Research on multi-agent systems performing cooperative tasks has received considerable attention in recent years. Because multiple agents perform cooperative tasks in close proximity, the coordination control of multiple agents to avoid collisions holds one of the critical keys to mission success. The potential function approach has been extensively employed for collision avoidance, but it has one inherent limitation of local minimum. This dissertation proposes a new avoidance strategy for the issue of local minimum. The primary objective of this research is to construct novel potential-function-based control schemes that drive agents from their initial to the goal configurations while avoiding collision with other agents and obstacles. The control schemes enable agents to avoid being trapped at a local minimum by forcing them to exit from the regions that may contain a local minimum. This dissertation consists of three studies, each of which has different technical assumptions. In the first study, all-to-all communication ability among agents is assumed. In addition, each agent is assumed to a priori know the location of all obstacles. In the second study, all-to-all communication ability is again assumed, but each agent is assumed to determine the location of obstacles using a sensor with a limited sensing range. In the third study, limited communication ability is assumed (i.e., each agent exchanges information only with agents within its limited communication range), and each agent is assumed to determine the location of the obstacles using its sensor with a limited sensing range. Relative to existing solutions, the new control schemes presented here have three distinct advantages. First, our avoidance strategy can provide cost-efficient solutions in applications because agents will never be trapped at a local minimum. Second, our control signals are continuous, which allows agents to change their speed in a realistic manner that is consistent with their natural motion traits. Finally, our control scheme allows for setting the upper bound of the velocity of each agent, which guarantees that the speed of agents will never exceed a maximum speed limit. / text

This paper develops a potential reduction algorithm for solving a linear-programming problem directly from a "warm start" initial point that is neither feasible nor optimal. The algorithm is of an "interior point" variety that seeks to reduce a single potential function which simultaneously coerces feasibility improvement (Phase I) and objective value improvement (Phase II). The key feature of the algorithm is the ability to specify beforehand the desired balance between infeasibility and nonoptimality in the following sense. Given a prespecified balancing parameter /3 > 0, the algorithm maintains the following Phase I - Phase II "/3-balancing constraint" throughout: (cTx- Z*) < /3TX, where cTx is the objective function, z* is the (unknown) optimal objective value of the linear program, and Tx measures the infeasibility of the current iterate x. This balancing constraint can be used to either emphasize rapid attainment of feasibility (set large) at the possible expense of good objective function values or to emphasize rapid attainment of good objective values (set /3 small) at the possible expense of a lower infeasibility gap. The algorithm exhibits the following advantageous features: (i) the iterate solutions monotonically decrease the infeasibility measure, (ii) the iterate solutions satisy the /3-balancing constraint, (iii) the iterate solutions achieve constant improvement in both Phase I and Phase II in O(n) iterations, (iv) there is always a possibility of finite termination of the Phase I problem, and (v) the algorithm is amenable to acceleration via linesearch of the potential function.

Despite the first unmanned aerial vehicle (UAV) mission being flown on Aug 22 1849 to bomb Venice UAVs have only recently began to modernize into sophisticated tools beyond simple aerial vehicles. With an increasing number of potential applications, such as cargo delivery, communications, search and rescue, law enforcement, and homeland security, the need for appropriate UAV technology advancement also arose. Here, the development of a low-cost collision avoidance system is described. Hardware was tested and selected based on predetermined constraints and goals. Additionally, a variety of potential functions were explored and assessed at their effectiveness in preventing a collision of a UAV with mountainous terrain. Simulations were conducted using Cloud Cap’s Piccolo autopilot in conjunction with Matlab. Based on these simulations, a set of potential functions was selected to be used with the chosen hardware on subsequent UAV-development-related projects.

In this thesis, we discuss models for multi-agent dynamical systems. We study the tracking/migration problem for flocks and a theoretical framework for design and analysis of flocking algorithm is presented. The interactions between agents in the systems are denoted by potential functions that act as distance functions, hence, the design of proper potential functions are crucial in modelling and analyzing the flocking problem for multi-agent dynamical systems. Constructions for both non-smooth potential functions and smooth potential functions with finite cut-off are investigated in detail. The main contributions of this thesis are to extend the literature of continuous flocking models with impulsive control and delay. Lyapunov function techniques and techniques for stability of continuous and impulsive switching system are used, we study the asymptotic stability of the equilibrium of our models with impulsive control and discovery that by applying impulsive control to Olfati-Saber's continuous model, we can remove the damping term and improve the performance by avoiding the deficiency caused by time delay in velocity sensing. Additionally, we discuss both free-flocking and constrained-flocking algorithm for multi-agent dynamical system, we extend literature results by applying velocity feedbacks which are given by the dynamical obstacles in the environment to our impulsive control and successfully lead to flocking with obstacle avoidance capability in a more energy-efficient way. Simulations are given to support our results, some conclusions are made and future directions are given.

The Hill's equation is the Schrodinger equation $$-y'+qy=la y$$ with a periodic one-dimensional potential function $q$ and coupled with periodic boundary conditions $y(0)=y(1)$, $y'(0)=y'(1)$ or anti-periodic boundary conditions $y(0)=-y(1)$, $y'(0)=-y'(1)$. We study the inverse nodal problem for Hill's equation, in particular the reconstruction problem. Namely, we want to reconstruct the potential function using only nodal data ( zeros of eigenfunctions ). In this thesis, we give a reconstruction formula for $q$ using the periodic nodal data or using anti-periodic nodal data We show that the convergence is pointwise for all $x in (0,1)$ where $q$ is continuous; and pointwise for $a.e.$ $x in (0,1)$ as well as $L^1$ convergence when $qin L^1(0,1)$. We do this by making a translation so that the problem becomes a Dirichlet problem. The idea comes from the work of Coskun and Harris.

In recent year, the quantum device has been rapid developed. The quantum conductor has been of great interest for most authors, and one of that is gold nanowire. As the diameter of the gold nanowire is smaller than 2nm, the structure arrangement is affected by surface tensor, and therefore the FCC structure will self assemble to a helical structure. However, the nanowire would be used in quantum devices, therefore, the material property must be understood and investigated. The properties of nanowire would be a significant on development of quantum device in the future. In this study, the molecular dynamics is employed to investigate the mechanical properties of the helical multi-shall gold nanowires and nanowries of the bulk FCC. The stress and strain relationship is obtained form the tensile and compressed tests. In addition, the yielding stress, maximum stress, Young¡¦s modulus, and breaking force can be determined from the tensile test and compressed test. Moreover, the different length/diameter ratio, temperature, and strain rate effects on mechanical properties and deformation behaviors are also investigated. The structure transform from crystalline to non-crystalline is also observed by the variation of radial distribution function (RDF) and angular correlation function (ACF). In this study, the tight-binding many body potential is employed to model the interaction between gold atoms.

In this thesis, we discuss models for multi-agent dynamical systems. We study the tracking/migration problem for flocks and a theoretical framework for design and analysis of flocking algorithm is presented. The interactions between agents in the systems are denoted by potential functions that act as distance functions, hence, the design of proper potential functions are crucial in modelling and analyzing the flocking problem for multi-agent dynamical systems. Constructions for both non-smooth potential functions and smooth potential functions with finite cut-off are investigated in detail. The main contributions of this thesis are to extend the literature of continuous flocking models with impulsive control and delay. Lyapunov function techniques and techniques for stability of continuous and impulsive switching system are used, we study the asymptotic stability of the equilibrium of our models with impulsive control and discovery that by applying impulsive control to Olfati-Saber's continuous model, we can remove the damping term and improve the performance by avoiding the deficiency caused by time delay in velocity sensing. Additionally, we discuss both free-flocking and constrained-flocking algorithm for multi-agent dynamical system, we extend literature results by applying velocity feedbacks which are given by the dynamical obstacles in the environment to our impulsive control and successfully lead to flocking with obstacle avoidance capability in a more energy-efficient way. Simulations are given to support our results, some conclusions are made and future directions are given.

Yes / Gas hydrates, or clathrate hydrates, are solid crystalline compounds, which are formed by combination of water and gas and/or some volatile liquid molecules. Prediction of hydrate stability/dissociation/equilibrium conditions of natural gases is important in separation processes, gas storage, and in preventing blockage of gas transmission pipelines. In this study, initially, the different sets of the Kihara Potential Function Parameters, KPFP, reported in the literature were used to predict the experimental hydrate dissociation conditions of methane, ethane, propane and i-butane and mixtures of these four compounds. In most cases, however, based on these sets of KPFP, the hydrate structure cannot be predicted correctly. Consequently due to incorrect estimation of the hydrate structure, especially for natural gas mixture, the predicted hydrate dissociation conditions are found inaccurate. For overcoming this fault and by using a genetic algorithm, a new set of KPFP were optimized based on the new definition of the objective function considering hydrate structure. The results show good agreement with experimental data, both in the prediction of hydrate dissociation conditions and hydrate structure.

The reliability and quality of suppliers' components are inevitably two factors that impact the performance of the supply chain. Stochastic reliability affects the final production quantity and hence makes it more difficult to predict the manufacturer's best ordering quantity as opposed to the simpler traditional news vendor model. In addition, the quality of suppliers' products directly influence the potential demand in the market. Hence every firm in the supply chain system faces the needs to invest time, money and effort to improve the product quality even though it may bring a higher production and investment cost. Thus our dissertation is divided into two parts. In the first part, we build a model for a two echelon supply chain system in which a single manufacturer sells his product to a market with stochastic demand. A group of suppliers provide essential components for the manufacturer. They may be: 1) homogeneous component suppliers, 2) complementary component suppliers or 3) divided into subgroups, suppliers in the same subgroup provide the same component while the components from different subgroups are assembled in the final product. The fraction of effective component ordered from each supplier is a random variable. We first analyze the manufacturer's optimal ordering quantity decision. We identify several important properties of the optimal decision. Then based on those properties, we devise optimal solution procedures and heuristic methods for the above three systems. Finally, in the case of Bernoulli reliability, we investigate the suppliers' price competition by non-cooperative game theory. In the second part, we model a two echelon assembly system which faces deterministic demand affected by the market price and quality of the product. Therefore, the decisions of the firms are divided into two stages: in the first stage, they decide on how much effort to invest in the quality of the components or the final product to stimulate the market. They may make decisions simultaneously or sequentially. Then after the efforts are invested, in the second stage, the component suppliers first decide on their components' wholesale price and then the manufacture decides on the market price given the wholesale price. We identify the existence of Nash equilibrium in each stage through potential functions. Moreover, in the first stage decision, we find that the competition with a leader can always benefit the whole system compared with simultaneous competition. / Ph. D.

The first and most imperative step when designing a biologically inspired robot is to identify the underlying mechanics of the system or animal of interest. It is most common, perhaps, that this process generates a set of coupled nonlinear ordinary or partial differential equations. For this class of systems, the models derived from morphology of the skeleton are usually very high dimensional, nonlinear, and complex. This is particularly true if joint and link flexibility are included in the model. In addition to complexities that arise from morphology of the animal, some of the external forces that influence the dynamics of animal motion are very hard to model. A very well-established example of these forces is the unsteady aerodynamic forces applied to the wings and the body of insects, birds, and bats. These forces result from the interaction of the flapping motion of the wing and the surround- ing air. These forces generate lift and drag during flapping flight regime. As a result, they play a significant role in the description of the physics that underlies such systems. In this research we focus on dynamic and kinematic models that govern the motion of ground based robots that emulate flapping flight. The restriction to ground based biologically inspired robotic systems is predicated on two observations. First, it has become increasingly popular to design and fabricate bio-inspired robots for wind tunnel studies. Second, by restricting the robotic systems to be anchored in an inertial frame, the robotic equations of motion are well understood, and we can focus attention on flapping wing aerodynamics for such nonlinear systems. We study nonlinear modeling, identification, and control problems that feature the above complexities. This document summarizes research progress and plans that focuses on two key aspects of modeling, identification, and control of nonlinear dynamics associated with flapping flight. / Ph. D. / In this work we focus on modeling flapping flight mechanics by focusing our attention in two aspects of modeling. We first model the behavior of aerodynamic forces in charge of keeping the flying animal airborn. We present a mathematical model for history dependent profile of these forces. Also, we propose a novel adaptive controller to compensate these unknown forces in the dynamic model of the system. We also propose an algorithm to derive dynamic equations of the animal motion by using video data. We expect the model derived by this novel method to emulate the animal motion closely.