Research Interests of Rafal Goebel

I am a mathematician. My research interests include

convex analysis, non-smooth analysis, and set-valued analysis;
control theory, including optimal control;
applications of convex, nonsmooth, and set-valued analysis to dynamical and control systems;
hybrid dynamical systems and hybrid control systems;
optimization.

Representative work:

convex duality concepts in dynamical systems and optimal control:
- R. Goebel, Duality and uniqueness of convex solutions to stationary Hamilton-Jacobi equations, Transactions of the AMS, Volume 357, 2005.
- R. Goebel, Lyapunov functions and duality for convex processes, R. Goebel, SIAM Journal on Control and Optimization, accepted June 2013.
- R. Goebel and M. Subbotin, Continuous time constrained linear quadratic regulator - convex duality approach, IEEE Transactions on Automatic Control, Volume 52, Issue 5, 2007 .
hybrid dynamical systems / hybrid inclusions:
- R. Goebel, R.G. Sanfelice, and A.R. Teel, Hybrid Dynamical Systems: Modeling, Stability, and Robustness, Princeton University Press, 2012.
- R. Goebel and A.R. Teel, Solutions to hybrid inclusions via set and graphical convergence with stability theory applications, Automatica, Volume 42, Issue 4, 2006.
convex analysis:

R. Goebel, Self-dual smoothing of convex and saddle functions, Journal of Convex Analysis, Volume 15, Number 1, 2008.
E.N. Barron, R. Goebel, and R.R. Jensen, Functions which are quasiconvex under linear perturbations , SIAM Journal on Optimization, Volume 22, Issue 3, 2012.
R. Goebel and R.T. Rockafellar, Local strong convexity and local Lipschitz continuity of the gradient of convex functions, Journal of Convex Analysis, Volume 15, Number 2, 263-270, 2008.
J. Borwein and R. Goebel, Notions of relative interior in Banach spaces, Journal of Mathematical Sciences, Volume 115, Issue 4, 2003.

applications of set-valued analysis to dynamical systems:
- R. Goebel, Set-valued Lyapunov functions for difference inclusions, Automatica,Volume 47, Issue 1, 127-132, 2011
feedback stabilization
- R. Goebel, Stabilizing a linear systems with saturation through optimal control, IEEE Transactions on Automatic Control, Volume 50, Issue 5, 2005.
- C. Prieur, R. Goebel, and A. Teel, Hybrid feedback control and robust stabilization of nonlinear systems, IEEE Transactions on Automatic Control, Volume 52, Issue 11, 2007.