Research Summaries

Back Stochastic Analysis and Control of Compressible Flow with General Levy Noise

Fiscal Year 2014
Division Research & Sponsored Programs
Department Center for Decision, Risk, Controls & Signals Intelligence
Investigator(s) Sritharan, Sivaguru S.
Sponsor Army Research Office (Army)
Summary In this project we will extend our previous work on stochastic control and estimation of fluid dynamics to a wide range of compressible flows and closely related nonlinear physics subject to abrupt noise disturbances. Through suitable transformations a surprising variety of important Army problems can be brought to a unified framework of nonlinear partial differential equations of fluid dynamic type. We will address in particular (1) compressible and incompressible flow past single and multiple moving and rotating obstacles with the specific goal of shedding light in to the type of problems that arise in U.S. Army's unmanned and autonomous systems programs including helicopter aerodynamics; (2) control and stochastic analysis of High Energy Laser Propagation in turbulence with thermal blooming; (3) Control of Free Electron and Solid State Lasers; (4) Control and stochastic analysis of quantum fluid dynamics. Moreover, we will also study a range of noise models including space-time fractional (and conventional) Levy processes as well as stable processes. Survivability, lethality and reliability requirements of manned and unmanned (autonomous) system, helicopters blade aerodynamics and also High Energy Laser (HEL) weapons of the U.S. Army's combat arsenal pose exciting new and mathematically sophisticated research challenges to infinite dimensional control and systems theory. In the proposed research we will develop nonlinear estimation and control techniques incorporating physics based state space models to address such problems. As a part of this program we will develop new theories for (I) stochastic compressible Navier-Stokes equation in domains exterior to moving and rotating bodies subject to general Levy noise; (2) stochastic compressible fluid dynamics with quantum pressure terms which are obtained by applying Madelung transformation to stochastic nonlinear Schrodinger equation describing Laser propagation in turbulent media; and (3) stochastic Maxwell-Dirac equations describing the dynamics of Free Electron Lasers; and (4) stochastic "functional" Navier-Stokes equation with hereditary viscosity describing average turbulent fields. We then build nonlinear filtering and feedback controller design for system identification and active management. This research builds upon more than two decades of ground breaking work by the principal investigator on control and stochastic analysis of fluid dynamics with the consistent support of the department of defense. A unique component of this project is the education as well as MS and PhD thesis supervision of US Army and other US military officers.
Publications Publications, theses (not shown) and data repositories will be added to the portal record when information is available in FAIRS and brought back to the portal
Data Publications, theses (not shown) and data repositories will be added to the portal record when information is available in FAIRS and brought back to the portal