Optimal Path Finding in Direction, Location and Time Dependent Environments.

This dissertation examines optimal path finding problems where cost function and constraints are direction, location and time dependent. Path-finding problems have been studied for decades in various applications; however, the published work introduces numerous assumptions to make the problem more tractable. These assumptions are often so strong as to render the model unrealistic for real life applications. In our research, we relax a number of such restrictive assumptions to create an accurate and yet tractable model suitable for implementation for a large class of problems. We first discuss optimal path finding in an anisotropic (direction-dependent), time and space homogeneous environment. We find a closed form solution for the problems with obstacle-free domain without making any assumptions on the structure of the speed function. We employ our findings to adapt a emph{visibility graph search} method of computational geometry to an anisotropic environment and deliver an optimal obstacle-avoiding path finding algorithm for a direction-dependent medium. Next, we extend our analysis to a set of problems where path curvature is constrained by a direction-dependent minimum turning radius function. We invoke techniques from optimal control theory to demonstrate the problem's controllability (by reducing the problem to Dubins car problem), prove existence of an optimal path (via Filippov's Theorem), and derive a necessary condition for optimality (using Pontryagin's Principle). Further analysis delivers a closed form characterization of an optimal path and presents an algorithm that facilitates the implementation of our results. %the solution of our problem. Finally, the assumption of time and space homogeneity is relaxed, and we develop a dynamic programming model to find an optimal path in a location, direction and time dependent environment. The results for anisotropic homogeneous environment are integrated into the model to improve its accuracy, efficiency and run-time. The path finding model addresses limited information availability, control-feasibility and computational demands of a time-dependent environment. To demonstrate the applicability and performance of our path-finding methods, computational experiments for an optimum vessel performance in evolving wave-field project are presented.Ph.D.Industrial & Operations EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/64828/1/dolira_1.pd

Vibration, Control and Stability of Dynamical Systems

From Preface: This is the fourteenth time when the conference “Dynamical Systems: Theory and Applications” gathers a numerous group of outstanding scientists and engineers, who deal with widely understood problems of theoretical and applied dynamics. Organization of the conference would not have been possible without a great effort of the staff of the Department of Automation, Biomechanics and Mechatronics. The patronage over the conference has been taken by the Committee of Mechanics of the Polish Academy of Sciences and Ministry of Science and Higher Education of Poland. It is a great pleasure that our invitation has been accepted by recording in the history of our conference number of people, including good colleagues and friends as well as a large group of researchers and scientists, who decided to participate in the conference for the first time. With proud and satisfaction we welcomed over 180 persons from 31 countries all over the world. They decided to share the results of their research and many years experiences in a discipline of dynamical systems by submitting many very interesting papers. This year, the DSTA Conference Proceedings were split into three volumes entitled “Dynamical Systems” with respective subtitles: Vibration, Control and Stability of Dynamical Systems; Mathematical and Numerical Aspects of Dynamical System Analysis and Engineering Dynamics and Life Sciences. Additionally, there will be also published two volumes of Springer Proceedings in Mathematics and Statistics entitled “Dynamical Systems in Theoretical Perspective” and “Dynamical Systems in Applications”

Dynamical systems : mechatronics and life sciences

Proceedings of the 13th Conference „Dynamical Systems - Theory and Applications" summarize 164 and the Springer Proceedings summarize 60 best papers of university teachers and students, researchers and engineers from whole the world. The papers were chosen by the International Scientific Committee from 315 papers submitted to the conference. The reader thus obtains an overview of the recent developments of dynamical systems and can study the most progressive tendencies in this field of science

Applications of Mathematical Models in Engineering

The most influential research topic in the twenty-first century seems to be mathematics, as it generates innovation in a wide range of research fields. It supports all engineering fields, but also areas such as medicine, healthcare, business, etc. Therefore, the intention of this Special Issue is to deal with mathematical works related to engineering and multidisciplinary problems. Modern developments in theoretical and applied science have widely depended our knowledge of the derivatives and integrals of the fractional order appearing in engineering practices. Therefore, one goal of this Special Issue is to focus on recent achievements and future challenges in the theory and applications of fractional calculus in engineering sciences. The special issue included some original research articles that address significant issues and contribute towards the development of new concepts, methodologies, applications, trends and knowledge in mathematics. Potential topics include, but are not limited to, the following: Fractional mathematical models; Computational methods for the fractional PDEs in engineering; New mathematical approaches, innovations and challenges in biotechnologies and biomedicine; Applied mathematics; Engineering research based on advanced mathematical tools

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal