The flock-guidance problem enjoys a challenging structure where multiple optimization objectives are solved simultaneously. This usually necessitates different control approaches to tackle various objectives, such as guidance, collision avoidance, and cohesion. The guidance schemes, in particular, have long suffered from complex tracking-error dynamics. Furthermore, techniques that are based on linear feedback or output feedback strategies obtained at equilibrium conditions either may not hold or degrade when applied to uncertain dynamic environments. Relying on potential functions, embedded within pre-tuned fuzzy inference architectures, lacks robustness under dynamic disturbances. This thesis introduces two adaptive distributed approaches for the autonomous control of multi-agent systems. The first proposed technique has its structure based on an online fuzzy reinforcement learning Value Iteration scheme which is precise and flexible. This distributed adaptive control system simultaneously targets a number of flocking objectives; namely: 1) tracking the leader, 2) keeping a safe distance from the neighboring agents, and 3) reaching a velocity consensus among the agents. In addition to its resilience in the face of dynamic disturbances, the algorithm does not require more than the agent’s position as a feedback signal. The effectiveness of the proposed method is validated with two simulation scenarios and benchmarked against a similar technique from the literature. The second technique is in the form of an online fuzzy recursive least squares-based Policy Iteration control scheme, which employs a recursive least squares algorithm to estimate the weights in the leader tracking subsystem, as a substitute for the original reinforcement learning actor-critic scheme adopted in the first technique. The recursive least squares algorithm demonstrates a faster approximation weight convergence. The time-invariant communication graph utilized in the fuzzy reinforcement learning method is also improved with time-varying graphs, which can smoothly guide the agents to reach a speed consensus. The fuzzy recursive least squares-based technique is simulated with a few scenarios and benchmarked against the fuzzy reinforcement learning method. The scenarios are simulated in CoppeliaSim for a better visualization and more realistic results.

Jeffrey proposed a graphic representation of DNA sequences using Barnsley's iterative function systems. In spite of further developments in this direction (Oliver et. al, 1993), (Roman-Roldan et. al, 1994), (Li, 1997), the proposed graphic representation of DNA sequences has been lacking a rigorous connection between its spatial scaling characteristics and the statistical characteristics of the DNA sequences themselves. We 1) generalize Jeffrey's graphic representation to accommodate (possibly infinite) sequences over an arbitrary finite number of symbols, 2) establish a direct correspondence between the statistical characterization of symbolic sequences via Renyi entropy spectra and the multifractal characteristics (Renyi generalized dimensions) of the sequences' spatial representations, 3) show that for general symbolic dynamical systems, the multifractal fH-spectra in the sequence space coincide with the fH-spectra on spatial sequence representations. (author's abstract) / Series: Working Papers SFB "Adaptive Information Systems and Modelling in Economics and Management Science"

PIM (Processor-In-Memory) architectures have been proposed in recent years. One major objective of PIM is to reduce the performance gap between the CPU and memory. To exploit the potential benefits of PIM, we designed a statement base parallelizing system ¡VSAGE in [1, 2]. In order to make all processors take the best-fit workload in PIM, iteration base analysis is another research issue in this paper. We extend this system to achieve better performance by devising several comprehensive optimizing techniques, which include IMOP (Intelligent Memory Operation) recognition, tiling for PIM, and a precise mechanism to get workload balance execution schedule. The experimental results are also presented and discussed.

Würzburg, Univ., Diss., 2008

The purpose of this paper is to study two differential equations. A method of approximation by iteration is used to define sequences of functions which converge to solutions of these equations. Some properties of the solutions are proved for general boundary conditions and certain special solutions are studied in detail.

The goal of this thesis is to explore the properties of a certain class of sequences, rigid divisibility sequences, generated by the iteration of certain polynomials whose coefficients are algebraic integers. The main goal is to provide, as far as is possible, a classification and description of those polynomials which generate rigid divisibility sequences.

Companies developing new products have a wide variety of product development (PD) processes from which to choose. Each process offers a different method of iteration to manage risk. Companies must therefore consider the nature and level of risks they face in order to determine the most appropriate iteration and PD process. This paper identifies principles of risk and iteration inherent in product development and then explains how several different PD processes manage risk through iteration. It explains current research on PD decision criteria and concludes by proposing a framework to help companies better select PD processes. / Singapore-MIT Alliance (SMA)

This report explores several applications of iteration and the various connections that can be made to different areas of mathematics. The ties iteration has to the Wada Property, bifurcation diagram, root finding, and applications in geometry are all investigated. Finally, a rationale for incorporating iteration into secondary mathematics courses to support a more robust curriculum is discussed. / text

Paderborn, Universiẗat, Diss., 1989. / Paderborn, Univ. Gesamthochsch., Diss., 1989.

In current economic research, there are many problems that are difficult to solve without powerful computers, unique software, or novel approaches. I wrote this thesis because I believe that a powerful solution technique known as the Riccati Iteration is such a novel approach, and can be applied to complex problems that would otherwise be infeasible to solve. This thesis will demonstrate the power of the Riccati iteration by employing the Riccati iteration with spreadsheet software to solve a difficult dynamic optimization problem - a capital replacement problem posed by Lotfi where multiple objectives have been identified. The Riccati iteration will be shown to be the most practicable method for solving this problem, especially when compared to the Lagrange and Least-Squares solution methods. It is hoped that the demonstration in this thesis is so compelling that others may consider using the Riccati approach in their own research. / Master of Arts