Optimal Control of Convective FitzHugh-Nagumo Equation

We investigate smooth and sparse optimal control problems for convective FitzHugh-Nagumo equation with travelling wave solutions in moving excitable media. The cost function includes distributed space-time and terminal observations or targets. The state and adjoint equations are discretized in space by symmetric interior point Galerkin (SIPG) method and by backward Euler method in time. Several numerical results are presented for the control of the travelling waves. We also show numerically the validity of the second order optimality conditions for the local solutions of the sparse optimal control problem for vanishing Tikhonov regularization parameter. Further, we estimate the distance between the discrete control and associated local optima numerically by the help of the perturbation method and the smallest eigenvalue of the reduced Hessian

Nonlinear, nonhomogeneous periodic problems with no growth control on the reaction

We consider a nonlinear periodic problem driven by a nonhomogeneous differential operator, which includes as a particular case the scalar p-Laplacian. We assume that the reaction is a Carathéodory function which admits time-dependent zeros of constant sign. No growth control near ±∞ is imposed on the reaction. Using variational methods coupled with suitable truncation and comparison techniques, we prove two multiplicity theorems providing sign information for all the solutions

A vision-based optical character recognition system for real-time identification of tractors in a port container terminal

Automation has been seen as a promising solution to increase the productivity of modern sea port container terminals. The potential of increase in throughput, work efficiency and reduction of labor cost have lured stick holders to strive for the introduction of automation in the overall terminal operation. A specific container handling process that is readily amenable to automation is the deployment and control of gantry cranes in the container yard of a container terminal where typical operations of truck identification, loading and unloading containers, and job management are primarily performed manually in a typical terminal. To facilitate the overall automation of the gantry crane operation, we devised an approach for the real-time identification of tractors through the recognition of the corresponding number plates that are located on top of the tractor cabin. With this crucial piece of information, remote or automated yard operations can then be performed. A machine vision-based system is introduced whereby these number plates are read and identified in real-time while the tractors are operating in the terminal. In this paper, we present the design and implementation of the system and highlight the major difficulties encountered including the recognition of character information printed on the number plates due to poor image integrity. Working solutions are proposed to address these problems which are incorporated in the overall identification system.postprin

Job shop scheduling with artificial immune systems

The job shop scheduling is complex due to the dynamic environment. When the information of the jobs and machines are pre-defined and no unexpected events occur, the job shop is static. However, the real scheduling environment is always dynamic due to the constantly changing information and different uncertainties. This study discusses this complex job shop scheduling environment, and applies the AIS theory and switching strategy that changes the sequencing approach to the dispatching approach by taking into account the system status to solve this problem. AIS is a biological inspired computational paradigm that simulates the mechanisms of the biological immune system. Therefore, AIS presents appealing features of immune system that make AIS unique from other evolutionary intelligent algorithm, such as self-learning, long-lasting memory, cross reactive response, discrimination of self from non-self, fault tolerance, and strong adaptability to the environment. These features of AIS are successfully used in this study to solve the job shop scheduling problem. When the job shop environment is static, sequencing approach based on the clonal selection theory and immune network theory of AIS is applied. This approach achieves great performance, especially for small size problems in terms of computation time. The feature of long-lasting memory is demonstrated to be able to accelerate the convergence rate of the algorithm and reduce the computation time. When some unexpected events occasionally arrive at the job shop and disrupt the static environment, an extended deterministic dendritic cell algorithm (DCA) based on the DCA theory of AIS is proposed to arrange the rescheduling process to balance the efficiency and stability of the system. When the disturbances continuously occur, such as the continuous jobs arrival, the sequencing approach is changed to the dispatching approach that involves the priority dispatching rules (PDRs). The immune network theory of AIS is applied to propose an idiotypic network model of PDRs to arrange the application of various dispatching rules. The experiments show that the proposed network model presents strong adaptability to the dynamic job shop scheduling environment.postprin

Real and Complex Monotone Communication Games

Noncooperative game-theoretic tools have been increasingly used to study many important resource allocation problems in communications, networking, smart grids, and portfolio optimization. In this paper, we consider a general class of convex Nash Equilibrium Problems (NEPs), where each player aims to solve an arbitrary smooth convex optimization problem. Differently from most of current works, we do not assume any specific structure for the players' problems, and we allow the optimization variables of the players to be matrices in the complex domain. Our main contribution is the design of a novel class of distributed (asynchronous) best-response- algorithms suitable for solving the proposed NEPs, even in the presence of multiple solutions. The new methods, whose convergence analysis is based on Variational Inequality (VI) techniques, can select, among all the equilibria of a game, those that optimize a given performance criterion, at the cost of limited signaling among the players. This is a major departure from existing best-response algorithms, whose convergence conditions imply the uniqueness of the NE. Some of our results hinge on the use of VI problems directly in the complex domain; the study of these new kind of VIs also represents a noteworthy innovative contribution. We then apply the developed methods to solve some new generalizations of SISO and MIMO games in cognitive radios and femtocell systems, showing a considerable performance improvement over classical pure noncooperative schemes.Comment: to appear on IEEE Transactions in Information Theor

Virtual element methods for fourth-order problems : implementation and analysis

In this thesis we aim to create a unified framework for the implementation and analysis of virtual element spaces. The approach we take for the virtual element discretisation allows us to easily construct vector field spaces as well as consider both variable coefficient and nonlinear problems. On top of this, the approach can be integrated more readily into existing finite element software packages. These are significant advantages of the method we present and something that has not been easy to achieve within the original virtual element setting. We exploit these key advantages in this thesis. In particular, we present a straightforward and generic way to define the projection operators, which form a crucial part of the virtual element discretisation, for a wide range of problems. We demonstrate how to build Hm-conforming for m = 1, 2 and nonconforming spaces as well as divergence and curl free spaces. All of which have been implemented in the open source Dune software framework as part of the Dune-Fem module. As a consequence of the projection approach taken in our framework, we are able to carry out a priori error analysis for higher order approximations of the following fourth-order problems: a general linear fourth-order PDE with non-constant coefficients; a singular perturbation problem; and the nonlinear time-dependent Cahn-Hilliard equation. Furthermore, we showcase the versatility of the projection approach with the introduction of a novel nonconforming scheme for the singular perturbation problem. The modified nonconforming method is uniformly convergent with respect to the perturbation parameter and unlike modifications in the literature, does not require an enlargement of the space. Numerical tests are carried out to verify the theoretical results

Advances in Optimization and Nonlinear Analysis

The present book focuses on that part of calculus of variations, optimization, nonlinear analysis and related applications which combines tools and methods from partial differential equations with geometrical techniques. More precisely, this work is devoted to nonlinear problems coming from different areas, with particular reference to those introducing new techniques capable of solving a wide range of problems. The book is a valuable guide for researchers, engineers and students in the field of mathematics, operations research, optimal control science, artificial intelligence, management science and economics