On controllability and control laws for discrete linear repetitive processes

Repetitive processes are a distinct class of 2D systems (i.e. information propagation in two independent directions) of both systems theoretic and applications interest. They cannot be controlled by the direct extension of existing techniques from either standard (termed 1D here) or 2D systems theory. This article develops significant new results on the relationships between one physically motivated concept of controllability for the so-called discrete linear repetitive processes and the structure and design of control laws, including the case when disturbances are present.     

PI control of discrete linear repetitive processes

Repetitive processes are a distinct class of 2D systems (i.e. information propagation in two independent directions) of both systems theoretic and applications interest. They cannot be controlled by direct extension of existing techniques from either standard (termed 1D here) or 2D systems theory. In this paper, we exploit their unique physical structure to show how two term, i.e. proportional plus integral (or PI) action, can be used to control these processes to produce desired behavior (as opposed to just stability).     

Control theory for a class of 2D continuous-discrete linear systems

This paper considers a general class of 2D continuous-discrete linear systems of both systems theoretic and applications interest. The focus is on the development of a comprehensive control systems theory for members of this class in a unified manner based on analysis in an appropriate algebraic and operator setting. In particular, important new results are developed on stability, controllability, stabilization and optimal control.     

Relaxed pass profile controllability of discrete linear repetitive processes

Repetitive processes are a distinct class of 2D systems (i.e. information propagation in two independent directions) of both systems theoretic and applications interest. They cannot be controlled by direct extension of existing techniques from either standard (termed 1D here) or 2D systems theory. In this paper we develop significant new results on controllability of so-called discrete linear repetitive processes. The end result is necessary and sufficient conditions for this property in terms of matrix rank based tests. The application of these tests is illustrated by a numerical example.     

Stabilisation of discrete 2D time switching systems by state feedback control

This article deals with sufficient conditions of asymptotic stability for discrete two-dimensional (2D) time switching systems represented by a model of Roesser type with state feedback control. This class of systems can correspond to 2D state space or 2D time space switching systems. This work is based on common and multiple Lyapunov functions. The results are presented in LMI form. Two examples are given to illustrate the results.     

Robust stabilization of nonlinear stochastic 2‐D systems: LaSalle‐type theorem approach

LaSalle theorem (also known as the LaSalle invariance principle) plays an essential role in the systems and control theory. Recently, it has been extensively studied and developed for various types of one‐dimensional (1‐D) systems including deterministic and stochastic 1‐D systems in discrete‐ and continuous‐time domains. For two‐dimensional (2‐D) systems, such studies have received considerably less attention. In this article, based on discrete martingale theory, a LaSalle‐type theorem is first developed for a class of discrete‐time nonlinear stochastic 2‐D systems described by a Roesser model. The proposed result can be regarded as an extension of stochastic Lyapunov‐like theorem, which guarantees the convergence almost surely of system state trajectories. Extensions to the problem of optimal guaranteed cost control of nonlinear stochastic 2‐D systems are also presented. The proposed schemes are then utilized to derive tractable synthesis conditions of a suboptimal state‐feedback controller for uncertain 2‐D systems with multiplicative stochastic noises. The effectiveness of the obtained results is illustrated by given numerical examples and simulations.     

Bearing-based formation manoeuvre control of nonholonomic multi-agent systems

ABSTRACT

This paper concerns on the bearing-based leader–follower formation manoeuvre control problem for two- (2D) and three-dimensional (3D) multi-agent systems with nonholonomic constraint. The target formation is defined by relative-bearing measurements, which, for example, can be obtained from onboard cameras. The contributions of this paper are twofold. Firstly, a distributed formation manoeuvre control law is proposed for 2D nonholonomic agents according to the inter-bearing measurement. The multi-agent systems can achieve the desired formation which is defined by the bearings information. The formation manoeuvre can be achieved by steering at least two leaders. Secondly, the control law is nontrivially extended to 3D nonholonomic multi-agents systems. The leader–follower formation tracking problem can also be solved by the proposed proportional-integral control scheme. Simulation results for 2D and 3D nonholonomic multi-agents systems are presented. Experiments that used ground mobile robots verify the effectiveness of the proposed control laws.     

LMI based stability analysis and robust controller design for discrete linear repetitive processes

Discrete linear repetitive processes are a distinct class of 2D linear systems with applications in areas ranging from long‐wall coal cutting through to iterative learning control schemes. The main feature which makes them distinct from other classes of 2D linear systems is that information propagation in one of the two independent directions only occurs over a finite duration. This, in turn, means that a distinct systems theory must be developed for them. In this paper, the major new development is that an LMI based re‐formulation of the stability conditions can used to enable the design of a family of control laws which have a well defined physical basis. It is also noted that this setting can be used to investigate robustness aspects. Copyright © 2003 John Wiley & Sons, Ltd.     

Gold nanoparticle synthesis in microfluidic systems and immobilisation in microreactors designed for the catalysis of fine organic reactions

Our work is focused on two applications of fine tunable microfluidic systems, first to optimize heterogeneous size nanoparticle synthesis and second to build catalytic microreactors for advanced organic reactions. The first part of our work consists in the use of an original microfluidic setup for gold nanoparticle synthesis, which allows a high control of the reaction parameters as the reactants flow, the concentration, the temperature, and the reaction time. We show that using such microfluidic systems permit a better control of the reaction parameters for producing homodispersed 1–2 nm gold nanoparticle. The second part of our work deals with the incorporation of gold nanoparticles into silica capillaries to build catalytic microreactors dedicated to fine chemical reactions. Our strategy consists in the immobilization of gold nanopadiegolirticles onto the inner surface (2D dispersion) or into the inner volume (3D dispersion) of functionalized silica microcapillaries. Characterizations show that by different functionalization procedures, those gold nanoparticles are well anchored inside the microcapillary.     

On optimal node spacing for immersed boundary–lattice Boltzmann method in 2D and 3D

A computational study on optimal spacing of Lagrangian nodes discretizing a rigid and immobile immersed body boundary in 2D and 3D is presented in order to show how the density of the Lagrangian points affects the numerical results of the Immersed Boundary–Lattice Boltzmann Method (IB–LBM). The study is based on the implicit velocity correction-based IB–LBM proposed by Wu and Shu (2009, 2010) that allows computing the fluid–body interaction force. However, the (original) method fails for densely spaced Lagrangian points due to ill-conditioned or even singular linear systems that arise from the derivation of the method. We propose a modification that improves the solvability of the linear systems and compare the performance of both methods using several benchmark problems. The results show how the spacing of the Lagrangian points affects the numerical results, mainly the permeability of the discretized body boundary in applications to fluid flows over rigid obstacles and blood flows in arteries in 2D and 3D.     

Application of interval type-2 fuzzy neural networks in non-linear identification and time series prediction

Neural networks (NNs), type-1 fuzzy logic systems and interval type-2 fuzzy logic systems (IT2FLSs) have been shown to be important methods in real world applications, which range from pattern recognition, time series prediction, to intelligent control. Recent research shows that embedding an IT2FLS on an NN can be very effective for a wide number of non-linear complex systems, especially when handling imperfect or incomplete information. In this paper we are presenting several models of interval type-2 fuzzy neural networks (IT2FNNs) that use a set of rules and interval type-2 membership functions for that purpose. Simulation results of non-linear function identification using the IT2FNN for one and three variables and for the Mackey–Glass chaotic time series prediction are presented to illustrate that the proposed models have potential for real world applications.     

Multiple two-dimensional displays as an alternative to three-dimensional displays in telerobotic tasks

In this study a multiple-view two-dimensional (2D) display was compared with a three-dimensional (3D) monocular display and a 3D stereoscopic display using a simulated telerobotic task. As visual aids, three new types of visual enhancement cues were provided and evaluated for each display type. The results showed that the multiple-view 2D display was superior to the 3D monocular and the 3D stereoscopic display in the absence of the visual enhancement depth cues. When participants were provided with the proposed visual enhancement cues, the stereoscopic and monocular displays became equivalent to the multiple-view 2D display. Actual or potential applications of this study include the design of visual displays for teleoperation systems.     

Anti-synchronization of four-wing chaotic systems via sliding mode control

Sliding mode control is an important method used in nonlinear control systems. In robust control systems, the sliding mode control is often adopted due to its inherent advantages of easy realization, fast response and good transient performance as well as its insensitivity to parameter uncertainties and disturbances. In this paper, we derive new results based on the sliding mode control for the anti-synchronization of identical Qi three-dimensional (3D) four-wing chaotic systems (2008) and identical Liu 3D four-wing chaotic systems (2009). The stability results for the anti-synchronization schemes derived in this paper using sliding mode control (SMC) are established using Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the SMC method is very effective and convenient to achieve global chaos anti-synchronization of the identical Qi four-wing chaotic systems and identical Liu four-wing chaotic systems. Numerical simulations are shown to illustrate and validate the synchronization schemes derived in this paper.     

Iterative Learning Control Design for Multiagent Systems Based on 2D Models

This paper considers a group of systems (agents) described by linear continuous or discrete models. All systems operate in the repetitive mode with a constant pass length, with resetting to the initial state after each pass is complete. Information exchange among the systems is described by a directed graph. The problem of reaching a consensus is formulated as designing an iterative learning control law (protocol) under which the output variable of each agent converges to a reference trajectory (pass profile) as the number of passes grows infinitely. This problem is solved using an original approach based on 2D models and a 2D modification of the vector Lyapunov function method. The ultimate results are written in form of linear matrix inequalities. 2D counterparts of the Fax–Murray theorem are established. An illustrative example is given.     

Experimental tests of resolution-based theorem-proving strategies

Many potential applications of mechanical theorem proving exist in such areas as question answering, robot control, program writing, proof of program correctness, verification of mathematical proofs, general problem solving, and command and control systems. Theorem-proving systems must become much more efficient before applications become generally practical, and much statistical testing will be necessary to select the strategies to be used in practical systems.This paper reports on the results of experimental testing of some major theorem-proving strategies and their interactions. Test results are based on CPU time. The paper concludes that (1) subsumption and factoring should not be used (at least, in this implementation), (2) set of support and P1-deduction should be used, (3) the choice between breadth-first searching and unit preference searching is highly problem dependent, and (4) merge and linear strategies have little effect on the proof process. No statistically significant interaction among the strategies was discovered.     

Sliding mode control for a class of nonlinear It ô stochastic systems with state and input delays

This paper deals with the problem of sliding mode control (SMC) for a class of nonlinear stochastic systems. The nonlinear uncertainties are unknown and unmatched. There exist state and input delays. A special switching function is designed such that the insensitivity of the system can be guaranteed throughout the entire response of the system from the initial time instance. Both the sliding surface and the sliding mode controller exist if a set of matrix inequalities is feasible. A simulation example is given to illustrate the proposed method. Recommended by Editorial Board member Poo Gyeon Park under the direction of Editor Young Il lee. The research was partially supported by NNSF under Grant (60674015, 60674089), the Technology Innovation Key Foundation of Shanghai Municipal Education Commission (09ZZ60), Shanghai Leading Academic Discipline Project (B504), China. Yugang Niu received the Ph.D. degree in Control Theory and Control Engineering Automation from Nanjing University of Science and Technology in 2001. His research interests include nonlinear control, stochastic control systems, sliding mode control and network congestion control. Bei Chen received the B.S. degree in Automation from East China University of Science & Technology in 2008. Her current research areas are sliding mode control, and networked control systems. Xingyu Wang received the Ph.D. degree in Industrial Automation from the East China Chemical Institute in 1984. His current research areas primarily cover control theory and applications, intelligent control, and brain control with its wide range of applications.     

Conics-enhanced vision approach for easy and low-cost 3D tracking

This paper presents a conics-enhanced vision approach for low-cost and easy-to-operate 3D tracking. The idea is to use paper disks as markers and recover the 3D positions of these paper disks by a property of conics: the 3D rotation and translation information of a planar circle with known radius could be recovered from its elliptic projection in one image (Int. J. Comput. Vision 10(1) (1993) 7). This property implies that tracking a paper disk in 3D could be done by tracking its elliptic projection in a sequence of 2D images. Since ellipse tracking has to consider many factors such as occlusion, background, light and so on, it is difficult to develop a general algorithm that works for all situations. In this paper, we discuss algorithms for two types of ellipse tracking: real-time tracking of single, non-occluded ellipse and off-line tracking of multiple ellipses. They are used to develop a real-time tracker to control the camera movement in a virtual environment and a multiple-tracker system that works off-line to acquire human motion data to animate a 3D human model. Implementation details and experimental results of the tracking systems are presented. The proposed 3D tracking approach is valuable for applications where accuracy and speed are not very critical but affordability and operational ease are most concerned, e.g., the educational-purpose virtual environments for kids.     

Some new stability conditions for two-dimensional difference systems

This paper considers robust stability of two-dimensional (2D) difference systems in the Fornasini-Marchesini (F-M) state space setting. An approach based on the MacL aurine series expansion is presented. First, a new and less conservative sufficient condition for asymptotic stability of nominal 2D discrete systems is derived. Then sufficient conditions for robust stability of 2D discrete systems subjected to both structured and unstructured perturbations are given. Finally, new robust stability conditions for 2D discrete-delay systems are derived. Numerical examples are given to illustrate the results.     

Recent advances in visual and infrared face recognition—a review

Face recognition is a rapidly growing research area due to increasing demands for security in commercial and law enforcement applications. This paper provides an up-to-date review of research efforts in face recognition techniques based on two-dimensional (2D) images in the visual and infrared (IR) spectra. Face recognition systems based on visual images have reached a significant level of maturity with some practical success. However, the performance of visual face recognition may degrade under poor illumination conditions or for subjects of various skin colors. IR imagery represents a viable alternative to visible imaging in the search for a robust and practical identification system. While visual face recognition systems perform relatively reliably under controlled illumination conditions, thermal IR face recognition systems are advantageous when there is no control over illumination or for detecting disguised faces. Face recognition using 3D images is another active area of face recognition, which provides robust face recognition with changes in pose. Recent research has also demonstrated that the fusion of different imaging modalities and spectral components can improve the overall performance of face recognition.     

Robust uniform triangulation algorithm for computer aided design

This paper presents a new robust uniform triangulation algorithm that can be used in CAD/CAM systems to generate and visualize geometry of 3D models. Typically, in CAD/CAM systems 3D geometry consists of 3D surfaces presented by the parametric equations (e.g. surface of revolution, NURBS surfaces) which are defined on a two dimensional domain. Conventional triangulation algorithms (e.g. ear clipping, Voronoi-Delaunay triangulation) do not provide desired quality and high level of accuracy (challenging tasks) for 3D geometry. The approach developed in this paper combines lattice tessellation and conventional triangulation techniques and allows CAD/CAM systems to obtain the required surface quality and accuracy. The algorithm uses a Cartesian lattice to divide the parametric domain into adjacent rectangular cells. These cells are used to generate polygons that are further triangulated to obtain accurate surface representation. The algorithm allows users to control the triangle distribution intensity by adjusting the lattice density. Once triangulated, the 3D model can be used not only for rendering but also in various manufacturing and design applications. The approach presented in this paper can be used to triangulate any parametric surface given in S(u,v) form, e.g. NURBS surfaces, surfaces of revolution, and produces good quality triangulation which can be used in CAD/CAM and computer graphics applications.