Invariance and polynomial design of strategies in the linear-quadratic game

A new algorithm to solve the H ^∞ control problem in the case of full information was presented. It combines the spectral and matrix methods. The polynomial Lur’e-Riccati operator was introduced. Parametrization of all solutions of the controlled plant equation by hidden variables was presented within the framework of the J.C. Willems behavioral approach. The kernel of the polynomial Lur’e-Riccati operator was decomposed into the direct sum of subspaces that are similar to the Jordan blocks. The saddle point of the linear-quadratic game which was found by V.A. Yakubovich in 1970 was shown to provide solution to the H ^∞ control problem for a considerable class of controlled plants.     

Stability of systems with several monotone nonlinearities

This paper is devoted to stability problems of automatic control systems. Frequency domain criteria for global asymptotic stability of equilibrium sets for new classes of nonlinearities are derived. Results are illustrated by examples.     

Stability analysis of discrete-time recurrent neural networks

We address the problem of global Lyapunov stability of discrete-time recurrent neural networks (RNNs) in the unforced (unperturbed) setting. It is assumed that network weights are fixed to some values, for example, those attained after training. Based on classical results of the theory of absolute stability, we propose a new approach for the stability analysis of RNNs with sector-type monotone nonlinearities and nonzero biases. We devise a simple state-space transformation to convert the original RNN equations to a form suitable for our stability analysis. We then present appropriate linear matrix inequalities (LMIs) to be solved to determine whether the system under study is globally exponentially stable. Unlike previous treatments, our approach readily permits one to account for non-zero biases usually present in RNNs for improved approximation capabilities. We show how recent results of others on the stability analysis of RNNs can be interpreted as special cases within our approach. We illustrate how to use our approach with examples. Though illustrated on the stability analysis of recurrent multilayer perceptrons, the approach proposed can also be applied to other forms of time-lagged RNNs.     

Effect of titanium–magnesium catalyst morphology on the properties of polypropylene upon propylene polymerization in a liquid monomer

The effect of the particle size of an IK-8-21 domestic titanium-magnesium catalyst on the properties of polypropylene (PP) produced during the polymerization of propylene in a liquid monomer is studied. Catalysts with particle sizes of 20 to 64 μm are shown to have high activity and identical sensitivity to hydrogen and allow PP to be obtained with a narrow distribution of particles over size, high isotacticity, and close values of crystallinity, melting temperature, and physicomechanical properties. A slight decrease in the activity and bulk density of PP powder is observed when the average size of catalyst particles is increased from 20 to 43 μm. A more notable reduction in the activity and bulk density of PP powder is observed for catalyst with particle sizes of 62 to 64 μm. IK-8-21 catalyst is not inferior to its foreign analogues with respect to the properties of the resulting PP.     

Stabilization of Oscillations in a Periodic System by Choosing Appropriate Couplings

We study a model containing coupled subsystems (MCCS) defined by a system of ordinary differential equations, where subsystems are systems of autonomous ordinary differential equations. The model splits into unrelated systems when the numerical parameter that characterizes couplings is ε = 0, and the couplings are given by time-periodic functions. We solve the natural stabilization problem which consists in finding relationships that simultaneously guarantee the existence and asymptotic stability of MCCS oscillations. We generalize results previously obtained for the case of two coupled subsystems each of which is defined on its own plane.     

On the Protective Properties of Electrostatically Spraged Fluoroplastic and Epoxy Coatings

The protective and insulating properties of fluoroplastic and epoxy coatings applied by high-voltage electrostatic spraying were studied. The epoxy coatings were found to be less permeable than the fluoroplastic ones, yet they cannot be used to protect metal parts in corrosive environment because of their low chemical resistance.     

Limit cycles with chattering in relay feedback systems

Relay feedback has a large variety of applications in control engineering. Several interesting phenomena occur in simple relay systems. In the paper, scalar linear systems with relay feedback are analyzed. It is shown that a limit cycle where part of the limit cycle consists of fast relay switchings can occur. This chattering is analyzed in detail and conditions for approximating it by a sliding mode are derived. A result on existence of limit cycles with chattering is given, and it is shown that the limit cycles can have arbitrarily many relay switchings each period. Limit cycles with regular sliding modes are also discussed. Examples illustrate the results.     

Application of a new algorithm using Doppler information to retrieve complex wind fields over the Black Sea from ENVISAT SAR images

Several algorithms have been proposed to retrieve near-surface wind fields from C-band synthetic aperture radar (SAR) images acquired over the ocean. They mainly differ in the way they retrieve the wind direction. Conventionally, the wind direction is taken from atmospheric models or is extracted from the linear features sometimes visible in SAR images. Recently, a new wind retrieval algorithm has been proposed, which also includes the Doppler shift induced by motions of the sea surface. In this article, we apply three wind retrieval algorithms, including the one using Doppler information, to three complex wind events encountered over the Black Sea and compare the SAR-derived wind fields with model wind fields calculated using the high-resolution weather research and forecasting (WRF) model. It is shown that the new algorithm is very efficient in resolving the 180° ambiguity in the wind direction, which is often a problem in the streak-based wind retrieval algorithms. However, the Doppler-based algorithm only yields good results for wind directions that have a significant component in the look direction of the SAR antenna. Furthermore, it is dependent on good separation of the contributions to the Doppler shift induced by surface currents and wind-related effects (wind drift and wind-sea components of the ocean wave spectrum). We conclude that an optimum wind retrieval algorithm should consist of a combination of the algorithms based on linear features and Doppler information.