Robustly complete synthesis of sampled-data control for continuous-time nonlinear systems with reach-and-stay objectives

Formal methods are becoming favorable for control and verification of safety-critical systems because of the rigorous model-based computation. Relying on an over-approximated model of the original system behaviors, formal control synthesis algorithms are not often complete, which means that a controller cannot necessarily be synthesized even if there exists one. The main result of this paper shows that, for continuous-time nonlinear systems, a sample-and-hold control strategy for a reach-and-stay specification can be synthesized whenever such a strategy exists for the same system with its dynamics perturbed by small disturbances. Control synthesis is carried out by a fixed-point algorithm that adaptively partitions the system state space into a finite number of cells. In each iteration, the reachable set from each cell after one sampling time is over-approximated within a precision determined by the bound of the disturbances. To meet such a requirement, we integrate validated high-order Taylor expansion of the system solution over one sampling period into every fixed-point iteration and provide a criterion for choosing the Taylor order and the partition precision. Two nonlinear system examples are given to illustrate the effectiveness of the proposed method.     

Preparation and characterization of theβ-cyclodextrin inclusion complex with sulfafurazole

The 1 : 1 inclusion complex involving sulfafurazole (SF) and-cyclodextrin (-CD) is prepared by the freeze-drying method and characterized on the basis of its chemical analysis, thermal behavior, infrared spectrum, X-ray powder pattern and¹³C NMR spectrum in DMSO-d₆ solution. The stability constant of the inclusion complex was determined by the solubility method. The effect of cyclodextrin on the UV absorption spectrum of sulfafurazole was also observed.     

Carbocyclic and nitrogen-containing fused CH-acids with an annelated indenyl fragment. Thermogravimetric and X-ray structural analysis of 6H-indeno[1,2-b]quinoline

Based on thermogravimetric characteristics first obtained for the model 6H-indeno [1,2-b]quinoline, the scheme of thermal conversions of this compound in the temperature range 20–700 °C has been proposed, and the limit of its thermal stability (300 °C) has been determined. This temperature is recommended as the optimum for synthesizing fused benzoaza(diaza)fluorenes. Based on the results of X-ray structural analysis, the molecules of the studied indenoquinoline form centrosymmetric pairs, which are arranged in (110) layers. The molecules are orientationally disordered. The observed self-association of these molecules is similar to the - association of fused heterocyclic systems with-excessive and ****- deficient fragments. It has been suggested that interferon-inducing and antitumor compounds with an annelated indenyl fragment have a common mechanism of action according to the intercalation model of stacking structures.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 4, pp. 703–709, April, 1995.     

Synthesis,spectroscopic studies,and x-ray crystallographic analysis of the organotin carbohydrate: 1,2∶3,4-di-O-isopropylidene-6-O-triphenylstannylmethyl-α-D-galactopyranose

The title organotin carbohydrate, C₃₁H₃₆O₆Sn, has been synthesized and its molecular structure has been determined in solution and in the solid state. NMR, infrared, mass and X-ray crystallographic techniques were used. The chiral molecules crystallize in the monoclinic space group P2₁ withZ=2. The triphenyltin and carbohydrate moieties are linked by a trans methylene-oxygen-methylene arrangement. The pyranosyl ring adopts a twist-boat conformation and the isopropylidene rings adopt different (half-chair and envelope) forms. Solution and solid-state conformations are similar as only three ¹³C shift values are greater than 2ppm; the ¹¹⁹Sn value is 12 ppm.     

Finding normal solutions in piecewise linear programming

Letf: ⁿ (–, ] be a convex polyhedral function. We show that if any standard active set method for quadratic programming (QP) findsx(t)= arg min _x ¦x¦²/2+t f(x) for somet> 0, then its final working set defines a simple equality QP subproblem, whose Lagrange multiplier can be used both for testing ift is large enough forx(t) to coincide with the normal minimizer off, and for increasingt otherwise. The QP subproblem may easily be solved via the matrix factorizations used for findingx(t). This opens up the way for efficient implementations. We also give finite methods for computing the whole trajectory {x(t)} _t 0, minimizingf over an ellipsoid, and choosing penalty parameters inL ₁QP methods for strictly convex QP.This research was supported by the State Committee for Scientific Research under Grant 8S50502206.     

Sampled-data minimumH ∞-norm regulation of linear continuous-time systems using multirate-output controllers

This paper deals with the problem of designing multirate-output contrlleers for sampled-dataH -optimal control of linear continuous-time systems. Two formulations of the problem are studied. In the first, the intersample behavior of the disturbance and the controlled output signals is not considered, whereas in the second the continuous-time nature of these signals is taken into account. It is shown that, in both cases and unter appropriate conditions, it is plausible to reduce the repective initial problem to an associated discrete-timeH -optimization problem for which a fictitious static state feedback controller is to be designed. This fact has a beneficial influence on the theoretical and numerical complexity of the problem, since only one algebraic Riccati equation is to be solved here, as compared to two algebraic Riccati equations needed in known techniques concerning theH -optimization problem with dynamic measurement feedback.The work described in this paper has been partially funded by the General Secretariat for Research and Technology of the Greek Ministry of Industry, Research, and Technology and by the Heracles General Cement Company of Greece.     

Precise bounds for the petersen time-varying real parameter uncertainty system stabilized via linear static controllers

Using a class of linear static controllers, we stabilize the Petersen open-loop two-dimensional linear system (Ref. 1), which consists of one time-varying uncertainty in the state matrixA and one timevarying uncertainty in the input matrixB. We show that the worst-case uncertainty strategy for the closed-loop system is a piecewise constant strategy of the angular state with three switches on the half-turn, –/2/2; it is unique with respect to a set of measure zero. Formulas are derived for the worst-case half-turn radius gainr _HT as a function of the parameters of the class of stabilizing linear static controllers. Using the class of scalar-quadratic Lyapunov functions, we show that a necessary and sufficient condition for the closed-loop system to be robustly stable against all time-varying admissible uncertainties is thatr _HT be less than unity. The bound on the time-varying real parameter uncertainties for the closed-loop system to be robustly stable is derived for the class of linear static feedback controllers. We obtain stabilizing linear static controllers such that the bound is as close to infinity as desired. The derived results are compared with numerical results obtained using commerical robust-control software.     

Products and transforms of white-noise functionals (in general setting)

Some sharp results about Weiner and Wick products of whitenoise functionals are obtained. Using the inequality of Wick products we show to what extent scaling transformations, translations, and Sobolev differentiations can be performed on white-noise functionals.This work was supported by the National Natural Science Foundation of China. This paper is an enlargement and revised version of the paper entitled Products and Transforms of White-Noise Functionals (preprint, 1990).     

LOWLAD: a locally weightedL 1 smoothing spline algorithm with cross validated choice of smoothing parameters

The computation ofL ₁ smoothing splines on large data sets is often desirable, but computationally infeasible. A locally weighted, LAD smoothing spline based smoother is suggested, and preliminary results will be discussed. Specifically, one can seek smoothing splines in the spacesW _m (D), with [0, 1] ⁿ D. We assume data of the formy _i =f(t _i )+ _i ,i=1,..., N with {t _i } _i=1 ^N D, the _i are errors withE( _i )=0, andf is assumed to be inW _m . An LAD smoothing spline is the solution,s , of the following optimization problem

Residual stress/strain analysis in thin films by X-ray diffraction

Residual stresses are found in the majority of multilayer thin film structures used in modem technology. The measurement and modeling of such stress fields and the elucidation of their effects on structural reliability and device operation have been a “growth area” in the literature, with contributions from authors in various scientific and engineering disciplines.

In this article the measurement of the residual stresses in thin film structures with X-ray diffraction techniques is reviewed and the interpretation of such data and their relationship to mechanical reliability concerns are discussed.