University of Freiburg, IMTEK, Systemtheorie
Tuesday, December 15, 2015, 11:00
Room 01-012, Georges-Köhler-Allee 102, Freiburg 79110, Germany
The talk reviews numerical approaches to approximate the propagation of uncertainty in nonlinear dynamic systems in a conservative fashion. We review and extend results from linear system theory and discuss extensions to the case of nonlinear systems that satisfy Lipschitz bounds on their nonlinearity. We present linearization based approaches as a particularly useful heuristic. Their computational efficiency is significantly affected by the way derivatives are generated, and we discuss the advantages and disadvantages of forward mode, reverse mode, and Lyapunov matrix based approaches. We finally make a connection between robust optimization and stability optimization and show how to solve periodic stability optimization problems for nonlinear systems with parameterized feedback policies numerically by use of the Lyapunov matrix based approach.
The talk presents joint work with Boris Houska, Joris Gillis and Greg Horn.