Controlled Synchronization of One Class of Nonlinear Systems under Information Constraints

Output feedback controlled synchronization problems for a class of nonlinear unstable systems under information constraints imposed by limited capacity of the communication channel are analyzed. A binary time-varying coder-decoder scheme is described and a theoretical analysis for multi-dimensional master-slave systems represented in Lurie form (linear part plus nonlinearity depending only on measurable outputs) is provided. An output feedback control law is proposed based on the Passification Theorem. It is shown that the synchronization error exponentially tends to zero for sufficiantly high transmission rate (channel capacity). The results obtained for synchronization problem can be extended to tracking problems in a straightforward manner, if the reference signal is described by an {external} ({exogenious}) state space model. The results are applied to controlled synchronization of two chaotic Chua systems via a communication channel with limited capacity.Comment: 8 pages, 2 figure

Frequency locking of modulated waves

We consider the behavior of a modulated wave solution to an $\mathbb{S}^1$-equivariant autonomous system of differential equations under an external forcing of modulated wave type. The modulation frequency of the forcing is assumed to be close to the modulation frequency of the modulated wave solution, while the wave frequency of the forcing is supposed to be far from that of the modulated wave solution. We describe the domain in the three-dimensional control parameter space (of frequencies and amplitude of the forcing) where stable locking of the modulation frequencies of the forcing and the modulated wave solution occurs. Our system is a simplest case scenario for the behavior of self-pulsating lasers under the influence of external periodically modulated optical signals

МЕТОДИКА ПРОВЕРКИ В НАЗЕМНЫХ УСЛОВИЯХ ЛИНЕЙНОГО РАЗРЕШЕНИЯ ПО АЗИМУТУ В РАДИОЛОКАТОРЕ С СИНТЕЗОМ АПЕРТУРЫ КОСМИЧЕСКОГО БАЗИРОВАНИЯ

By working out of a radar with the aperture synthesis of the aerial (RAS) of space basing there is a necessity of its debugging and verification at the land conditions. The most difficult verification task is requirement performance on resolution maintenance of RAS on an azimuth. It is caused by the given resolution provided in RAS at an orbit during stable moving in space with a speed about 7,6 km/s. The verification method of maintenance of the demanded linear resolution of RAS on an azimuth in land conditions with turned synthesis of aerial aperture is offered. It operates when RAS is unmoved and objects of resolution are placed at a moving ship.При разработке радиолокатора с синтезом апертуры антенны (РСА) космического базирования возникает необходимость его отладки и проверки в наземных условиях. Наиболее сложно проверить выполнение требования по обеспечению разрешающей способности РСА по азимуту. Это обусловлено тем, что разрешающая способность по азимуту обеспечивается в РСА при его стабильном перемещении на орбите в космосе со скоростью около 7,6 км/с. Предложена методика проверки обеспечения требуемого линейного разрешения РСА по азимуту в наземных условиях с использованием обращенного синтеза апертуры, когда РСА неподвижен, а объекты разрешения размещены на движущемся носителе, в частности, на плавсредстве

On iterating concentration and periodic regimes at the anomalous diffusion in polymers

Diffusion of a penetrating liquid in a polymeric material does not often satisfy the classical diffusion equations and requires taking relaxational (viscoelastic) properties of the polymer into account. We investigate a boundary value problem on a bounded domain in space for the set of equations modelling this abnormal diffusion. It is proved that, for any sufficiently short time segment and any stress prescribed at the beginning of this segment, there exists a global in time weak solution of the boundary value problem (a pair: concentration - stress) such that the concentrations at the beginning and at the end of the segment are the same. Under an additional assumption on coefficients, existence of time-periodic weak solutions (without any restrictions of the period length) is shown.Comment: 26 pages, in Russia

Tunability experiments at the FERMI@Elettra free-electron laser

FERMI@Elettra is a free electron-laser (FEL)-based user facility that, after two years of commissioning, started preliminary users' dedicated runs in 2011. At variance with other FEL user facilities, FERMI@Elettra has been designed to deliver improved spectral stability and longitudinal coherence. The adopted scheme, which uses an external laser to initiate the FEL process, has been demonstrated to be capable of generating FEL pulses close to the Fourier transform limit. We report on the first instance of FEL wavelength tuning, both in a narrow and in a large spectral range (fine- and coarse-tuning). We also report on two different experiments that have been performed exploiting such FEL tuning. We used fine-tuning to scan across the 1s–4p resonance in He atoms, at ≈23.74 eV (52.2 nm), detecting both UV–visible fluorescence (4p–2s, 400 nm) and EUV fluorescence (4p–1s, 52.2 nm). We used coarse-tuning to scan the M4,5 absorption edge of Ge (∼29.5 eV) in the wavelength region 30–60 nm, measured in transmission geometry with a thermopile positioned on the rear side of a Ge thin foil