Optimal infinite-horizon feedback laws for a general class of constrained discrete-time systems: stability and moving-horizon approximations

Stability results are given for a class of feedback systems arising from the regulation of time-varying discrete-time systems using optimal infinite-horizon and moving-horizon feedback laws. The class is characterized by joint constraints on the state and the control, a general nonlinear cost function and nonlinear equations of motion possessing two special properties. It is shown that weak conditions on the cost function and the constraints are sufficient to guarantee uniform asymptotic stability of both the optimal infinite-horizon and movinghorizon feedback systems. The infinite-horizon cost associated with the moving-horizon feedback law approaches the optimal infinite-horizon cost as the moving horizon is extended.

Vitamin A and thyroxine carrier proteins in chicken plasma Steady-state control of the plasma level of free retinol-binding protein and free thyroxine

1. 1. The binding parameters of prealbumin-2 with retinol-binding protein and thyroxine (T4) revealed the existence of distinct and multiple sites for both retinol-binding protein and T4. 2. 2. From the analysis of binding parameters of retinol-binding protein with prealbumin-2 it is clear that under steady-state conditions about 99% of the holo-retinol-binding protein remains bound to prealbumin-2. 3. 3. Equilibrium dialysis studies on binding properties of thyroid hormones with prealbumin-2 revealed that it has a single high affinity site and three low affinity sites. 4. 4. The occurrence of three carrier proteins for thyroid hormones, thyroxine-binding globulin, prealbumin-2 and albumin has been demonstrated. However, the chicken thyroxine-binding globulin differs from human thyroxine-binding globulin by being relatively less acidic and occuring at a two-fold lower concentration. But the thyroid hormone binding parameters are comparable. 5. 5. Highly sensitive methods were developed for determination of T4 binding capacities of the various proteins and plasma level of total T4 by fractionation of carrier proteins and further quantitatively employing in electrophoresis and equilibrium dialysis. 6. 6. The thyroxine-binding proteins were found to be two types, one (viz., thyroxine-binding globulin) of great affinity but of low binding capacity, which mainly acts as reservoir of T4, and another (viz.,prealbumin-2) of low affinity but of high binding capacity, which can participate predominantly in the control of the free T4 pool.

First-principles analysis of electron correlation, spin ordering and phonons in the normal state of FeSe1-x

We present first-principles density-functional-theory-based calculations to determine the effects of the strength of on-site electron correlation, magnetic ordering, pressure and Se vacancies on phonon frequencies and electronic structure of FeSe1-x. The theoretical equilibrium structure (lattice parameters) of FeSe depends sensitively on the value of the Hubbard parameter U of on-site correlation and magnetic ordering. Our results suggest that there is a competition between different antiferromagnetic states due to comparable magnetic exchange couplings between first- and second-neighbor Fe sites. As a result, a short range order of stripe antiferromagnetic type is shown to be relevant to the normal state of FeSe at low temperature. We show that there is a strong spin-phonon coupling in FeSe (comparable to its superconducting transition temperature) as reflected in large changes in the frequencies of certain phonons with different magnetic ordering, which is used to explain the observed hardening of a Raman-active phonon at temperatures (similar to 100 K) where magnetic ordering sets in. The symmetry of the stripe antiferromagnetic phase permits an induced stress with orthorhombic symmetry, leading to orthorhombic strain as a secondary order parameter at the temperature of magnetic ordering. The presence of Se vacancies in FeSe gives rise to a large peak in the density of states near the Fermi energy, which could enhance the superconducting transition temperature within the BCS-like picture.

Free vibration of circular plates of arbitrary thickness

Free vibration of circular plates of arbitrary thickness is investigated using the method of initial functions. State-space approach is used to derive the governing equations of the above method. The formulation is such that theories of any desired order can be obtained by deleting higher terms in the infinite-order differential equations. Numerical results are obtained for flexural and extensional vibration of circular plates. Results are also computed using Mindlin's theory and they are in agreement with the present analysis.

Solid-state chemistry of high-temperature oxide superconductors:The experimental situation

High-temperature superconductivity in oxides of the type(La, Ln)2?xBax(Sr)xCuO4, Y(Ln)Ba2Cu3O7??, La3?xBa3+xCu6O14, and related systems is discussed with emphasis on aspects related to experimental solid-state chemistry. All of these oxides possess perovskite-related structures. Oxygen-excess and La-deficient La2CuO4 also exhibit superconductivity in the 20�40 K just as La2?xBax(Srx)CuO4; these oxides are orthorhombic in the superconductivity phase. The crucial role of oxygen stoichiometry in the superconductivity ofYBa2Cu3O7?? (Tc = 95 ± 5K) is examined; this oxide remains orthorhombic up to ? ? 0.6 and becomes tetragonal and nonsuperconducting beyond this value of ?. Oxygen stoichiometry in this and related oxides has to be understood in terms of structure and disorder. The structure of La3?xBa3+xCu6O14 is related to that of YBa2Cu3O7, the orthorhombic structure manifesting itself when the population of O1 oxygens (along the Cusingle bondOsingle bondCu chains) is preponderant compared to that of O5 oxygens (along thea-axis); nearly equal populations of O1 and O5 sites give rise to the tetragonal structure. A transition from a high-Tc (95 K) superconductivity regime to a low-Tc (not, vert, similar60 K) regime occurs in YBa2Cu3O7?? accompanying a change in ?. There is no evidence for Cu3+ in these nominally mixed valent copper oxides. Instead, holes are present on oxygens giving rise to O? or O2?2 species, the concentration of these species increasing with the lowering of temperature. Certain interesting aspects of the superconducting oxides such as domain or twin boundaries, Raman spectra, microwave absorption, and anomalous high-temperature resistivity drops are presented along with the important material parameters. Preparative aspects of the superconducting oxides are briefly discussed. Phase transitions seem to occur atTc as well as at not, vert, similar240 K in YBa2Cu3O7.

Steady-State Stability of Current Mode Active-Clamp ZVS DC-DC Converters

Active-clamp dc-dc converters are pulsewidth-modulated converters having two switches featuring zero-voltage switching at frequencies beyond 100 kHz. Generalized equivalent circuits valid for steady-state and dynamic performance have been proposed for the family of active-clamp converters. The active-clamp converter is analyzed for its dynamic behavior under current control in this paper. The steady-state stability analysis is presented. On account of the lossless damping inherent in the active-clamp converters, it appears that the stability region in the current-controlled active-clamp converters get extended for duty ratios, a little greater than 0.5, unlike in conventional hard-switched converters. The conventional graphical approach fails to assess the stability of current-controlled active-clamp converters due to the coupling between the filter inductor current and resonant inductor current. An analysis that takes into account the presence of the resonant elements is presented to establish the condition for stability. This method correctly predicts the stability of the current-controlled active-clamp converters. A simple expression for the maximum duty cycle for subharmonic free operation is obtained. The results are verified experimentally.

An integer arithmetic method to compute generalized matrix inverse and solve linear equations exactly

An algorithm that uses integer arithmetic is suggested. It transforms anm ×n matrix to a diagonal form (of the structure of Smith Normal Form). Then it computes a reflexive generalized inverse of the matrix exactly and hence solves a system of linear equations error-free.

Structure of 6-acetoxycoumarin: topochemical photodimerization and analysis of acetoxy...acetoxy interactions in the solid state

C~HaO 4, Mr=204.2, monoclinic, P2Jn,a=3.900(1), =37.530(6), c=6.460(1)A, fl=103.7 (1) °, V= 918.5 (5) A 3, Z = 4, D m = 1.443, D x --- 1.476 Mg m -3, Cu Ks, 2 = 1.5418 ,/k, /t = 0.86 mm -~, F(000) = 424, T= 293 K, R = 0.075 for 1019 significant reflections. Molecules pack in fl-type stacking mode which is characterized by the close packing of parallel and nearly planar reactive double bonds with a separation of 3.900/~ along the a axis.The syn head-head dimer obtained is the direct consequence of this packing arrangement. Molecular packing is stabilized by intermolecular C-H...O hydrogen bonding. Analysis of acetoxy...acetoxy interactions in the acetoxy compounds retrieved from the Cambridge Structural Database reveal that the majority of them are anti-dipolar.

Thermodynamics of Cobalt (II, III) Oxide (Co3O4): Evidence of Phase Transition

The Gibbs' energy change for the reaction, 3CoO (r.s.)+1/2O2(g)→Co3O4(sp), has been measured between 730 and 1250 K using a solid state galvanic cell: Pt, CuO+Cu2O|(CaO)ZrO2|CoO+Co3O4,Pt. The emf of this cell varies nonlinearly with temperature between 1075 and 1150 K, indicating a second or higher order phase transition in Co3O4around 1120 (±20) K, associated with an entropy change of ∼43 Jmol-1K-1. The phase transition is accompanied by an anomalous increase in lattice parameter and electrical conductivity. The cubic spinel structure is retained during the transition, which is caused by the change in CO+3 ions from low spin to high spin state. The octahedral site preference energy of CO+3 ion in the high spin state has been evaluated as -24.8 kJ mol-1. This is more positive than the value for CO+2 ion (-32.9 kJ mol-1). The cation distribution therefore changes from normal to inverse side during the phase transition. The transformation is unique, coupling spin unpairing in CO+3 ion with cation rearrangement on the spinel lattice, DTA in pure oxygen revealed a small peak corresponding to the transition, which could be differentiated from the large peak due to decomposition. TGA showed that the stoichiometry of oxide is not significantly altered during the transition. The Gibbs' energy of formation of Co3O4 from CoO and O2 below and above phase transition can be represented by the equations:ΔG0=-205,685+170.79T(±200) J mol-1(730-1080 K) and ΔG0=-157,235+127.53T(±200) J mol-1(1150-1250 K).

Use of the Nasicon/Na2SO4 couple in a solid state sensor for SOx (x=2,3)

The e.m.f. of a concentration cell for SO x (x=2,3)-O2 incorporating Nasicon as the main solid electrolyte has been measured in the temperature range 720 to 1080 K. The cell arrangement can be represented as,$$Pt, O'_2 + SO'_2 + SO'_3 \left| {Na_2 SO_4 \left\| {\left. {Nasicon} \right\|} \right.} \right.\left. {Na_2 SO_4 } \right|SO''_3 + SO''_2 + O''_2 , Pt$$ The Na2SO4 acts both as an auxiliary electrode, converting chemical potentials of SO x and O2 to equivalent sodium potentials, and as an electrolyte. The presence of Na2SO4 provides partial protection of Nasicon from chemical reaction with gas mixtures containing SO x . The open circuit e.m.f. of the cell is in close agreement with values given by the Nernst equation. For certain fixed inlet gas compositions of SO2+O2, the e.m.f. varies non-linearly with temperature. The intrinsic response time of the cell to step changes in gas composition is estimated to vary from sim2.0 ksec at 723K to sim 0.2 ksec at 1077K. The cell functions well for large differences in partial pressures of SO3(pPrimeSO 3/pprimeSO 3ap104) at the electrodes.

A parallel multistep predictor-corrector algorithm for solving ordinary differential equations

In this paper we give a generalized predictor-corrector algorithm for solving ordinary differential equations with specified initial values. The method uses multiple correction steps which can be carried out in parallel with a prediction step. The proposed method gives a larger stability interval compared to the existing parallel predictor-corrector methods. A method has been suggested to implement the algorithm in multiple processor systems with efficient utilization of all the processors.

Polarization Caging in Diffusion-Controlled Electron Transfer Reactions in Solution

In some bimolecular diffusion-controlled electron transfer (ET) reactions such as ion recombination (IR), both solvent polarization relaxation and the mutual diffusion of the reacting ion pair may determine the rate and even the yield of the reaction. However, a full treatment with these two reaction coordinates is a challenging task and has been left mostly unsolved. In this work, we address this problem by developing a dynamic theory by combining the ideas from ET reaction literature and barrierless chemical reactions. Two-dimensional coupled Smoluchowski equations are employed to compute the time evolution of joint probability distribution for the reactant (P-(1)(X,R,t)) and the product (p((2))(X,R,t)), where X, as is usual in ET reactions, describes the solvent polarization coordinate and R is the distance between the reacting ion pair. The reaction is described by a reaction line (sink) which is a function of X and R obtained by imposing a condition of equal energy on the initial and final states of a reacting ion pair. The resulting two-dimensional coupled equations of motion have been solved numerically using an alternate direction implicit (ADI) scheme (Peaceman and Rachford, J. Soc. Ind. Appl. Math. 1955, 3, 28). The results reveal interesting interplay between polarization relaxation and translational dynamics. The following new results have been obtained. (i) For solvents with slow longitudinal polarization relaxation, the escape probability decreases drastically as the polarization relaxation time increases. We attribute this to caging by polarization of the surrounding solvent, As expected, for the solvents having fast polarization relaxation, the escape probability is independent of the polarization relaxation time. (ii) In the slow relaxation limit, there is a significant dependence of escape probability and average rate on the initial solvent polarization, again displaying the effects of polarization caging. Escape probability increases, and the average rate decreases on increasing the initial polarization. Again, in the fast polarization relaxation limit, there is no effect of initial polarization on the escape probability and the average rate of IR. (iii) For normal and barrierless regions the dependence of escape probability and the rate of IR on initial polarization is stronger than in the inverted region. (iv) Because of the involvement of dynamics along R coordinate, the asymmetrical parabolic (that is, non-Marcus) energy gap dependence of the rate is observed.

A generalised cole-hopf transformation for nonlinear parabolic and hyperbolic equations

The Cole-Hopf transformation has been generalized to generate a large class of nonlinear parabolic and hyperbolic equations which are exactly linearizable. These include model equations of exchange processes and turbulence. The methods to solve the corresponding linear equations have also been indicated.La transformation de Cole et de Hopf a été généralisée en vue d'engendrer une classe d'équations nonlinéaires paraboliques et hyperboliques qui peuvent être rendues linéaires de façon exacte. Elles comprennent des équations modèles de procédés d'échange et de turbulence. Les méthodes pour résoudre les équations linéaires correspondantes ont également été indiquées.

Curie-temprature of a spin one xy ferromagnet with uniaxial anisotropy

A spin one XY ferromagnet with uniaxial anisotropy has been investigated, using Green's function technique in random phase approximation (RPA). The Green functions associated with the anisotropy energy are treated without decoupling. A set of coupled equations have been obtained to find the critical temperature Tc and left angle bracket(SZ)2right-pointing angle bracket at Tc as function of the uniaxial anisotropy parameter D. Tc and left angle bracket(SZ)2right-pointing angle bracket at Tc are found to increase with D. The results are compared with the earlier results obtained in the Narath type of RPA.