Abstract
| 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 | |
| State | 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 |
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A delta–sampling verification theorem for discrete–time, possibly discontinuous systems. / Bobiti, R.V.; Lazar, M.
Proceedings of the 18th International Conference on Hybrid Systems: Computation and Control (HSCC '15), 14-16 April 2015, Seattle, Washington. New York : Association for Computing Machinery, Inc, 2015.Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review
TY - GEN
T1 - A delta–sampling verification theorem for discrete–time, possibly discontinuous systems
AU - Bobiti,R.V.
AU - Lazar,M.
PY - 2015
Y1 - 2015
N2 - 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.
AB - 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.
U2 - 10.1145/2728606.2728631
DO - 10.1145/2728606.2728631
M3 - Conference contribution
BT - Proceedings of the 18th International Conference on Hybrid Systems: Computation and Control (HSCC '15), 14-16 April 2015, Seattle, Washington
PB - Association for Computing Machinery, Inc
CY - New York
ER -