Wavelets in Control and Optimization

CMS-0510259控制和优化中的小波Tsiotras，Panagiotis摘要在这项研究中，我们提出了应用最近开发的基于小波的方法来解决控制和轨迹优化问题。小波变换在分析信号的时频特性方面的优势在过去的二十年里已经被科学界和工程界所认识。在过去，小波已经成功地用于信号图像处理、信号压缩、去噪等。然而，小波在动力系统控制中的应用还没有得到充分利用。在这方面，小波固有的多分辨率特性，预计将提供上级的数值精度和更快的执行速度为几个航空航天和机械应用，其中的状态敏感性，不同的时间尺度和环境的不确定性，使控制和轨迹生成非常具有挑战性的使用标准的方法。例如，在最佳路径生成方面，小波可以允许环境的多分辨率分解以及自适应网格化（在时间和空间上都是如此），可以用于并行计算机实现，从而在保持数值准确性的同时进一步加快执行时间。自动化车辆和机器改变了我们的生活方式，我们的旅行方式，我们的工作方式，我们的战斗方式，以及我们提供服务或制造产品的方式。自主或半自主导航车辆已成为民用（消防，核废料处理，执法，深海勘探和钻井，运输）和军事（制导导弹，航天器，无人驾驶飞机）应用不可或缺的。 同样，工业中的自主控制系统提高了产量、增强了安全性、减少了浪费，同时提高了最终产品质量并减少了人类操作员的工作量。自动化技术在危险或非常不健康的环境中扮演了替代人类操作员的角色，从而消除了对人类生命的风险。这些趋势将在未来持续下去。自动化，特别是与资讯科技结合后，将继续以更高的水平渗透我们的社会。在这项研究中开发的理论和方法将使人们有可能在这些自主系统的“大脑”中运行高度复杂、优化设计的算法，从而提高其可靠性、性能和故障安全操作。

CMS-0510259Wavelets in Control and OptimizationTsiotras, PanagiotisABSTRACTIn this research we propose to apply recently developed wavelet-based methods to address problems in control and trajectory optimization. The advantages of wavelet transforms in analyzing both the time and frequency properties of a signal have been recognized by the scientific and engineering community over the past two decades. Wavelets have been used with great success in the past for signal image processing, signal compression, denoising, etc. The use of wavelets in control of dynamical systems has not been fully exploited, however. In that respect the multiresolution properties inherent in wavelets are expected to provide superior numerical accuracy and faster execution speeds for several aerospace and mechanical applications, where state sensitivities, diverse time scales and uncertainty of the environment make control and trajectory generation extremely challenging using standard methods. In terms of optimal path generation, for instance, wavelets can allow multiresolution decomposition of the environment, as well as adaptive gridding (both in time and space), which can be exploited for parallel computer implementation, thus further speeding up execution time while preserving numerical accuracy.Automated vehicles and machines have changed the way we live, the way we travel, we work, the way we fight, and the way we offer services or manufacture products. Autonomously or semi-autonomously guided vehicles have become indispensable both for civil (fire fighting, nuclear waste handling, law-enforcement, deep ocean exploration and drilling, transportation) and military (guided missiles, spacecraft, unmanned drones) applications. Similarly, autonomous control systems in industry have increased production, enhanced safety, reduced waste, while at the same time improving final product quality and reducing the workload of human operators. Automation technology has played the role of surrogate human operators in case of hazardous or very unhealthy environments, thus eliminating the risk to human lives. These trends will be sustained in the future. Automation, especially when coupled with information technology, will continue to permeate our society at ever increasing levels. The theory and methodologies developed in this research will make it possible to run highly sophisticated, optimally designed algorithms inside the ``brain'' of these autonomous systems, thus increasing their reliability, performance and fail-safe operation.