Algorithms for solving a class of problems of <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript>-optimization of control systems

Problems of synthesis of feedbacks providing H _∞-norm-maximal suppression of disturbances, acting on a linear stationary SISO system with account of limitedness of control resources, are considered. Two methods for solving are proposed. The first one is based on the Nevanlinna-Pick interpolation, and the second one is constructed on the ground of guaranteeing singularities of controllers. Within the framework of these approaches, simple computation algorithms that do not require solving Riccati equations or linear matrix inequalities are generated. The application of the developed algorithms is illustrated by an example.     

Synthesis and modeling of the <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript>-system of magnetic control of the plasma in the tokamak-reactor

The article deals with the development of a two-contour system of magnetic control of the position, current, and shape of the plasma in the tokamak-reactor. The H _∞-theory of control is used for the synthesis of a scalar and a multidimensional feedback controller. The controllers are synthesized on the basis of the multidimensional linear model DINA-L of an object (plasma in the tokamak). The linear model DINA-L is obtained from the nonlinear model implemented by the plasmophysical DINA code for conditions of the international thermonuclear experimental reactor (ITER). The numerical modeling of a closed control system is carried out on the linear DINA-L model and the nonlinear DINA model of an object at disturbances of the type of small disruptions. The modeling results for both of the cases were superimposed on each other, which showed their good coincidence at the acceptable quality of control of the synthesized system.     

Flow of CO<Subscript>2</Subscript>–ethanol and of CO<Subscript>2</Subscript>–methanol in a non-adiabatic microfluidic T-junction at high pressures

In this work, an experimental investigation of the single- and multiphase flows of two sets of fluids, CO₂–ethanol and CO₂–methanol, in a non-adiabatic microfluidic T-junction is presented. The operating conditions ranged from 7 to 18 MPa, and from 294 to 474 K. The feed mass fraction of CO₂ in the mixtures was 0.95 and 0.87, respectively. Under these operating conditions, CO₂ was either in liquid, gas or supercritical state; and the mixtures experienced a miscible single phase or a vapour–liquid equilibrium (VLE), with two separated phases. Taylor, annular and wavy were the two-phase flow regimes obtained in the VLE region. In the single phase region, the observed flows were classified into standard single-phase flows, “pseudo” two-phase flows and local phenomena in the T-junction. Flow regime maps were generated, based on temperature and pressure conditions. Two-phase flow void fractions and several parameters of Taylor flow were analysed. They showed a clear dependency on temperature, but were mostly insensitive to pressure. A continuous accumulation of liquid, either in the CO₂ channel or at the CO₂-side wall after the T-junction, disturbed most of the experiments in VLE conditions by randomly generating liquid plugs. This phenomenon is analysed, and capillary and wetting effects due to local Marangoni stresses are suggested as possible causes.     

Design of discrete ℋ<Subscript>2</Subscript>-optimal reduced-order controllers

Consideration was given to the design of discrete dynamic reduced-order controllers minimizing the ℋ₂-norm of the transfer matrix of a closed-loop system. The problem of reducing the controller order is related to the solution of the singular problem of filtration (no measurement noise) and control (no control at the controlled output). Using the well-known structures of controllers based on the corresponding minimum-order observers, these problems were shown to be reducible to the solution of two Riccati equations of which one is of a reduced order. Peculiarities of solution that are characteristic of the digital controllers and caused by the allowance for astatism and presence of control delays were examined. An example of an ℋ₂-optimal reduced-order controller was presented to illustrate the results obtained.     

Boundary control of string vibrations that minimizes the integral of power <Emphasis Type="Italic">p</Emphasis> ⩾ 1 of the module of control or its derivative

In terms of the generalized solution to a wave equation for different boundary conditions, integral minimization of the module of the boundary control, raised to an arbitrary power p ? 1, or its derivative is conducted.     

Design of robust <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript>-controllers of multivariable systems based on the given stability degree

For the linear multivariable plants whose physical parameters are subject to deviations from the rated values, the measurable output-based controllers were designed providing the given degree of stability of the closed-loop system which defines the desired time of control. This approach relies on the “technique of opening the plant-controller system” for the investigated physical parameters and comes to a standard problem of H _∞-optimization. An example was presented.     

Representation of ℤ<Subscript>4</Subscript>-Linear Preparata Codes Using Vector Fields

A binary code is called ℤ₄-linear if its quaternary Gray map preimage is linear. We show that the set of all quaternary linear Preparata codes of length n = 2^m, m odd, m ≥ 3, is nothing more than the set of codes of the form with

On ℤ<Subscript>4</Subscript>-linear codes with the parameters of Reed-Muller codes

For any pair of integers r and m, 0 ≤ r ≤ m, we construct a class of quaternary linear codes whose binary images under the Gray map are codes with the parameters of the classical rth-order Reed-Muller code RM(r, m).     

Structural,optical and electrical properties of Cu<Subscript>2</Subscript>Zn<Subscript>1−x</Subscript>Cd<Subscript>x</Subscript>SnS<Subscript>4</Subscript> quinternary alloys nanostructures deposited on porous silicon

The Cu₂Zn_1?xCd_xSnS₄ quinternary alloy nanostructures with different Cd contents were grown using spin coating technique on porous silicon (63.93 %) substrate. The structural properties of Cu₂Zn_1?xCd_xSnS₄/PS were investigated by X-ray diffraction and field emission-scanning electron microscope (FE-SEM). The optical properties studied through photoluminescence technique, indicated that the band gap is shifted as Cd content increases from 1.84 eV at x = 0 to 1.76 eV at x = 1. The electrical characterization of the Ag/n-PS/Cu₂Zn_1?xCd_xSnS₄/Ag diode through current to voltage (I–V) characterization shows the highest photo-response of (value if any) at Cu₂Zn_0.4Cd_0.6SnS₄ composition.     

Generalized <Emphasis Type="Italic">H</Emphasis> <Subscript>∞</Subscript>-optimal control of continuous-discrete linear plant

For the linear continuous nonstationary plants whose states are measured at fixed time instants, the notion of perturbation damping level was introduced as an index of joint impact of the initial and external perturbations on the worst-case objective output and terminal state. The H_∞-optimal laws of control were formulated as the state feedbacks minimizing the level of feedback damping of the closed-loop system.     

Multidimensional system of cascaded control of plasma form and current in tokamak with channel decoupling and <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript>-controller

Consideration was given to the development and numerical modeling of the multidimensional cascaded system with H _∞-controller in the external cascade for control of the plasma form and current in tokamak. For controller design, the problem of mixed sensitivity was solved by selecting the weight functions in the composite matrix of the performance criterion. The internal loop was intended for decoupling the current control channels in the magnetic coils of the tokamak poloidal fields and following the given scenario currents. Linearized models obtained from the nonlinear plasma-physical DINA code by linearizing the ITER scenario at different points were used to design the controllers. The robust stability margin was estimated in the frequency domain using singular numbers of the matrix transfer functions of the closed-loop control system. The designed cascaded system was modeled in the DINA code.     

Robust stabilizing regions of fractional-order PI<Superscript>λ</Superscript> controllers for fractional-order systems with time-delays

This study focuses on a graphical approach to determine the stabilizing regions of fractional-order PI^λ(proportional integration) controllers for fractional-order systems with time-delays. By D-decomposition technique, the existence conditions and calculating methods of the real root boundary (RRB) curves, complex root boundary (CRB) curves and infinite root boundary (IRB) lines are investigated for a given stability degree. The stabilizing regions in terms of the RRB curves, CRB curves and IRB lines are identified by the proposed criteria in this paper. Finally, two illustrative examples are given to verify the effectiveness of this graphical approach for different stability degrees.     

Robust finite-time <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> control of stochastic jump systems

This paper provides the stochastic finite-time stabilization and H _∞ control problem of Markov jump systems with norm-bounded uncertainties and state delays that possess randomly jumping parameters. The transition of the jumping parameters is governed by a finite-state Markov process. The finite-time H _∞ controller via state feedback is provided to guarantee the stochastic finite-time bounded-ness and stochastic finite-time stabilization of the resulting closed-loop system for all admissible uncertainties and unknown time-delays. The control criterion is formulated in the form of linear matrix inequalities and the designed finite-time stabilization controller is described as an optimization one. Simulation results illustrate the effectiveness of the developed approaches.     

Difficult Configurations—On the Complexity of <Emphasis Type="Italic">LTrL</Emphasis>

The complexity of LTrL, a global linear time temporal logic over traces is investigated. The logic is global because the truth of a formula is evaluated in a global state, also called configuration. The logic is shown to be non-elementary with the main reason for this complexity being the nesting of until operators in formulas. The fragment of the logic without the until operator is shown to be EXPSPACE-hard.Supported by Polish KBN grant No. 8 T11C 002 11.     

The future of information systems – <Emphasis Type="Italic">Thinking Informatically</Emphasis>

Many of those who are active within the academic field of information systems (IS) are constantly seeking a firm disciplinary basis for their endeavours. In many respects, such efforts are based upon a mistaken view of how disciplines are actually constituted, and the purposes that they serve. In many respects, it would be far more fruitful if those working within the field of IS were to accept a more fluid and contingent notion of a discipline; simultaneously recognizing the contested nature of many of the core concepts – particularly information, communication and technology. In so doing, we will be Thinking Informatically.     

Space–time <Emphasis Type="Italic">hp</Emphasis>-approximation of parabolic equations

A new space–time finite element method for the solution of parabolic partial differential equations is introduced. In a mesh and degree-dependent norm, it is first shown that the discrete bilinear form for the space–time problem is both coercive and continuous, yielding existence and uniqueness of the associated discrete solution. In a second step, error estimates in this mesh-dependent norm are derived. In particular, we show that combining low-order elements for the space variable together with an hp-approximation of the problem with respect to the temporal variable allows us to decrease the optimal convergence rates for the approximation of elliptic problems only by a logarithmic factor. For simultaneous space–time hp-discretization in both, the spatial as well as the temporal variable, overall exponential convergence in mesh-degree dependent norms on the space–time cylinder is proved, under analytic regularity assumptions on the solution with respect to the spatial variable. Numerical results for linear model problems confirming exponential convergence are presented.     

Theory of truth degrees of formulas in Łukasiewicz<Emphasis Type="Italic">n</Emphasis>-valued propositional logic and a limit theorem

The concept of truth degrees of formulas in Łukasiewiczn-valued propositional logicL _n is proposed. A limit theorem is obtained, which says that the truth functionτ _n induced by truth degrees converges to the integrated truth functionτ whenn converges to infinite. Hence this limit theorem builds a bridge between the discrete valued Łukasiewicz logic and the continuous valued Łukasiewicz logic. Moreover, the results obtained in the present paper is a natural generalization of the corresponding results obtained in two-valued propositional logic.     

Theory and Software Implementations of Shor’s <Emphasis Type="Italic">r</Emphasis>-Algorithms<Superscript>*</Superscript>

Three computational forms of r-algorithms with different amount of computation per iteration are considered. The results on the convergence of the limit variant of r-algorithms for convex smooth functions and the r _μ (α)-algorithm for convex piecewise smooth functions are presented. Practical aspects of the variant of r (α)-algorithms with a constant coefficient of space dilation α and an adaptive method for step adjustment in the direction of the normalized anti-subgradient in the transformed space of variables are discussed.