control systems have been described. This chapter concerns a specific class of knowledge-based systems with a static plant described by a knowledge representation in the form of a set of facts given by an expert (logic knowledge representation). For the static plant described by a function y = r the control problem may consist in finding the decision Z such that = r is the required output value. For the plant described by the knowledge representation presented in this chapter, the control problem consists in finding the proper input p rope r ty which implies the required o u t p u t property. In the case with the logic knowledge representation the facts, input property and output property are logic formulas concerning x, y and some additional variables. For this class of knowledge-based systems the logicalgebraic m e t h o d has been developed [1, 2, 3, 4, 5, 6]. The main idea of the logic-algebraic method consists in replacing the individual reasoning concepts based on inference rules by unified algebraic procedures based on the rules in two-value logic algebra. The results may be considered as a unification and generalisation of the different individual reasoning algorithms for the class of systems determined by the form of the knowledge representation in Sec. 2. The purpose of this chapter is to show how the logic-algebraic method may be used for the determination of learning algorithms in control systems with unknown parameters in the knowledge representation. Sec. 3 presents a formulation and solution of the control problem for the known parameters. The main idea of the learning process consists in a modification of the control decisions based on a current estimation of the unknown parameters. The