2018 (vol. 28) - Number 1

*I. Duleba, I. Karcz-Duleba:*

A comparison of methods solving repeatable inverse kinematics for robot manipulators

*A. Niederliński:*

A new approach for modelling uncertainty in expert systems knowledge bases

*T.T. Tuan, L.D. Tufa, M.I.A. Mutalib, N.M. Ramli :*

Optimal operation of a process by integrating dynamic economic optimization and model predictive control formulated with empirical model

*M. Kaleta:*

Network winner determination problem

*A. Kowalewski:*

Extremal problems for parabolic systems with time-varying lags

*T. Rybus, K. Seweryn, J.Z. S±siadek:*

Application of predictive control for manipulator mounted on a satellite

*T. Kaczorek:*

Reachability and observability of positive discrete-time linear systems with integer positive and negative powers of the state Frobenius matrices

*G. Grassi, A. Ouannas, V-T. Pham:*

A general unified approach to chaos synchronization in~continuous-time systems (with or without equilibrium points) as well as in discrete-time systems

*D. Pazderski:*

A robust smooth controller for a unicycle-like robot

ACS Abstract:

**1995 (Volume 4)**

Number 1/2

**The programmed grammars and automata as tools for a construction of analytic expert systems**

M.Flasiński(Jagiellonian University, Poland) |

**Optimal control of discrete distributed systems with delays in the control: the finite horizon case**

Mostafa Rachik(Faculté des Sciences Ben M'sik, Morocco) | Jamila Karrakchou(Ecole Mahammadia d'Ingénieurs, Morocco) |

**keywords:** difference equation, diffusion system, discrete distributed systems, linear quadratic optimal control, optimal control.

**Multivariable nonlinear system identification by radial basis function neural networks**

Shaohua Tan(National University of Singapore, Singapore) | Jianbin Hao and Joos Vandewalle(Katholieke Universiteit Leuven, Belgium) |

**Repetitive regulator approximation**

Krzysztof Nowosad(Warsaw University of Technology, Poland) |

**Eigenvalue assignment and exponential stability in discrete-time systems**

Jerzy Tokarzewski(Military University of Technology, Poland) |

**A comparative study of ranking fuzzy sets deffined by a neural network algorithm - justification for a centroidal method**

Les M. Sztandera(Philadelphia College of Textiles and Science, USA) |

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.

**keywords:** fuzzy multi-attribute decision making, evaluation of fuzzy ranking methods, neural network architecture.

**Digital relaying in power system using fuzzy set theory**

Bogdan Kasztenny(Technical University of Wrocław, Poland) |

**Logical foundations for knowledge-based control systems. Part II: Representation of states, transformations and analysis of theoretical properties**

Antoni Ligęza(St. Staszic Technical University of Mining and Metallurgy, Poland) |

*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.

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