A transfer function approach to the realisation problem of nonlinear systems

This article studies the nonlinear realisation problem, i.e. the problem of finding the state equations of a nonlinear system from the transfer function representation being easily computable from the higher order input–output differential equation. The realisation in both observer and controller canonical forms is studied. The results demonstrate a clear connection with those from linear theory. In the solution the concept of adjoint polynomials, adjoint transfer function and right factorisation of the transfer function play a key role. Finally, the results are applied for system linearisation up to input–output injection used in the observer design.     

Transformation of Nonlinear MIMO Discrete‐Time Systems into the Extended Observer Form

The paper addresses the problem of transforming discrete‐time multi‐input multi‐output nonlinear state equations into the extended observer form, which, besides the inputs and outputs, also depends on a finite number of their past values. Necessary and sufficient conditions for the existence of the extended coordinate transformation are formulated in terms of differential one‐forms, associated with the input‐output equations, corresponding to the state equations. The difference between the single‐input single‐output and multi‐input multi‐output cases is described. The applicability of the conditions is illustrated by an example.     

Surfactant‐directed morphology of cross‐linked styrene‐ or vinylbenzyl chloride‐based materials

Polystyrene (PSt) or poly(vinylbenzyl chloride) (PVBC) crosslinked with divinylbenzyl (DVB) materials were synthesized through free radical polymerization into templates formed by the surfactant polyoxyethylene (4) lauryl ether (Brij‐30). The chemical composition of the final products was verified through attenuated total reflectance infrared spectroscopy (ATR‐IR) and the thermal behavior was investigated through thermogravimetric analysis (TGA). Depending on the organization of Brij‐30 in aqueous solution, three characteristic structures, namely spherical nanoparticles, platelet‐like objects and three‐dimensional networks, were identified through scanning electron microscopy (SEM) and transmission electron microscopy (TEM). The spherical nanoparticles and the platelet‐like objects form rather stable dispersions, especially in aqueous surfactant solutions, as exemplified by the evolution of the turbidity of the PSt‐based materials, using sodium dodecyl sulfate as surfactant. All materials retain their integrity even after thermal treatment at high temperature (～200–250°C). The benzyl chloride group of the PVBC‐based materials offers a significant potential for further elaboration and practical applications, since they can be further functionalized while retaining their integrity. This potential is demonstrated here through hydrolysis to obtain hydroxyl‐functionalized three‐dimensional networks. © 2015 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2016 , 133, 43297.     

Regioselective combinatorial-type synthesis, characterization, and physical properties of dendronized cellulose

Novel regioselective, homo-(4-6) and heterogeneous (7-10) dendronized cellulose derivatives have been prepared by the reaction of cellulose in a N,N-dimethylacetamide (DMAc)/LiCl solvent system with diverse dendrons (1-3) possessing an isocyanate focal group. The dendronized cellulose derivatives were characterized using Fourier transform infrared (FTIR), ¹³C NMR, thermogravimetric analysis (TGA), and dynamic mechanical thermal analysis (DMTA). These polyfunctionally coated cellulose-based materials showed diverse solubility characteristics in organic solvents ranging from DMAc to methyl alcohol.     

Application of inverse system for linearization and decoupling

We show that for a special class of nonlinear systems the linearization and/or decoupling of nonlinear dynamics by immersion under feedback is in fact an application of the right inverse system.     

Enhanced dissolution and bioavailability of grapefruit flavonoid Naringenin by solid dispersion utilizing fourth generation carrier

Context: Naringenin (NRG), the aglycone flavonoid present in grapefruits, possesses anti-inflammatory, anti-carcinogenic, anti-lipid peroxidation and hepato-protective effects. However, it is poorly soluble in water and exhibits slow dissolution after oral ingestion, thus restricting its therapeutic efficacy.

Objective: With the aim to enhance the dissolution rate and oral bioavailability of NRG, solid dispersion technique has been applied using Soluplus® as carrier.

Methods: Solid dispersions of NRG were prepared by solvent evaporation and kneading methods using various ratios (1:4, 3:7, 2:3 and 1:1) of NRG:Carrier. Characterization of the optimized formulations was performed using Fourier transform infrared spectroscopy, differential scanning calorimetry (DSC) and X-ray diffraction (XRD) analysis. The in vivo behavior of the optimized formulations was also investigated in Wistar Albino rats.

Results: NRG solid dispersion showed a significantly higher solubility and drug dissolution rate than pure NRG (p?Conclusion: Based on these results, it was concluded that solid dispersion technique markedly enhances the in vitro drug release and in vivo behavior of the grapefruit flavonoid NRG.     

Transformation of nonlinear discrete-time system into the extended observer form

The paper addresses the problem of transforming discrete-time single-input single-output nonlinear state equations into the extended observer form, which, besides the input and output, also depends on a finite number of their past values. Necessary and sufficient conditions for the existence of both the extended coordinate and output transformations, solving the problem, are formulated in terms of differential one-forms, associated with the input–output equation, corresponding to the state equations. An algorithm for transformation of state equations into the extended observer form is proposed and illustrated by an example. Moreover, the considered approach is compared with the method of dynamic observer error linearisation, which likewise is intended to enlarge the class of systems transformable into an observer form.     

Fast and robust retrieval of Minkowski sums of rotating convex polyhedra in 3-space

We present a novel method for fast retrieval of exact Minkowski sums of pairs of convex polytopes in R³, where one of the polytopes frequently rotates. The algorithm is based on pre-computing a so-called criticality map, which records the changes in the underlying graph structure of the Minkowski sum of the two polytopes, while one of them rotates. We give tight combinatorial bounds on the complexity of the criticality map when the rotating polytope rotates about one, two, or three axes. The criticality map can be rather large already for rotations about one axis, even for summand polytopes with a moderate number of vertices each. We therefore focus on the restricted case of rotations about a single, though arbitrary, axis.Our work targets applications that require exact collision detection such as motion planning with narrow corridors and assembly maintenance where high accuracy is required. Our implementation handles all degeneracies and produces exact results. It efficiently handles the algebra of exact rotations about an arbitrary axis in R³, and it well balances between preprocessing time and space on the one hand, and query time on the other.We use Cgal arrangements and in particular the support for spherical Gaussian maps to efficiently compute the exact Minkowski sum of two polytopes. We conducted several experiments (i) to verify the correctness of the algorithm and its implementation, and (ii) to compare its efficiency with an alternative (static) exact method. The results are reported.