Fast finite-time consensus of a class of high-order uncertain nonlinear systems

This paper poses and solves a new problem of consensus control where the task is to make the fixed-topology multi-agent network, with each agent described by an uncertain nonlinear system in chained form, to reach consensus in a fast finite time. Our development starts with a set of new sliding mode surfaces. It is proven that, on these sliding mode surfaces, consensus can be achieved if the communication graph has the proposed directed spanning tree. Next, we introduce the multi-surface sliding mode control to drive the sliding variables to the sliding mode surfaces in a fast finite time. The control Lyapunov function for fast finite time stability, motivated by the fast terminal sliding mode control, is used to prove the reachability of the sliding mode surface. A recursive design procedure is provided, which guarantees the boundedness of the control input.

Existence and design of reduced-order scalar functional observers

In the existing literature, the existence conditions and design procedures for scalar functional observers are available for the cases where the observers’ order p is either p=1 or p=(v-1), where v is the observability index of the matrix pair (C,A). Therefore, if an observer with an order p=1 does not exist, the other option is to use a high-order observer with p=(v-1). This paper provides the existence conditions and a design procedure for scalar functional observers of order 0≤p≤2, and demonstrates the presented results with a numerical example. where K, M, E, H and G are constant matrices to be designed. The problem of observing a scalar functional or multi functionals (z(t)∈Rk , k>1) of the state vector has been the subject of numerous papers, and different algorithms have been proposed (see, [1]-[13] and references therein). There are also papers that deal with the order reduction of multi-dimensional functional observers [9,10,12,13]. For scalar functional observers, a well-known Luenberger’s classic result [1] provides an upper bound on the order with p=(v-1). It is interesting to note here that, except for a recent result of Darouach [12,13], little results have been reported on the order reduction for scalar functional observers.

A fault detection scheme for time-delay systems using minimum-order functional observers

This paper presents a method for designing residual generators using minimum-order functional observers to detect actuator and component faults in time-delay systems. Existence conditions of the residual generators and functional observers are first derived, and then based on a parametric approach to the solution of a generalized Sylvester matrix equation, we develop systematic procedures for designing minimum-order functional observers to detect faults in the system. The advantages of having minimum-order observers are obvious from the economical and practical points of view as cost saving and simplicity can be achieved, particularly when dealing with high-order complex systems. Extensive numerical examples are given to illustrate the proposed fault detection scheme. In all the numerical examples, we design minimum-order residual generators and functional observers to detect faults in the system.

Minimal-order functional observer-based residual generators for fault detection and isolation of dynamical systems

This paper examines the design of minimal-order residual generators for the purpose of detecting and isolating actuator and/or component faults in dynamical systems. We first derive existence conditions and design residual generators using only first-order observers to detect and identify the faults. When the first-order functional observers do not exist, then based on a parametric approach to the solution of a generalized Sylvester matrix equation, we develop systematic procedures for designing residual generators utilizing minimal-order functional observers. Our design approach gives lower-order residual generators than existing results in the literature. The advantages for having such lower-order residual generators are obvious from the economical and practical points of view as cost saving and simplicity in implementation can be achieved, particularly when dealing with high-order complex systems. Numerical examples are given to illustrate the proposed fault detection and isolation schemes. In all of the numerical examples, we design minimum-order residual generators to effectively detect and isolate actuator and/or component faults in the system.

On rapid vector alignment in permanent magnet brushless motor

A software replacement for the commutation signals of a permanent magnet brushless motor is presented. The feedback observed acceleration loop or equivalently the high-order position polynomial controller allows finding the initial relative orientation between the two magnetic fields of the motors within a fraction of a second. Also, using the proposed method allows a considerable cost saving, since the transducer that is usually used for this purpose can be eliminated. The cost saving is most obvious in the case of linear motors and angle motors with large diameters. The way the problem is posed is an essential part of this work and it is the reason behind the apparent simplicity of the solution. The method has been tested when a relative encoder was used and the motor current was regulated.

China's defence industries : change and continuity

Asia looks and feels very different now compared to the days of the Cold War. The sense that Asia now works differently can be traced to a single source – the re-emergence of China. China was the dominant power in greater Asia for most of recorded history. This historical norm was interrupted from the early 19th century, too far into the past to be recognisable and readily accommodated by the actors in today’s international arena. A powerful China feels new and unfamiliar.

Arriving peacefully at mutually acceptable relationships of power and influence that are very different from those that have prevailed for the past half century will be a demanding process. The world’s track record on challenges of this kind is not terrific. It will call for statesmanship of a consistently high order from all the major players, and building the strongest possible confidence among these players that there are no hidden agendas.

Towards prefabricated sustainable housing - an introduction

Prefabricated building systems are once again gaining popularity. The new prefabricated paradigm offers the integration of several approaches previously ignored: automated manufacturing, integrated building services and environmental sustainable principles. Consistency, predictable environmental control, modular flexibility, quick assembly and affordability are promising features of modern manufactured construction. Though the concept of prefabricated building is not new, this type of construction may be the only hope in obtaining a truely sustainable architecture for our future.

This paper attempts to define and evaluate several prefabricated building systems, ranging from a ‘kit-of-parts’ to fully assembled ‘volumetric’ modules. It aims to categorise various manufactured types among a vast amount of information, and to observe their attributes regarding materials, flexibility, structural integrity, delivery and constructability. This paper suggests that pre-fabricated architecture can deliver high order design and diversity within the framework of waste reduction, renewable systems integration and optimal performance.

Adaptive data based neural network leader-follower control of multi-agent networks

In this paper, we propose a data based neural network leader-follower control for multi-agent networks where each agent is described by a class of high-order uncertain nonlinear systems with input perturbation. The control laws are developed using multiple-surface sliding control technique. In particular, novel set of sliding variables are proposed to guarantee leader-follower consensus on the sliding surfaces. Novel switching is proposed to overcome the unavailability of instantaneous control output from the neighbor. By utilizing RBF neural network and Fourier series to approximate the unknown functions, leader-follower consensus can be reached, under the condition that the dynamic equations of all agents are unknown. An O(n) data based algorithm is developed, using only the network’s measurable input/output data to generate the distributed virtual control laws. Simulation results demonstrate the effectiveness of the approach.

Computable social patterns from sparse sensor data

We present a computational framework to automatically discover high-order temporal social patterns from very noisy and sparse location data. We introduce the concept of social footprint and present a method to construct a codebook, enabling the transformation of raw sensor data into a collection of social pages. Each page captures social activities of a user over regular time period, and represented as a sequence of encoded footprints. Computable patterns are then defined as repeated structures found in these sequences. To do so, we appeal to modeling tools in document analysis and propose a Latent Social theme Dirichlet Allocation (LSDA) model - a version of the Ngram topic model in [6] with extra modeling of personal context. This model can be viewed as a Bayesian clustering method, jointly discovering temporal collocation of footprints and exploiting statistical strength across social pages, to automatically discovery high-order patterns. Alternatively, it can be viewed as a dimensionality reduction method where the reduced latent space can be interpreted as the hidden social 'theme' - a more abstract perception of user's daily activities. Applying this framework to a real-world noisy dataset collected over 1.5 years, we show that many useful and interesting patterns can be computed. Interpretable social themes can also be deduced from the discovered patterns.

Image reconstruction using Loop subdivision

It is an ultimate objective to reconstruct an image with high quality using a compact representation, which is the basic step in image-manipulation fields. We propose an effective vectorization based approach to reconstruct an image using a triangular mesh associated with Loop subdivision scheme in the present paper. With an initial control mesh obtained by simplifying a dense mesh from a quality-preserved triangulation, we produce the final optimal control mesh by optimizing a mesh over topologies and colors to approximate the given image. The main advantages of the approach include: (1) the reconstruction of an image is not restricted to be aligned with image coordinate axes; (2) a high order continuous function is defined over a triangle instead of a bilinear interpolation; (3) it is a compact and vector-based representation easy to edit and transmit. Experimental results are presented to confirm the effectiveness of the method. Comparisons with the bi-cubic spline and the mesh simplification methods demonstrate the merits of our method in reconstruction quality and representation size.

Adaptive fast finite-time multiple-surface sliding control for a class of uncertain non-linear systems

This paper concerns the adaptive fast finite-time multiple-surface sliding control (AFFTMSSC) problem for a class of high-order uncertain non-linear systems of which the upper bounds of the system uncertainties are unknown. By using the fast control Lyapunov function and the method of so-called adding a power integrator merging with adaptive technique, a recursive design procedure is provided, which guarantees the fast finite-time stability of the closed-loop system. Further, it is proved that the control input is bounded.

In vivo chromatic aberration in eyes implanted with intraocular lenses

Purpose. To measure in vivo and objectively the monochromatic aberrations at different wavelengths, and the chromatic difference of focus between green and infrared wavelengths in eyes implanted with two models of intraocular lenses (IOL).


Methods. Eighteen eyes participated in this study: nine implanted with Tecnis ZB99 1-Piece acrylic IOL and nine implanted with AcrySof SN60WF IOL. A custom-developed laser ray tracing (LRT) aberrometer was used to measure the optical aberrations, at 532 nm and 785 nm wavelengths. The monochromatic wave aberrations were described using a fifth-order Zernike polynomial expansion. The chromatic difference of focus was estimated as the difference between the equivalent spherical errors corresponding to each wavelength.


Results. Wave aberration measurements were highly reproducible. Except for the defocus term, no significant differences in high order aberrations (HOA) were found between wavelengths. The average chromatic difference of focus was 0.46 ± 0.15 diopters (D) in the Tecnis group, and 0.75 ± 0.12 D in the AcrySof group, and the difference was statistically significant (P < 0.05). Chromatic difference of focus in the AcrySof group was not statistically significantly different from the Longitudinal chromatic aberration (LCA) previously reported in a phakic population (0.78 ± 0.16 D). The impact of LCA on retinal image quality (measured in terms of Strehl ratio) was drastically reduced when considering HOA and astigmatism in comparison with a diffraction-limited eye, yielding the differences in retinal image quality between Tecnis and AcrySof IOLs not significant.


Conclusions. LRT aberrometry at different wavelengths is a reproducible technique to evaluate the chromatic difference of focus objectively in eyes implanted with IOLs. Replacement of the crystalline lens by the IOL did not increase chromatic difference of focus above that of phakic eyes in any of the groups. The AcrySof group showed chromatic difference of focus values very similar to physiological values in young eyes.

Grain boundary segregation in Fe-Mn-C twinning-induced plasticity steels studied by correlative electron backscatter diffraction and atom probe tomography

We report on the characterization of grain boundary (GB) segregation in an Fe-28Mn-0.3C (wt.%) twinning-induced plasticity (TWIP) steel. After recrystallization of this steel for 24 h at 700 °C, ∼50% general grain boundaries (GBs) and ∼35% Σ3 annealing twin boundaries were observed (others were high-order Σ and low-angle GBs). The segregation of B, C and P and traces of Si and Cu were detected at the general GB by atom probe tomography (APT) and quantified using ladder diagrams. In the case of the Σ3 coherent annealing twin, it was necessary to first locate the position of the boundary by density analysis of the atom probe data, then small amounts of B, Si and P segregation and, surprisingly, depletion of C were detected. The concentration of Mn was constant across the interface for both boundary types. The depletion of C at the annealing twin is explained by a local change in the stacking sequence at the boundary, creating a local hexagonal close-packed structure with low C solubility. This finding raises the question of whether segregation/depletion also occurs at Σ3 deformation twin boundaries in high-Mn TWIP steels. Consequently, a previously published APT dataset of the Fe-22Mn-0.6C alloy system, containing a high density of deformation twins due to 30% tensile deformation at room temperature, was reinvestigated using the same analysis routine as for the annealing twin. Although crystallographically identical to the annealing twin, no evidence of segregation or depletion was found at the deformation twins, owing to the lack of mobility of solutes during twin formation at room temperature.