Robust Optimal Estimation and Control for Dynamic Systems with Additive Heavy-Tailed Uncertainty for Aerospace Applications
Abstract
The Gaussian probability density function (pdf), also known as the bell-shaped curve, has been widely used in engineering and financial algorithms to process data in dynamic systems. The Gaussian pdf, however, does not provide an accurate representation of many physical random processes. Unlike the rapidly decaying tail of the Gaussian pdf, many physical systems encountered in nature and engineering have been found to follow heavy-tailed distributions. Heavy-tailed distributions have been found to more appropriately characterize phenomena in aerospace systems (i.e. radar, sonar, air turbulence, adversarial motion) than the Gaussian pdf does. However, current estimation, control, and data processing algorithms almost solely rely on the Gaussian pdf assumption, despite their setbacks, as they lead to easy, tractable, and real-time solutions. To address this issue, we have proposed a paradigm shift with new robust stochastic optimal estimators and controllers that use the heavy-tailed Cauchy and lighter-tailed Laplace pdfs. These algorithms are recursive and analytic and can adapt to impulsive data, making them far richer in structure than their Gaussian counterparts. Although they may be more computationally intense, they offer a more accurate representation of physical random processes with heavy-tailed distributions. Therefore, these estimators are particularly effective in capturing impulsive noises. Recent focused effort has been on the real-time computational efficiency, speed, and stability of the Cauchy estimator. A three year study to develop estimation and control algorithms for systems with additive Cauchy and Laplace uncertainties will focus on their fundamental structure; the development of new stochastic control laws based on the expected value of new cost criteria with respect to their conditional pdf; demonstrate the stochastic stability and robustness of these estimators and controllers; advance the computational efficiency of these schemes by improved numerical algorithms and distributed computation; and implement these algorithms on aerospace problems of interest to the Air Force.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Feb 06, 2025
- Source ID
- FA95502410161
Entities
People
- Jason Speyer
Organizations
- Air Force Office of Scientific Research
- United States Air Force
- University of California, Los Angeles