Romanenko V.D.

Stability analysis of univariate and multivariate systems with multirate sampling

The present paper discusses stability and minimum phase of multirate univariate and multivariate dynamic systems. We demonstrate that transition from a singlerate to a corresponding multirate model does not violate properties of stability and minimum phase. Specifically, we establish the zeroespoles ratio of singlerate and multirate models.

Optimal Decision-Making on Stabilization of Euro/Dollar Rate on the Basis of Mathematical Models with Multirate Sampling

The present paper describes development of the model structure of the euro/dollar with 2 lags members of input, 11 input factors with sampling 5 days or month and 2 controls with sampling 5 days. We choose the factors to take into account the theoretical material on the subject and to achieve the highest possible quality at such high rate sampling. 5 days sampling characterized by significant speculative fluctuations require frequent adjustment of the coefficient. At the second stage we synthesize the optimality criterion in the form of generalized variance.

Adaptive Forecasting Method for Maximal Conditional Variances of Multirate Process Outputs’ Ratios

The paper proposes the concept of maximal conditional sample variance of ratio’s discrepancy. We consider the GARCH model design method for forecasting these variances in case of multivariate heteroskedastic processes with a small sample period for input disturbances and a large period for outputs. The dynamics of processes in stochastic environment is described with polynomial matrix models with multirate sampling. Furthermore, the adaptive tuning of GARCH model coefficients is based on the recursive least squares method. Additionally, we provide the research results.

Optimal Decision-Making on the Stabilization of Hryvnia/Dollars Course on the Basis of Mathematical Models with Multirate Sampling

The present paper describes the development of the model structure of the hryvnia/dollar in the ARMAX form. The model inputs are seven factors and one control, which are measured at different time intervals. This allows us considering the model with multirate sampling, where the output coordinate and control are measured every ten days, and the factors in their turn have three time rates: every ten days, monthly and quarterly. Based on this model, we propose and test the approach to the optimal decision based on the optimality decision-making in the form of the generalized variance.

The design of coordinating control algorithm for the thermal mixing aggregate under external disturbances

The present paper proposes the control algorithm for the thermal mixing aggregate to stabilize a water level and temperature under non-stationary external disturbance (water consuming). We show that an additional coordinating control loop for outputs’ ratio should be utilized to increase the control quality. The specific control laws for basic and coordinating regulators are proposed. Furthermore, numerical modeling is presented to ensure effectiveness of the present algorithm.