DynSyst_Special_Topics: Convex Optimization Based Approach for High Fidelity Uncertainty Propagation Through Nonlinear Dynamic Systems

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The main focus of this research work is on the problem of accurate uncertainty propagation through nonlinear dynamical systems with stochastic forcing term and the design of data assimilation algorithms to determine optimal and multi-hypothesis estimates of the actual physical phenomenon. A main feature of the proposed research work is to pose the uncertainty evolution problem as a convex optimization problem with guaranteed convergence. The Fokker-Planck-Kolmogorov equation (FPKE) and Chapman-Kolmogorov equation (CKE) will be used to determine evolution of state pdf due to probabilistic uncertainty in initial or boundary conditions, model parameters and forcing function. By accurately characterizing the uncertainty associated with both process and measurement models, the proposed research offers systematic design of low-complexity data assimilation algorithms with significant improvement in nominal performance. The proposed research effort will focus on demonstrating, through rigorous analysis, simulation and design, the applicability and feasibility of these new ideas in accurate forecasting of complex physical phenomenon such as the dispersion of toxic material through atmosphere. Release of hazardous material from one or multiple source locations creates a plume, which is diffused and transported by local meteorological conditions. Any model used to represent the dispersion of a pollutant is a reflection of numerous assumptions and simplifications to permit determination of a tractable model. The uncertainties resulting from the lack of knowledge of local meteorological conditions or numerous assumptions in the modeling process can have a profoundly detrimental effect on the accurate estimate of the toxic plume. The application of the proposed methodologies to the dispersion of toxic material through the atmosphere will provide governmental agencies such as EPA or DHS means to control or monitor the emission of harmful air pollutants.An extensive plan to integrate the research plan into an educational and outreach plan will be put in place that involves graduate, undergraduate as well as high-school students and under-represented minorities in science and engineering fields