Uncertainty Quantification, Estimation, and Optimal Control for Stochastic Hybrid Systems on a Manifold
Abstract
Uncertainties are ubiquitous in science and engineering, and they arise from multiple sourcessuch as unmodeled dynamics and parametric uncertainties. Careful characterization of uncertainties is criticalin control and estimation as a decision based on stochastic information can be drastically different fromdeterministic approaches. However, it is often assumed that uncertainties are small and they follow Gaussiandistributions propagated through continuous systems in a linear space. Stochastic information that can beobtained from such standardized uncertainties and regularized dynamics is severely limited.Here, we propose to construct comprehensive computational techniques for stochastic analysis of hybridsystems evolving on a nonlinear configuration manifold, including geometric integration, uncertaintypropagation, model reduction, Bayesian estimation, and stochastic optimal control schemes. In particular,a Fokker–Planck equation that characterizes the evolution of uncertainty distributions over the flow of generalizedstochastic hybrid systems will be formulated on a manifold. Then, it will be solved by using theGalerkin method, utilizing noncommutative harmonic analysis to represent uncertainties on a manifold ina global fashion. The proposed research will provide an intrinsic, global framework for uncertainty propagation,estimation, and stochastic optimization on a large class of complex dynamical systems undergoingnontrivial maneuvers with both continuous stochastic processes and discrete random transitions.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Aug 28, 2018
- Source ID
- FA95501810288
Entities
People
- Taeyoung Lee
Organizations
- Air Force Office of Scientific Research
- George Washington University
- United States Air Force