Abstract
This paper develops a new sampling-based method for stability verification of piecewise continuous nonlinear systems via Lyapunov functions. Depending on the nonlinear system dynamics, the candidate Lyapunov function and the set of states of interest, verifying stability requires solving complex, possibly non-convex or infeasible optimization problems. To avoid such problems, the proposed approach firstly distributes the verification of Lyapunov's inequality on a finite sampling of a bounded set of states of interest. Secondly, it extends the validity of Lyapunov's inequality to an infinite, bounded set of states by automatically exploiting local continuity properties. A sampling-based method for estimating the domain of attraction (DOA) via level sets of a validated Lyapunov function is also presented. Efficient state-space exploration is achieved using multi-resolution sampling and hyper-rectangles as basic sampling blocks. The operations that need to be performed for each sampling point in the state-space can be carried out in parallel, which improves scalability. The proposed methodology is illustrated for various benchmark examples from the literature.
| Original language | English |
|---|---|
| Pages (from-to) | 3659-3674 |
| Journal | IEEE Transactions on Automatic Control |
| Volume | 63 |
| Issue number | 11 |
| DOIs | |
| Publication status | Published - 1 Nov 2018 |
Fingerprint
Keywords
- Direction-of-arrival estimation
- Estimation
- Level set
- Lyapunov methods
- Nonlinear systems
- Optimization
- Stability analysis
Cite this
}
Automated sampling-based stability verification and DOA estimation for nonlinear systems. / Bobiti, R.V.; Lazar, M.
In: IEEE Transactions on Automatic Control, Vol. 63, No. 11, 01.11.2018, p. 3659-3674.Research output: Contribution to journal › Article › Academic › peer-review
TY - JOUR
T1 - Automated sampling-based stability verification and DOA estimation for nonlinear systems
AU - Bobiti, R.V.
AU - Lazar, M.
PY - 2018/11/1
Y1 - 2018/11/1
N2 - This paper develops a new sampling-based method for stability verification of piecewise continuous nonlinear systems via Lyapunov functions. Depending on the nonlinear system dynamics, the candidate Lyapunov function and the set of states of interest, verifying stability requires solving complex, possibly non-convex or infeasible optimization problems. To avoid such problems, the proposed approach firstly distributes the verification of Lyapunov's inequality on a finite sampling of a bounded set of states of interest. Secondly, it extends the validity of Lyapunov's inequality to an infinite, bounded set of states by automatically exploiting local continuity properties. A sampling-based method for estimating the domain of attraction (DOA) via level sets of a validated Lyapunov function is also presented. Efficient state-space exploration is achieved using multi-resolution sampling and hyper-rectangles as basic sampling blocks. The operations that need to be performed for each sampling point in the state-space can be carried out in parallel, which improves scalability. The proposed methodology is illustrated for various benchmark examples from the literature.
AB - This paper develops a new sampling-based method for stability verification of piecewise continuous nonlinear systems via Lyapunov functions. Depending on the nonlinear system dynamics, the candidate Lyapunov function and the set of states of interest, verifying stability requires solving complex, possibly non-convex or infeasible optimization problems. To avoid such problems, the proposed approach firstly distributes the verification of Lyapunov's inequality on a finite sampling of a bounded set of states of interest. Secondly, it extends the validity of Lyapunov's inequality to an infinite, bounded set of states by automatically exploiting local continuity properties. A sampling-based method for estimating the domain of attraction (DOA) via level sets of a validated Lyapunov function is also presented. Efficient state-space exploration is achieved using multi-resolution sampling and hyper-rectangles as basic sampling blocks. The operations that need to be performed for each sampling point in the state-space can be carried out in parallel, which improves scalability. The proposed methodology is illustrated for various benchmark examples from the literature.
KW - Direction-of-arrival estimation
KW - Estimation
KW - Level set
KW - Lyapunov methods
KW - Nonlinear systems
KW - Optimization
KW - Stability analysis
UR - http://www.scopus.com/inward/record.url?scp=85040966101&partnerID=8YFLogxK
U2 - 10.1109/TAC.2018.2797196
DO - 10.1109/TAC.2018.2797196
M3 - Article
AN - SCOPUS:85040966101
VL - 63
SP - 3659
EP - 3674
JO - IEEE Transactions on Automatic Control
JF - IEEE Transactions on Automatic Control
SN - 0018-9286
IS - 11
ER -