The new pattern recognition- and formal linguistics- based approach for constructing analytic expert systems is proposed. The expert systems implemented with this approach are able to diagnose and control hard real-time distributed computerized systems. The practical usefulness of a methodology proposed has been positively verified by an application for constructing a real-time expert system for a high energy physics experiment. The proposed formalisms are compatible with rule-based systems paradigm.

The linear quadratic optimal control of discrete-time distributed systems with delays in the control is considered. A new approach for solving this problem is presented. It is based on the construction of an appropriate Hilbert space structure. In order to illustrate the theory an example of diffusion system is given.

This paper addresses the problem of identifying nonlinear discrete-time multivariable systems using radial-basis-function neural networks. A recursive identification scheme is proposed that first builds recursively a RBF (Radial-Basis-Function) neural net model structure and then uses a stable recursive weight updating algorithm to modify the weights. The convergence of the scheme is established using the Lyapunov stability theory. The scheme is also applied to an illustrative example to show its efficacy.

In this paper the repetitive control algorithm is considered. It is shown that the repetitive regulator is the limit case of this control algorithm when the sampling frequency becomes infinite.

The eigenvalue assignment problem in a linear sampled-data system using a continuous reduced-dimensional state estimator and constant gain feedback (in a double feedback loop configuration) from the estimated state is discussed. The proposed design procedure gives freedom in the simultaneous selection of poles of the closed-loop discrete-time system and of the sampling frequency. Moreover, the procedure enables one to obtain exponentially stable (in a wide range of sampling frequencies) closed-loop discrete-time system and in consequence to take into account intersampling behaviour of continuous-time signals (e.g., the output signal). Appropriate quantitative stability conditions are provided. The design procedure is illustrated by a simple numerical example.

Ranking fuzzy subsets is an important event in dealing with fuzzy decision problems in many areas, such as social sciences, management sciences and engineering. However, until now, no thorough investigation has been made to evaluate the relative performance of all the ranking methods, and to analyze the differences between these methods for a particular application.

A recent breakthrough calls on a neural network algorithm, Fuzzy CID3 Algorithm, [109,111], which learns the needed membership functions from a set of training examples to differentiate between classes.

It is the purpose of this paper to evaluate and analyze the performance of available methods of ranking fuzzy subsets on a set of selected examples that cover possible situations we might encounter as defining fuzzy subsets at each node of a neural network. Through this analysis, suggestions as to which methods have better performance for utilization in neural network architectures, as well as criteria for choosing an appropriate method for ranking in corresponding fuzzy trees will be made.

This is the second part of a two-part paper. In Part I, a brief outline of a knowledge representation language based on simplified first order predicate calculus is presented. A restricted logical calculus, based on classical first-order logic is proposed. An idea of generalization among logical formulae is defined. A formal reasoning method, so-called backward dual resolution, is introduced; the method is aimed at performing reasoning in an efficient manner and can be applied to reasoning about states and situations, checking if preconditions of transformation rules are satisfied, and to the verification of some theoretical properties of knowledge-based systems.

In this part, an application of the introduced formalism to knowledge-based representation of physical states of dynamic systems is proposed. A generic scheme of state transformation rules is outlined. Definitions of properties such as determinism, completeness, conservativity, and other are introduced and an idea of potential correctness of knowledge formalization is given. Due to general format of the proposed formalization, the class of potential applications is very large. The applications of specific interest of the proposed formalism include design and implementation of knowledge-based control systems and modelling the behaviour of certain complex relational systems having no analytical models in the form of differential/difference equations, as well as analysis of theoretical properties of knowledge-based dynamic systems. Simple application examples are enclosed.