Seminar on Convex Optimization for Dynamical Systems (FAU Summer Semester 2024)
Date:
This presentation occurred for the “Convex Optimization for Dynamical Systems” master’s seminar at Frierich-Alexander Universität Erlangen-Nürnberg.
Abstract:
Region of Attraction (ROA) estimation problems yield interesting optimization approaches when considering polynomial dynamics. In this study, a method presented in [2] is shown, providing an outer approximation to the ROA, solving a Polynomial Optimization problem, induced by occupation measures, approximating an initial infinite dimensional problem with a hierarchy of finite dimensional linear matrix inequalities, with convergence for an arbitrarily large polynomial degree.
Report link: Report_ConvexOptiDynSys_Bloess.pdf
References
[1] ApS, M. Mosek optimizer api for julia.
[2] Henrion, D., and Korda, M. Convex computation of the region of attraction of polynomial control systems. IEEE Transactions on Automatic Control 59 (08 2012).
[3] Hirsch, M. W. Differential topology, vol. 33. Springer Science & Business Media, 2012.
[4] O’Meara, O. T. Introduction to quadratic forms, vol. 117. Springer, 2013.
[5] Putinar, M. Positive polynomials on compact semi-algebraic sets. Indiana University Mathematics Journal 42, 3 (1993), 969–984.