Wavelets in Control and Optimization

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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.