Development of Ellipsoidal Analysis and Filtering Methods for Nonlinear Control Stochastic Systems

Abstract

The methods of the control stochastic systems (CStS) research based on the parametrization of the distributions permit to design practically simple software tools. These methods give the rapid increase of the number of equations for the moments, the semiinvariants, coefficients of the truncated orthogonal expansions of the state vector Y, and the maximal order of the moments involved. For structural parametrization of the probability (normalized and nonnormalized) densities, we shall apply the ellipsoidal densities. A normal distribution has an ellipsoidal structure. The distinctive characteristics of such distributions consist in the fact that their densities are the functions of positively determined quadratic form of the centered state vector. Ellipsoidal approximation method (EAM) cardinally reduces the number of parameters. For ellipsoidal linearization method (ELM), the number of equations coincides with normal approximation method (NAM). The development of EAM (ELM) for CStS analysis and CStS filtering are considered. Based on nonnormalized densities, new types of filters are designed. The theory of ellipsoidal Pugachev conditionally optimal control is presented. Basic applications are considered.

Role of the Solid–Aqueous Medium Interface in Transferring Light-Induced Excitation of Silicon

“…We can therefore assume that when hypersonic waves propagate along the interface between the aqueous medium and fluoroplastic or sodium-containing glass, the absorption coefficient is anomalously low. This assumption is consistent with data obtained in [1,8] according to which the properties of surface water layers and water-solid interfaces differ from volume properties. In our case, the role of sodium ions, which form Na + -[H 2 O] n clusters roughly 1 nm across [9], should also be taken into consideration.…”

“…For those engaged in studying the anomalous properties of water and water solutions [1], this effect is of interest regarding interfacial phenomena and clustering in these media [1,5,9]. With the above model representations confirmed, this effect will stimulate more detailed studies of the liquid-solid interface [1,3,8]. For acoustics, radiophysics, and electronics, the aspect of the effect that is related to EHF wave propagation in heterogeneous media with nanometer inhomogeneities is of importance.…”

“…The effect is of special interest for biomedical applications of EHF radiation, since it has much in common with acoustoelectric phenomena in living organisms [2,3,6,8]. The role of the aqueous medium in them is played by blood, lymph, and cytoplasm, whereas cell membranes (possessing piezoelectric properties [2]) play the role of solids.…”

“…The unusual properties of surface water layers and water layers bordering solids have long attracted the attention of researchers involved in different fields of science [1][2][3][4][5][6][7][8][9]. Interest in this problem among those engaged in biomedicine and radiophysics was provoked by investigations carried out at the Kotel'nikov Institute of Radio Electronics (Moscow), which were launched as early as in the last century under the leadership of Academician N.D. Devyatkov.…”

“…They were devoted to the role of extremely high-frequency (EHF) electromagnetic waves in cellular processes taking place in living organisms and the use of these waves in medicine [2]. It was concluded that such processes are associated with the properties of an aqueous medium that is in contact with cell membranes [8]. An intriguing factor that is being discussed in connection with this problem is the anomalously deep penetration of the effect of irradiation compared with the penetration depth of the EHF electromagnetic wave.…”