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.