Dynamic Robust Output Min–Max Control for Discrete Uncertain Systems

Min–max control is a robust control, which guarantees stability in the presence of matched uncertainties. The basic min–max control is a static state feedback law. Recently, the applicability conditions of discrete static min–max control through the output have been derived. In this paper, the results for output static min–max control are further extended to a class of output dynamic min–max controllers, and a general parametrization of all such controllers is derived. The dynamic output min–max control is shown to exist in many circumstances under which the output static min–max control does not exist, and usually allows for broader bounds on uncertainties. Another family of robust output min–max controllers, constructed from an asymptotic observer which is insensitive to uncertainties and a state min–max control, is derived. The latter is shown to be a particular case of the dynamic min–max control when the nominal system has no zeros at the origin. In the case where the insensitive observer exists, it is shown that the observer-controller has the same stability properties as those of the full state feedback min–max control.     

Apparatus for testing samples of glass plastic subject to high-frequency fatigue in the symmetrical extension-compression mode

Using an instrument of the UM-20 type (made by the Scientific-Research and Design Institute of Testing Instruments, Moscow) as a basis, an apparatus is designed for subjecting glass-plastic samples to high-frequency fatigue tests at frequencies of 10–20 kHz. In order to stabilize the thermal state of the sample, water cooling is incorporated.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 4, pp. 756–758, July–August, 1972.     

Determination of the stresses in polymeric coatings with allowance for "frozen" strains

The state of stress and strain of polymeric coatings is determined in the case of a time varying temperature field that includes the range on which the coating goes over into the glassy state.Leningrad Mechanical Institute. Translated from Mekhanika Polimerov, No. 1, pp. 66–71, January–February, 1973.     

Consideration of friction between layers in determining the stress-strain state of structures with nonideal layer contact

A mathematical model for calculation of structures in a three-dimensional installation allowing for layer slippage with friction was constructed. The examples examined show that consideration of friction in problems of calculating laminated structures with nonideal layer contact can introduce an essential correction in the stress—strain state of the structure. In slabs with a freely sagging lower surface, friction is perceived for important friction coefficients and increases when the slippage surface approaches the loaded surface. In masses with a rigidly attached lower surface, even insignificant friction coefficients lead to essential redistribution of the stress—strain state.Ukraine Transportation University, Kiev, Ukraine. Translated from Mekhanika Kompozitnykh Materialov, Vol. 33, No. 2, pp. 192–199, March–April, 1997.     

Nonequilibrium stationary states of noninteracting electrons in a one-dimensional lattice

Nonequilibrium stationary states of a one-dimensional quantum conductor placed between two reservoirs are investigated. Applying the theory of C^*-algebra, as t→+∞, any state including the degrees of freedom of reservoirs is shown to weakly evolve to a quasifree stationary state with nonvanishing currents. The stationary state exhibits transports which are consistent with nonequilibrium thermodynamics and, in this sense, it has broken time symmetry. Particularly, the electric and energy currents are shown to be expressed by two-probe Landauer-type formulas and they reduce to the results by Sivan–Imry and Bagwell–Orlando in appropriate regimes. As a consequence of the time reversal symmetry, there exists another stationary state with anti-thermodynamical transports, which is the t→−∞ limit of the initial state. The consistency between the dynamical reversibility and the irreversibility of the evolution of states is discussed as well.     

Strength of orthogonally reinforced plastics in uniaxial tension

Failure conditions are proposed for an orthogonally reinforced plastic in uniaxial tension at an arbitrary angle to the directions of reinforcement. The failure conditions are formulated for the case when the strength of the bond between the resin and the reinforcement is greater than the strength of the resin. The strength of the resin, which is in a volume state of stress, is determined by an energy criterion.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 4, pp. 629–633, July–August, 1973.     

Stress Distribution in an Infinite Elastic Body with a Locally Curved Fiber in a Geometrically Nonlinear Statement

Within the framework of a piecewise homogeneous body model, with the use of three-dimensional geometrically nonlinear exact equations of elasticity theory, a method for determining the stress—strain state in unidirectional fibrous composites with locally curved fibers is developed for the case where the interaction between the fibers is neglected. All the investigations are carried out for an infinite elastic body containing a single locally curved fiber. Numerical results illustrating the effect of geometrical nonlinearity on the distribution of the self-balanced normal and shear stresses acting on the interface and arising as a result of local curving of the fiber are presented.__________Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 41, No. 4, pp. 433–448, July–August, 2005.     

Time-temperature superposition applied to crosslinked polymers in creep with superimposed hydrostatic pressure

The creep of an epoxy composition under combined tension and hydrostatic pressure (up to 800 kgf/cm²) has been investigated. The applicability of time-temperature superposition to a complex state of stress is demonstrated. Hydrostatic pressure is shown to affect the deformability of crosslinked polymers in tension.Leningrad Technological Institute of the Refrigeration Industry. Plastpolimer Research-Production Association, Leningrad. Translated from Mekhanika Polimerov, No. 3, pp. 541–544, May–June, 1976.     

Effect of gaseous oxygen pressure on the kinetics of accumulation of residual deformation in resins

The authors studied changes in the properties of resins in the static deformed state under the effect of gaseous oxygen pressures of up to 200 atm at 25, 50, and 70° C for 20–500 days, depending on the experimental conditions. It was shown that an increase in gaseous oxygen pressure significantly affects the process of accumulation of residual deformation up to 30–40 atm while a further pressure rise has practically no effect on changes in the accumulation rate of residual deformation.Scientific-Research Institute of the Resin Industry, Moscow. Translated from Mekhanika Polimerov, Vol. 9, No. 3, pp. 552–554, May–June, 1973.     

Propagation of sound in oriented polymers

The propagation of sound in oriented polymers is considered. Starting from an assumption concerning the superposition of relaxation processes in polymers, expressions are obtained for the speed and absorption of sound as functions of the relaxation spectrum, molecular orientation, and crystallinity. It is shown that the orientation dependence of the acoustic properties is more distinctly expressed in the region of the glassy state.Scientific-Research Institute of Plastics, Moscow. Translated from Mekhanika Polimerov, No. 3, pp. 437–441, May–June, 1969.     

Flow of a nonlinear viscoelastic liquid in cylindrical channels

The problem of nonrectilinear steady-state flow of a nonlinear viscoelastic liquid in an arbitrary cylindrical channel is examined. On the assumption that the cross flows are insignificant as compared with the longitudinal flows an equation of state is derived for the flow regime in question. A variational principle established for steady-state flows of the investigated media is proposed as the basis of a method of solving problems of the flow of polymer materials in arbitrary cylindrical channels. The flow of a polymer solution in rectangular channels is investigated.Institute of Mechanics, AS UkrSSR, Kiev. Translated from Mekhanika Polimerov, Vol. 4, No. 6, pp. 1103–1111, November–December, 1968.     

Infrared spectroscopic study of the prefracture state of rigid polymers

A correspondence has been established between the effects of stress and temperature on the half-width and the position of the maximum of the 972-cm^–1 absorption band for polyethylene terephthalate. It is shown that the prefracture state of polyethylene terephthalate is a softened state.A. F. Ioffe Physicotechnical Institute, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, No. 3, pp. 520–523, May–June, 1976.     

An optimal compressed circular cylindrical shell

The stability is considered for a shell of optimum weight. An isotropic shell is found to be suitable, and the bifurcation in the undeformed state can occur via an axially symmetric or other form. This explains the sensitivity of an isotropic shell to perturbation.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 944–947, September–October, 1973.     

Optimal Evasion from a Pursuer with Delayed Information

A class of prescribed duration pursuit–evasion problems with first-order acceleration dynamics and bounded controls is considered. In this class, the pursuer has delayed information on the lateral acceleration of the evader, but knows perfectly the other state variables. Moreover, the pursuer applies a strategy derived from the perfect information pursuit–evasion game solution. Assuming that the evader has perfect information on all the state variables as well as on the delay of the pursuer and its strategy, an optimal evasion problem is formulated. The necessary optimality conditions indicate that the evader optimal control has a bang–bang structure. Based on this result, two particular cases of the pursuer strategy (continuous and piecewise continuous in the state variables) are considered for the solution of the optimal evasion problem. In the case of the continuous pursuer strategy, the switch point of the optimal control can be obtained as a root of the switch function. However, in the case of the piecewise continuous (bang–bang) pursuer strategy, this method fails, because of the discontinuity of the switch function at this very point. In this case, a direct method for obtaining the switch point, based on the structure of the solution, is proposed. Numerical results illustrating the theoretical analysis are presented leading to a comparison of the two cases.     

Evaluating the feasibility of using composites in ship shafting 1. Analysis of the loads and stress state of a composite shaft

Literature data is used to analyze the theoretical loads that develop in ship shafting. A study is made of the stress state of different thicknesses of shafts made of glass- and carbon-fiber-reinforced plastics loaded with an axial force, torque, and bending by a concentrated force. The results contain information needed for optimizing the design of composite ship shafting.Translated from Mekhanika Kompozitnykh Materialov, Vol. 31. No. 6, pp. 797–807. November–December, 1995.     

Feedback boundary stabilization of the three-dimensional incompressible Navier–Stokes equations

We study the local stabilization of the three-dimensional Navier–Stokes equations around an unstable stationary solution w, by means of a feedback boundary control. We first determine a feedback law for the linearized system around w. Next, we show that this feedback provides a local stabilization of the Navier–Stokes equations. To deal with the nonlinear term, the solutions to the closed loop system must be in H^{3/2+ε,3/4+ε/2}(Q), with 0<ε. In [V. Barbu, I. Lasiecka, R. Triggiani, Boundary stabilization of Navier–Stokes equations, Mem. Amer. Math. Soc. 852 (2006); V. Barbu, I. Lasiecka, R. Triggiani, Abstract settings for tangential boundary stabilization of Navier–Stokes equations by high- and low-gain feedback controllers, Nonlinear Anal. 64 (2006) 2704–2746], such a regularity is achieved with a feedback obtained by minimizing a functional involving a norm of the state variable strong enough. In that case, the feedback controller cannot be determined by a well posed Riccati equation. Here, we choose a functional involving a very weak norm of the state variable. The compatibility condition between the initial state and the feedback controller at t=0, is achieved by choosing a time varying control operator in a neighbourhood of t=0.     

Criteria for the primitivity of a system of elements of a free metabelian group

We state the criteria for the complementability of an arbitrary system of elements to a set of free generators of a free metabelian group.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, Nos. 7 and 8, pp. 996–1002, July–August, 1991.     

Temperature dependence of deformative properties of filled polyvinyl chloride of various degrees of plasticization in the highly elastic state

Conclusions 1. The relative increase in stiffness upon the filling of PVC in the highly elastic state decreases with increase in temperature according to an exponential law.2. For a given degree of filling, the relative increase in stiffness upon filling as a function of the plasticizer content in PVC composites passes through a maximum at a degree of plasticization of 5–10%.All-Union Scientific-Research Institute of the Use of Polymeric Materials in Reclamation and Water Management, Elgava. Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 4, pp. 646–650, July–August, 1977.     

The relative expansion of polymer gels in uniaxial stretching

In the stretching of undried polyacrylonitrile fibers in the gel state, an increase in the cross sectional area, calculated from the diameter, is observed as compared with the cross sectional area obtained from the fact that the volume of the sample remains constant during stretching. The effect of relative expansion of polymer gels during the stretching process is explained by a delay in the relaxation processes, related to the orientation of amorphous sections and the rearrangement of the microstructure on a supermolecular level.All-Union Scientific-Research Institute of Synthetic Fibers, Kalinin. Translated from Mekhanika Polimerov, No. 5, pp. 927–929, September–October, 1972.     

Allowance for the effect of hydrostatic pressure in calculating the deformation of polymer structural elements

Simple equations of state of hereditary type are introduced and the results of analyzing certain experiments are presented. A solution of the problem of determining the stresses and strains in the case where the average stress does not depend on the coordinates is given for the equations of state in question.Central Scientific-Research Institute of Chemistry and Mechanics, Moscow. Translated from Mekhanika Polimerov, No. 1, pp. 50–57, January–February, 1973.