TY  - INPR
A1  - Geiselhart, Roman
A1  - Gielen, Rob H.
A1  - Lazar, Mircea
A1  - Wirth, Fabian R.
T1  - An Alternative Converse Lyapunov Theorem for Discrete-Time Systems
N2  - This paper presents an alternative approach for obtaining a converse Lyapunov theorem for discrete–time systems. The proposed approach is constructive, as it provides an explicit Lyapunov function. The developed converse theorem establishes existence of global Lyapunov functions for globally exponentially stable (GES) systems and semi–global practical Lyapunov functions for globally asymptotically stable systems. Furthermore, for specific classes of sys- tems, the developed converse theorem can be used to establish non–conservatism of a particular type of Lyapunov functions. Most notably, a proof that conewise linear Lyapunov functions are non–conservative for GES conewise linear systems is given and, as a by–product, tractable construction of polyhedral Lyapunov functions for linear systems is attained.
KW  - Ljapunov-Funktion
KW  - stability analysis
KW  - conewise linear systems
KW  - discrete-time systems
KW  - converse Lyapunov theorems
Y1  - 2013
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-78512
ER  - 
TY  - INPR
A1  - Breitenbach, Tim
A1  - Borzì, Alfio
T1  - On the SQH scheme to solve non-smooth PDE optimal control problems
T2  - Numerical Functional Analysis and Optimization
N2  - A sequential quadratic Hamiltonian (SQH) scheme for solving different classes of non-smooth and non-convex PDE optimal control problems is investigated considering seven different benchmark problems with increasing difficulty. These problems include linear and nonlinear PDEs with linear and bilinear control mechanisms, non-convex and discontinuous costs of the controls, L\(^1\) tracking terms, and the case of state constraints.  

The SQH method is based on the characterisation of optimality of PDE optimal control problems by the Pontryagin's maximum principle (PMP). For each problem, a theoretical discussion of the PMP optimality condition is given and results of numerical experiments are presented that demonstrate the large range of applicability of the SQH scheme.
KW  - SQH method
KW  - non-smooth optimization
KW  - Pontryagin maximum principle
KW  - nonconvex optimization
Y1  - 2019
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-180936
N1  - This is an Accepted Manuscript of an article published by Taylor & Francis in Numerical Functional Analysis and Optimization on 27.04.2019, available online: http://www.tandfonline.com/10.1080/01630563.2019.1599911.
ER  -