Stochastic Analysis and Control of Transonic Helicopter Aerodynamics and Supersonic Projectiles

The main goal of this project is to develop a systematic mathematical theory for the robust real time feedback control and stochastic analysis of unsteady transonic aerodynamics of helicopter rotor blades, supersonic ballistic projectiles and propagation of blast waves in the presence of adverse external disturbances. The proposed work builds upon similar scientific advances by the principal investigator in the context of incompressible fluid dynamics, magneto-hydrodynamics and combustion models during the past two decades under ONR, DARPA and ARO sponsorship. The gas dynamic models to be used in the research will be either the Euler equations or the quasi- linear unsteady potential equations. These nonlinear hyperbolic or elliptic-hyperbolic type mixed equations are subjected to additive and multiplicative external disturbances modeled as Gaussian, Poisson and Levy type noise forces. Main results to be expected are mathematical characterization of entropy solutions for stochastic hyperbolic systems of conservation laws, state estimation and feedback control analysis as well as assessment of the impact of noise in controlled and uncontrolled aerodynamic flows of the above type. The outcomes of this research will be expected to impact a number of other subjects of importance to the Army such as combustion control and multiphase fluid dynamics. Random free stream velocities and boundary conditions will be incorporated in to the deterministic aerodynamic code developed by the principal investigator for supersonic cones at angle of attack and also in the a new code to be developed for the stochastic transonic small disturbance equation to gain further insights in to the theoretical work. A unique aspect of this research is the close interactions and connections.