Li-Wei Zhang and Huan-Wen Tang (Dalian University of Technology, China)
This paper presents a maximum entropy function with parameters, as that an extension of the original one proposed by A. B. Templeman and X.-S. Li (1987). It is proved that, under certain conditions, the maximum entropy function with a finite parameter p has the same optimum which is associated with the minimax problem. A maximum entropy algorithm with parameters is given and its properties are discussed. It is also proved that the optimum of a minimax problem can be obtained by solving a nonlinear system of algebraic equations and this nonlinear system can be solved by the Newton method.
keywords: minimax problem, nondifferentiable optimization, maximum entropy function, maximum entropy function with parameters, exact penalty function, the Newton method.
Kartik Chandra Patra and Bibhuti Bhusan Pati (Indira Gandhi Institute of Technology Sarang, India)
Janusz Kacprzyk (Polish Academy of Sciences, Poland)
In the paper, the feasibility of signal stabilisation of two-input/two-output (TITO) non-linear system exhibiting self oscillations by inserting high frequency dither has been investigated. The two interesting phenomena of desynchronisation and synchronisation are analysed. Further, the possibility of a TITO system exhibiting asynchronous excitation in presence of high frequency sinusoidal input has been examined. The method of analysis as well as the prediction of the above phenomena have been illustrated through several examples and the analytical results have been compared with those from digital simulation.
Zbigniew Świder (Technical University of Rzeszów, Poland)
Filtering of quantization errors caused by analog-to-digital conversion (A/D) is considered. One assumes that the filters cover both small and high sampling rates, so they must be implemented with 'delta' or 'gamma'
operators. The operators correspond to rectangular or trapezoidal integration rules, respectively. Analytic formulae and nomograms for noise attenuation in terms of time-constant-to-sampling ratio are given for a typical low-pass filters. The formulae may be used to design the filter for the control loop given A/D resolution, or conversely, to choose A/D converter following accuracy requirements.
Ryszard Gessing (Silesian University of Technology, Poland)
In this paper, an approximate, continuous-time model of the discrete-time system composed of a sampler, zero-order hold and continuous-time plant, in the form of modified plant transfer function, is utilised. A discrete-time controller is designed by means of the usual continuous-time methods. First, a continuous-time controller for the modified plant is designed and next the discrete-time controller is determined. The latter results from approximation of the former by means of Tustin rule. The method is illustrated on the examples considered earlier in the literature.
keywords: Discrete-time systems, controllers, control system design, digital system, microprocessor control.
Tadeusz Mikulczyński and Zdzisław Samsonowicz (Technical University of Wrocław, Poland)
Selected formalisms, Grafpol and SFC, of modelling and programming discrete manufacturing processes have been analyzed. The principles of process modelling by using the Grafpol-MS and SFC nets adopted in the IEC:1131-3 standard have been discussed. The superiority of the Grafpol-MS net over the SFC net which is a Petri net modification of the P/T type has been proven.
Krzysztof Nowosad (Warsaw University of Technology, Poland)
In the paper the linear predictive controller with the fixed control horizon and given final state is considered. This controller preserves the final state in the presence of process disturbances. The elementary proof of this fact is given.
Rajendra P. Srivastava (The University of Kansas, USA)
In this article, we discuss problems with probability theory in representing uncertainties encountered in the "real world" and show how belief functions can overcome these difficulties. Also, we discuss an expected utility approach of decision making under ambiguity using the belief function framework. In particular, we develop a proposition for decision making under ambiguity using the expected utility theory. This proposition is based on Strat's approach of resolving ambiguity in the problem using belief functions. We use the proposition to explain the Ellsberg paradox and model the decision making behavior under ambiguity. We use the empirical data of Einhorn and Hogarth to validate the proposition. Also, we use the proposition to predict several decision making behaviors under ambiguity for special conditions. Furthermore, we discuss the general condition under which the "switching" behavior, as observed by Einhorn and Hogarth, will occur using the concept of "precision measure" in the expected utility theory.
S. P. Banks, C. Riddalls, D. McCaffrey (University of Sheffield, England)
The frequency domain theory of nonlinear analytic input-output maps is studied, directly in the frequency domain. By expanding the "Fourier transform" of the input-output map as a Taylor series in an appropriate function space and applying Schwartz' kernel theorem, we obtain a general theory of nonlinear systems in the frequency domain. This obviates the necessity of using "association of variables" in the time domain and leads to a much more general theory.
keywords: Nonlinear Systems, Frequency Response, Kernel Theorem.