Bifurcations and Stability in Models of Infectious Diseases

This work is concerned with bifurcation and stability in models related to various aspects of infections diseases. First, we study the dynamics of a mathematical model on primary and secondary cytotoxic T-lymphocyte responses to viral infections by Wodarz et al. This model has three equilibria and the stability criteria of them are discussed. We analytically show that periodic solutions may arise from the third equilibrium via Hopf bifurcation. Numerical simulations of the model agree with the theoretical results. These dynamical behaviours occur within biologically realistic parameter range. After studying the single-strain model, we analyze the bifurcation dynamics of an in vivo multi-strain model of Plasmodium falciparum. Main attention of this model is focused on the dynamics of cross-reactivity from antigenic variation. We apply the techniques of coupled cell systems to the model and find that synchrony-breaking Hopf bifurcation occurs from a nontrivial synchronous equilibrium. We prove the existence and calculate the condition for the bifurcation. Aside from studying the previous models, we also study the clustering behaviour found in numerous multi-strain transmission models. Numerical solutions of these models have shown that steady-state, periodic, or even chaotic motions can be self-organized into clusters. We show that the steady-state clusterings in existing models can be analytically predicted. The clusterings occur via semi-simple double zero bifurcations from the quotient network of the models. We also calculate the stability criteria for different clustering patterns. Finally, the biological implications of these results are discussed

Covariance and Gramian matrices in control and systems theory.

Covariance and Gramian matrices in control and systems theory and pattern recognition are studied in the context of reduction of dimensionality and hence complexity of large-scale systems. This is achieved by the removal of redundant or 'almost' redundant information contained in the covariance and Grarrdan matrices. The Karhunen-Loeve expansion (principal component analysis) and its extensions and the singular value decomposition of matrices provide the framework for the work presented in the thesis. The results given for linear dynamical systems are based on controllability and observability Gramians and some new developments in singular perturbational analysis are also presented

Stability and Stabilization of Systems with Time Delay: Limitations and Opportunities

Time-delays are important components of many dynamical systems that describe coupling or interconnection between dynamics, propagation, or transport phenomena in shared environments, in heredity, and in competition in population dynamics. This monograph addresses the problem of stability analysis and the stabilisation of dynamical systems subjected to time-delays. It presents a wide and self-contained panorama of analytical methods and computational algorithms using a unified eigenvalue-based approach illustrated by examples and applications in electrical and mechanical engineering, biology, and complex network analysis

Motion Planning of UAV Swarm: Recent Challenges and Approaches

The unmanned aerial vehicle (UAV) swarm is gaining massive interest for researchers as it has huge significance over a single UAV. Many studies focus only on a few challenges of this complex multidisciplinary group. Most of them have certain limitations. This paper aims to recognize and arrange relevant research for evaluating motion planning techniques and models for a swarm from the viewpoint of control, path planning, architecture, communication, monitoring and tracking, and safety issues. Then, a state-of-the-art understanding of the UAV swarm and an overview of swarm intelligence (SI) are provided in this research. Multiple challenges are considered, and some approaches are presented. Findings show that swarm intelligence is leading in this era and is the most significant approach for UAV swarm that offers distinct contributions in different environments. This integration of studies will serve as a basis for knowledge concerning swarm, create guidelines for motion planning issues, and strengthens support for existing methods. Moreover, this paper possesses the capacity to engender new strategies that can serve as the grounds for future work

Coordination of Cooperative Multi-Robot Teams

This thesis is about cooperation of multiple robots that have a common task they should fulfill, i.e., how multi-robot systems behave in cooperative scenarios. Cooperation is a very important aspect in robotics, because multiple robots can solve a task more quickly or efficiently in many situations. Specific points of interest are, how the effectiveness of the group of robots completing a task can be improved and how the amount of communication and computational requirements can be reduced. The importance of this topic lies in applications like search and rescue scenarios, where time can be a critical factor and a certain robustness and reliability are required. Further the communication can be limited by various factors and operating (multiple) robots can be a highly complicated task. A typical search and rescue mission as considered in this thesis begins with the deployment of the robot team in an unknown or partly known environment. The team can be heterogeneous in the sense that it consists of pairs of air and ground robots that assist each other. The air vehicle – abbreviated as UAV – stays within vision range of the ground vehicle or UGV. Therefrom, it provides sensing information with a camera or similar sensor that might not be available to the UGV due to distance, perspective or occlusion. A new approach to fully use the available movement range is presented and analyzed theoretically and in simulations. The UAV moves according to a dynamic coverage algorithm which is combined with a tracking controller to guarantee the visibility limitation is kept. Since the environment is at least partly unknown, an exploration method is necessary to gather information about the situation and possible targets or areas of interest. Exploring the unknown regions in a short amount of time is solved by approaching points on the frontier between known and unknown territory. To this end, a basic approach for single robot exploration that uses the traveling salesman problem is extended to multirobot exploration. The coordination, which is a central aspect of the cooperative exploration process, is realized with a pairwise optimization procedure. This new algorithm uses minimum spanning trees for cost estimation and is inspired by one of the many multi-robot coordination methods from the related literature. Again, theoretical and simulated as well as statistical analysis are used as methods to evaluate the approach. After the exploration is complete, a map of the environment with possible regions of higher importance is known by the robot team. To stay useful and ready for any further events, the robots now switch to a monitoring state where they spread out to cover the area in an optimal manner. The optimality is measured with a criterion that can be derived into a distributed control law. This leads to splitting of the robots into areas of Voronoi cells where each robot has a maximum distance to other robots and can sense any events within its assigned cell. A new variant of these Voronoi cells is introduced. They are limited by visibility and depend on a delta-contraction of the environment, which leads to automatic collision avoidance. The combination of these two aspects leads to a coverage control algorithm that works in nonconvex environments and has advantageous properties compared to related work

Evolution of microgrids with converter-interfaced generations: Challenges and opportunities

© 2019 Elsevier Ltd Although microgrids facilitate the increased penetration of distributed generations (DGs) and improve the security of power supplies, they have some issues that need to be better understood and addressed before realising the full potential of microgrids. This paper presents a comprehensive list of challenges and opportunities supported by a literature review on the evolution of converter-based microgrids. The discussion in this paper presented with a view to establishing microgrids as distinct from the existing distribution systems. This is accomplished by, firstly, describing the challenges and benefits of using DG units in a distribution network and then those of microgrid ones. Also, the definitions, classifications and characteristics of microgrids are summarised to provide a sound basis for novice researchers to undertake ongoing research on microgrids

Model Development and Stability Analysis for a Turbocharger Rotor System under Multi-Field Coupled Forces

Automotive turbochargers have been widely applied in vehicles in order to increase the power output of internal combustion engines by increasing the air to fuel ratio entering the piston cylinders. Turbochargers use the exhaust flow to spin a turbine at speeds of up to 140,000 r/min. Under such extreme working conditions, even a weak vibration can lead to the bearing failure and the whole turbocharger destroyed. In order to guarantee a safe operation, it is necessary to carry out a theoretical research on the dynamics performance of turbochargers. Therefore, the primary objective of this research is to develop a dynamics model for the turbocharger rotor system under multi-field coupled forces and then to study the dynamic characteristics and the stability of its rotor system according to the simulation and experimental results. A turbocharger is a special kind of rotating machinery because of the following aspects: Firstly, the turbocharger rotor system is supported by floating ring bearings. The impact of nonlinear multi-field coupled forces must be considered. Secondly, the turbocharger rotor system is a multi-span rotor bearing system that makes the modeling and simulation more complicated. Thirdly, the working speed range of the turbocharger covers multiple orders of critical speeds. This flexible rotor system cannot be studied using the conventional theory of rigid rotors. In this thesis, the lubrication system of a turbocharger is initially investigated. The analytical expressions of the hydrodynamic pressure distribution in the floating ring bearing are derived using the infinitely long bearing theory, taking into account the oil inlet pressure and the cavitation area. The influences of external loads and oil inlet pressure on the oil flow rate into the inner clearance are analytically investigated, while considering the effect of the rotation of the ring. A finite element model is then developed for the turbocharger rotor system. In this model, the excitation forces considered include rotor imbalance, hydrodynamic forces, lubricant feed pressure and the dead weight. The dimensionless form of Capone hydrodynamic force model is extended into the floating ring bearing. Following model development, modal analysis is carried out on both a free rotor system and a turbocharger rotor system. The effects of the structural parameters and working conditions, such as the rotor imbalance, lubricant viscosity, bearing clearances and lubricant feed pressure, on the stability of the turbocharger rotor system are studied. A turbocharger test rig is then designed and developed to monitor the turbocharger shaft motion. The experimental data agree well with the simulation results from the theoretical model. The primary contribution of the current research can be categorized into the following aspects: Firstly, the analytical expressions of the hydrodynamic pressure distribution have been solved. The equilibrium positions of the journal and ring have been deduced under different external loads and lubricant feed pressure. The relationship between the oil flow rate and the rotational velocity of the shaft has been obtained. Secondly, Capone hydrodynamic force model is introduced and extended to simulate the dynamic performance of the floating ring bearing. The analytical expression of the hydrodynamic forces of double oil films have been derived based on the dimensionless form of the Reynolds Equations. Thirdly, the motion of the turbocharger shaft is simulated within a speed range of 0 to 8,000 rad/s. The influences of structural parameters and working conditions on the stability of the turbocharger rotor system are clearly understood. It should be noted that the developed model still needs to be validated when turbocharger is operated at a relatively high speed, although it agrees well with experimental results within the speed range of 0 to 2,000 rad/s