Journal:Informatica
Volume 5, Issues 3-4 (1994), pp. 261–282
Abstract
Control laws' design strategies in order to stabilize integro-differential systems with delays are developed by using an extended system and the delay measure.
Journal:Informatica
Volume 5, Issues 1-2 (1994), pp. 241–255
Abstract
Neural networks are often characterized as highly nonlinear systems of fairly large amount of parameters (in order of 103 – 104). This fact makes the optimization of parameters to be a nontrivial problem. But the astonishing moment is that the local optimization technique is widely used and yields reliable convergence in many cases. Obviously, the optimization of neural networks is high-dimensional, multi-extremal problem, so, as usual, the global optimization methods would be applied in this case. On the basis of Perceptron-like unit (which is the building block for the most architectures of neural networks) we analyze why the local optimization technique is so successful in the field of neural networks. The result is that a linear approximation of the neural network can be sufficient to evaluate the start point for the local optimization procedure in the nonlinear regime. This result can help in developing faster and more robust algorithms for the optimization of neural network parameters.
Journal:Informatica
Volume 5, Issues 1-2 (1994), pp. 231–240
Abstract
The problem of mathematical modelling and simulating of two-dimensional (2D) random fields, using space autoregressive models, is analyzed. Algorithms for the estimation of parameters of models, procedures for finding correlation coefficients and for synthesis of the realizations of given parameter fields are presented.
Journal:Informatica
Volume 5, Issues 1-2 (1994), pp. 211–230
Abstract
The paper deals with a simple model of the competition of two queuing systems, providing the same service. Each system may vary its service price and its service rate. The customers choose the system with less total service price, that depends on the waiting time and on the service price. The possibility for the existence of equilibrium is investigated. Simple cases are investigated analytically. It is shown that the Nash equilibrium exists in special cases only. A modification of the Stakelberg equilibrium is proposed as a model of competition with a prognosis. This prognosis helps form more stable prices and more stable strategies of competitors. The case of social economics is investigated, too. The dynamics of the competition of more realistic stochastic queuing systems is investigated by Monte Carlo simulation. The simulative analysis is realized by means of a rule-based simulation system.
Journal:Informatica
Volume 5, Issues 1-2 (1994), pp. 189–210
Abstract
In the previous papers (Novovičova, 1987; Pupeikis 1991) the problem of recursive least square (RLS) estimation of dynamic systems parameters in the presence of outliers in observations has been considered, when the filter, generating an additive noise, has a transfer function of a particular form, see Fig. 1, 2. The aim of the given paper is the development of well-known classical techniques for robust on-line estimation of unknown parameters of linear dynamic systems in the case of additive noises with different transfer functions. In this connection various ordinary recursive procedures, see Fig. 2–6, are worked out when systems' output is corrupted by the correlated noise containing outliers. The results of numerical simulation by IBM PC/AT (Table 1) are given.
Journal:Informatica
Volume 5, Issues 1-2 (1994), pp. 175–188
Abstract
An essentially new method for discrete sequential detection of abrupt or slow multiple changes in several unknown properties of random processes is considered. The method is based on a sequential nonlinear mapping into two-dimensional vectors of many-dimensional vectors of parameters which describe the properties of random process. The mapping error function is chosen and the expressions for sequential nonlinear mapping are presented along with some experimental results. Theoretical minimum amount of at the very beginning simultaneously mapped vectors is obtained.
Journal:Informatica
Volume 5, Issues 1-2 (1994), pp. 167–174
Abstract
We consider here the optimization problems of simple competitive model. There are two servers providing the some service. Each server fix the price and the rate of service. The rate of service defines the customer losses waiting in line for the service. The customer go to the server with lesser total service cost. The total cost includes the service price plus waiting losses. A customer goes away, if the total cost exceeds some critical level. The flow of customers and the service time both are stochastic. There is no known analytical solution for this model. We get the results by Monte Carlo simulation. We get the analytical solution of the simplyfied model.
We use the model as an illustration to show the possibilities and limitations of optimization theory and numerical techniques in the competitive models.
We consider optimization in two different mathematical frameworks: the fixed point and the Lagrange multipliers. We consider two different economic and social objectives, too: the equilibrium and the social cost minimization.
We use the model teaching Operations Research. The simple model may help to design more realistic models describing the processes of competition.
Journal:Informatica
Volume 5, Issues 1-2 (1994), pp. 123–166
Abstract
We consider here the average deviation as the most important objective when designing numerical techniques and algorithms. We call that a Bayesian approach.
We start by describing the Bayesian approach to the continuous global optimization. Then we show how to apply the results to the adaptation of parameters of randomized techniques of optimization. We assume that there exists a simple function which roughly predicts the consequences of decisions. We call it heuristics. We define the probability of a decision by a randomized decision function depending on heuristics. We fix this decision function, except for some parameters that we call the decision parameters.
We repeat the randomized decision procedure several times given the decision parameters and regard the best outcome as a result. We optimize the decision parameters to make the search more efficient. Thus we replace the original optimization problem by an auxiliary problem of continuous stochastic optimization. We solve the auxiliary problem by the Bayesian methods of global optimization. Therefore we call the approach as the Bayesian one.
We discuss the advantages and disadvantages of the Bayesian approach. We describe the applications to some of discrete programming problems, such as optimization of mixed Boolean bilinear functions including the scheduling of batch operations and the optimization of neural networks.
Journal:Informatica
Volume 5, Issues 1-2 (1994), pp. 110–122
Abstract
In the presented paper a method for treating a random signal bearing an information about the behaviour of a technological process is given. The main goal of the given method is to remove possible failures arising in analog sensors, which yield nonstationary behaviour of an observed signal. Then the smoothed signal is tested by a suitable test described in the paper for the regular or irregular behaviour of a technological process. One understands by the regular behaviour of a technological process that within prescribed bounds.
Journal:Informatica
Volume 5, Issues 1-2 (1994), pp. 98–109
Abstract
The input–output relationship of the periodically time-varying (PTV) systems, impulse response of the PTV state–space system, and the transfer function of the PTV system are presented. A coefficient sensitivity is investigated by using a virtual PTV state-space system in which periodically time-varying coefficients are stochastically varied.