Wavelets in Control and Optimization

CMS-0510259小波在控制和优化中的应用在这项研究中，我们建议应用最近发展起来的基于小波的方法来解决控制和轨迹优化中的问题。在过去的二十年里，小波变换在分析信号的时间和频率特性方面的优势已经得到了科学界和工程界的认可。小波在过去用于信号图像处理、信号压缩、去噪等方面已经取得了巨大的成功。然而，小波在动态系统控制中的应用还没有得到充分的开发。在这方面，小波固有的多分辨率特性有望为一些航空航天和机械应用提供更高的数值精度和更快的执行速度，在这些应用中，状态敏感性、不同的时间尺度和环境的不确定性使得使用标准方法进行控制和轨迹生成极具挑战性。例如，在最优路径生成方面，小波可以对环境进行多分辨率分解，以及可用于并行计算机实现的自适应网格(在时间和空间上)，从而在保持数值精度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、旅行方式、工作方式、战斗方式以及我们提供服务或制造产品的方式。自动或半自动制导车辆已成为民用(消防、核废料处理、执法、深海勘探和钻探、运输)和军事(制导导弹、航天器、无人驾驶飞机)应用中不可或缺的工具。同样，工业中的自主控制系统增加了产量，增强了安全性，减少了浪费，同时提高了最终产品质量，减少了人工操作员的工作量。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，特别是当与信息技术相结合时，将继续以越来越高的水平渗透到我们的社会中。这项研究开发的理论和方法将使在这些自主系统的“大脑”内运行高度复杂的、优化设计的算法成为可能，从而提高它们的可靠性、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.