Peter Giesl 4-Accepted-9.10.20.pdf (27.51 MB)
Computing complete Lyapunov functions for discrete-time dynamical systems
journal contribution
posted on 2023-06-09, 21:51 authored by Peter GieslPeter Giesl, Zachary Langhorne, Carlos Argáez, Sigurdur HafsteinA complete Lyapunov function characterizes the behaviour of a general discrete-time dynamical system. In particular, it divides the state space into the chain-recurrent set where the complete Lyapunov function is constant along trajectories and the part where the flow is gradient-like and the complete Lyapunov function is strictly decreasing along solutions. Moreover, the level sets of a complete Lyapunov function provide information about attractors, repellers, and basins of attraction. We propose two novel classes of methods to compute complete Lyapunov functions for a general discrete-time dynamical system given by an iteration. The first class of methods computes a complete Lyapunov function by approximating the solution of an ill-posed equation for its discrete orbital derivative using meshfree collocation. The second class of methods computes a complete Lyapunov function as solution of a minimization problem in a reproducing kernel Hilbert space. We apply both classes of methods to several examples.
History
Publication status
- Published
File Version
- Accepted version
Journal
Discrete and Continuous Dynamical Systems Series BISSN
1531-3492Publisher
American Institute of Mathematical SciencesExternal DOI
Issue
1Volume
26Page range
299-336Pages
32.0Department affiliated with
- Mathematics Publications
Full text available
- Yes
Peer reviewed?
- Yes
Legacy Posted Date
2020-10-12First Open Access (FOA) Date
2022-01-02First Compliant Deposit (FCD) Date
2020-10-09Usage metrics
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