Linear quadratic game and non-cooperative predictive methods for potential application to modelling driver-AFS interactive steering control

This paper is concerned with the modelling of strategic interactions between the human driver and the vehicle active front steering (AFS) controller in a path-following task where the two controllers hold different target paths. The work is aimed at extending the use of mathematical models in representing driver steering behaviour in complicated driving situations. Two game theoretic approaches, namely linear quadratic game and non-cooperative model predictive control (non-cooperative MPC), are used for developing the driver-AFS interactive steering control model. For each approach, the open-loop Nash steering control solution is derived; the influences of the path-following weights, preview and control horizons, driver time delay and arm neuromuscular system (NMS) dynamics are investigated, and the CPU time consumed is recorded. It is found that the two approaches give identical time histories as well as control gains, while the non-cooperative MPC method uses much less CPU time. Specifically, it is observed that the introduction of weight on the integral of vehicle lateral displacement error helps to eliminate the steady-state path-following error; the increase in preview horizon and NMS natural frequency and the decline in time delay and NMS damping ratio improve the path-following accuracy. © 2013 Copyright Taylor and Francis Group, LLC.

Self-assembled multilayer graphene oxide membrane and carbon nanotubes synthesized using a rare form of natural graphite

The fabrication of flexible multilayer graphene oxide (GO) membrane and carbon nanotubes (CNTs) using a rare form of high-purity natural graphite, vein graphite, is reported for the first time. Graphite oxide is synthesized using vein graphite following Hummer's method. By facilitating functionalized graphene sheets in graphite oxide to self-assemble, a multilayer GO membrane is fabricated. Electric arc discharge is used to synthesis CNTs from vein graphite. Both multilayer GO membrane and CNTs are investigated using microscopy and spectroscopy experiments, i.e., scanning electron microscopy (SEM), atomic force microscopy (AFM), high-resolution transmission electron microscopy (HRTEM), Fourier transform infrared spectroscopy (FTIR), X-ray diffraction (XRD), thermogravimetric analysis (TGA), core level photoelectron spectroscopy, and C K-edge X-ray absorption spectroscopy (NEXAFS), to characterize their structural and topographical properties. Characterization of vein graphite using different techniques reveals that it has a large number of crystallites, hence the large number of graphene sheets per crystallite, preferentially oriented along the (002) plane. NEXAFS and core level spectra confirm that vein graphite is highly crystalline and pure. Fourier transform infrared (FT-IR) and C 1s core level spectra show that oxygen functionalities (-C-OH, -CO,-C-O-C-) are introduced into the basal plane of graphite following chemical oxidation. Carbon nanotubes are produced from vein graphite through arc discharge without the use of any catalyst. HRTEM confirm that multiwalled carbon nanotube (MWNTs) are produced with the presence of some structure in the central pipe. A small percentage of single-walled nanotubes (SWNTs) are also produced simultaneously with MWNTs. Spectroscopic and microscopic data are further discussed here with a view to using vein graphite as the source material for the synthesis of carbon nanomaterials. © 2013 American Chemical Society.

A new approach to the analytical and numerical form-finding of tensegrity structures

We develop a new formulation for the form-finding of tensegrity structures in which the primary variables are the Cartesian components of element lengths. Both an analytical and a numerical implementation of the formulation are described; each require a description of the connectivity of the tensegrity, with the iterative numerical method also requiring a random starting vector of member force densities. The analytical and numerical form-finding of tensegrity structures is demonstrated through six examples, and the results obtained are compared and contrasted with those available in the literature to verify the accuracy and viability of the suggested methods. © 2013 Elsevier Ltd. All rights reserved.

Unified form language: A domain-specific language for weak formulations of partial differential equations

We present the Unified Form Language (UFL), which is a domain-specific language for representing weak formulations of partial differential equations with a view to numerical approximation. Features of UFL include support for variational forms and functionals, automatic differentiation of forms and expressions, arbitrary function space hierarchies formultifield problems, general differential operators and flexible tensor algebra. With these features, UFL has been used to effortlessly express finite element methods for complex systems of partial differential equations in near-mathematical notation, resulting in compact, intuitive and readable programs. We present in this work the language and its construction. An implementation of UFL is freely available as an open-source software library. The library generates abstract syntax tree representations of variational problems, which are used by other software libraries to generate concrete low-level implementations. Some application examples are presented and libraries that support UFL are highlighted. © 2014 ACM.