Ph.D., Washington (St. Louis), 1991
OverviewControl, optimization, computation, applications in material and molecular sciences.
My central focus in research, is the mathematics of control theory. especially as applied to new applications arising in the microworld. In addition to the core research in the theory of control and estimation of nonlinear systems, and its interaction with the theory of partial differential equations and exterior differential systems (and their Lie symmetries), I have been involved for the past 5 years in research in chemical physics. The principal thrust here has been the development of systematic design of external laser impulses for femtosecond photochemistry. Once again, since the mathematical basis is control theory and its role in the quantum regime these techniques are applicable to similar areas of application (and have indeed been applied) such as semiconductor heterostructures, inversion of molecular potentials and dipoles. I am currently working on developing algorithms for design of basic logic gates for quantum computation with a single atom or molecule (interacting with an external pulse) as the physical vehicle. Other related research has been in (collaboration with L. R. Hunt) the areas of nonlinear inversion and a version of the stable and unstable manifold theorems for systems interacting with an external input. Our hope is to extend this to say something meaningful about signal processing, filtering, and estimation in a nonlinear context. In addition I am interested in obtaining results on exterior differential systems of varying dimensions for applications to nonlinear partial differential equations with degeneracies.
- Ramakrishna, V. Local solvability of degenerate, overdetermined systems--a control-theoretic perspective. J. Differential Equations. To appear.
- Ramakrishna, V. Controlled invariance for singular distributions. SIAM J. Control Optimization 32:790-807, 1994.
- Updated: November 29, 2007