Abstract
This paper considers the problem of safety verification for discrete-time, possibly discontinuous dynamical systems. Typical solutions rely on finding invariant sets or Lyapunov functions and require solving optimization problems, which suffer from scalability and numerical solvers issues. Recently, a d-sampling method for verifying invariance for Lipschitz continuous dynamics was proposed, which does not make use of optimization. In this work we present a d-sampling verification theorem that extends the previous result to general discrete-time, possibly discontinuous dynamics. This opens up the application of d-sampling verification to hybrid systems. Moreover, this paper proposes verification of stability on a set by jointly verifying (finite-step) Lyapunov type functions on an annulus with a (finite-step) Lyapunov function on the inner hole. We further indicate that d-sampling can also be used to verify Lyapunov conditions on the annulus. Lastly, we employ finite-step invariant sets and finite-step Lyapunov functions, respectively, together with d-sampling to achieve more practical safety verification methods.
Original language | English |
---|---|
Title of host publication | Proceedings of the 18th International Conference on Hybrid Systems: Computation and Control (HSCC '15), 14-16 April 2015, Seattle, Washington |
Place of Publication | New York |
Publisher | Association for Computing Machinery, Inc |
DOIs | |
Publication status | Published - 2015 |
Event | 18th International Conference on Hybrid Systems: Computation and Control (HSCC 2015) - Seattle, United States Duration: 14 Apr 2015 → 16 Apr 2015 Conference number: 18 http://ljk.imag.fr/hscc2015/ |
Conference
Conference | 18th International Conference on Hybrid Systems: Computation and Control (HSCC 2015) |
---|---|
Abbreviated title | HSCC 2015 |
Country | United States |
City | Seattle |
Period | 14/04/15 → 16/04/15 |
Internet address |