Determination of optimal feedback terminal controllers for general boundary conditions using generating functions

Given a nonlinear system and a performance index to be minimized, we present a general approach to expressing the finite time optimal feedback control law applicable to different types of boundary conditions. Starting from the necessary conditions for optimality represented by a Hamiltonian system, we solve the Hamilton-Jacobi equation for a generating function for a specific canonical transformation. This enables us to obtain the optimal feedback control for fundamentally different sets of boundary conditions only using a series of algebraic manipulations and partial differentiations. Furthermore, the proposed approach reveals an insight that the optimal cost functions for a given dynamical system can be decomposed into a single generating function that is only a function of the dynamics plus a term representing the boundary conditions. This result is formalized as a theorem. The whole procedure provides an advantage over methods rooted in dynamic programming, which require one to solve the Hamilton-Jacobi-Bellman equation repetitively for each type of boundary condition. The cost of this favorable versatility is doubling the dimension of the partial differential equation to be solved.     

A disposable sensor based on immobilization of acetylcholinesterase to multiwall carbon nanotube modified screen-printed electrode for determination of carbaryl

A simple method has been devised for immobilization of acetylcholinesterase (AChE) covalent bonding to a multiwall carbon nanotube (MWNT)-cross-linked cellulose acetate composite on a screen-printed carbon electrode (SPCE) and a sensitive and disposable amperometric sensor for rapid determination of carbaryl pesticide is proposed. The immobilized enzyme was preserved on this film because of the excellent biocompatibility and non-toxicity of cellulose acetate. Based on the inherent conductive properties of the MWNT, the immobilized AChE had greater affinity for ATCl and excellent catalytic effect in the hydrolysis of ATCl. MWNT improved the interface enzymatic hydrolysis reaction and increased the amperometric response of the sensor. Under optimum conditions, the inhibition of carbaryl on AChE increased linearly with the increasing concentration of carbaryl in two ranges, from 0.01 to 0.5 μg mL⁻¹ and from 2 to 20 μg mL⁻¹, with the correlation coefficients of 0.9985 and 0.9977, respectively. The detection limit was 0.004 μg mL⁻¹ taken as the concentration equivalent to 10% decrease in signal. The sensor showed acceptable stability, accuracy and could be fabricated in batches, thus it is economic and portable. This type of disposable enzyme-based amperometric sensor has extensive application potential in environmental monitoring of pesticides.     

Synthesis and characterization of a novel proton‐exchange membrane for fuel cells operating at high temperatures and low humidities

The synthesis of a p‐toluidine/formaldehyde (PTF) resin was performed, and the effects of the molar ratio of the individual monomers and the polymerization conditions on the structure of the PTF resin were studied. Fourier transform infrared and ¹³C‐NMR spectra were used to characterize the PTF. Wide‐angle X‐ray diffraction patterns revealed the crystalline structures of various PTFs. Polarized optical microscopy revealed that the molar ratio of the monomers had a strong effect on the crystalline morphologies. A longer polymerization time turned out a polymer with a higher intrinsic viscosity and molecular weight, which led to differences in the proton conductivity. All of the PTFs showed a higher proton conductivity than a commercial Nafion membrane at 90–100°C and 0% relative humidity. The proton conductivity of the PTF series could be improved by sulfonation with sulfuric acid and could be maintained after blending with polyurethane. Pure methanol could be used as a fuel source because of the insolubility and nonwetting properties of PTF in methanol to increase the output current density for a PTF membrane electrode assembly. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci 2008     

Synthesis and applications of heterobifunctional poly(ethylene oxide) oligomers

Poly(ethylene oxide) (PEO) oligomers are employed extensively in pharmaceutical and biomedical arenas mainly due to their excellent physical and biological properties, including solubility in water and organic solvents, lack of toxicity, and absence of immunogenicity. PEO can be chemically modified and reacted with, or adsorbed onto, other molecules and surfaces. Sophisticated applications for PEO have increased the demand for PEO oligomers with tailored functionalities, and heterobifunctional PEOs are often needed. This review discusses the synthesis and applications of heterobifunctional PEO oligomers possessing amine, carboxylate, thiol, and maleimide functional groups.     

Modeling Multiterminal Spintronic Devices

We are encountering tremendous opportunities and challenges in combining emerging nanotechnology for developing nanoelectronic devices. Researchers are designing nanoelectronic circuits based on newly discovered nanoscale building blocks, such as spintronic devices. In this paper, we calculate conductance in spintronic gates using the nonequilibrium Green's function and show useful operations for "multiterminal" logic gates. These spintronic devices can be used to design complicated spin circuits     

Stability analysis of network-based cooperative resource allocation strategies

Resource allocation involves deciding how to divide a resource of limited availability among multiple demands in a way that optimizes current objectives. In this brief paper we focus on one type of distributed resource allocation problem where via an imperfect communication network multiple processors can share the load presented by multiple task types. We introduce asynchronous “cooperative” resource allocation strategies, and show that they lead to a bounded cumulative demand.     

Nonpathological Lyapunov functions and discontinuous Carathéodory systems

Differential equations with discontinuous right-hand side and solutions intended in Carathéodory sense are considered. For these equations, sufficient conditions which guarantee both Lyapunov stability and asymptotic stability in terms of nonsmooth Lyapunov functions are given. An invariance principle is also proven.