Name
Abstract | ||
|---|---|---|
We study the safety verification problem for a class of distributed parameter systems described by partial differential equations (PDEs), i.e., the problem of checking whether the solutions of the PDE satisfy a set of constraints at a particular point in time. The proposed method is based on an extension of barrier certificates to infinite-dimensional systems. In this respect, we introduce barrier functionals, which are functionals of the dependent and independent variables. Given a set of initial conditions and an unsafe set, we demonstrate that if such a functional exists satisfying two (integral) inequalities, then the solutions of the system do not enter the unsafe set. Therefore, the proposed method does not require finite-dimensional approximations of the distributed parameter system. Furthermore, for PDEs with polynomial data, we solve the associated integral inequalities using semi-definite programming (SDP) based on a method that relies on a quadratic representation of the integrands of integral inequalities. The proposed method is illustrated through examples. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1016/j.sysconle.2017.08.002 | Systems & Control Letters |
Keywords | Field | DocType |
Safety verification,Barrier certificates,Sum-of-Squares programming,Distributed parameter systems | Discrete mathematics,Mathematical optimization,Polynomial,Quadratic equation,Approximations of π,Variables,Distributed parameter system,Partial differential equation,Mathematics | Journal |
Volume | ISSN | Citations |
108 | 0167-6911 | 1 |
PageRank | References | Authors |
0.36 | 19 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Mohamadreza Ahmadi | 1 | 35 | 7.12 |
| Giorgio Valmorbida | 2 | 104 | 16.87 |
| Antonis Papachristodoulou | 3 | 990 | 90.01 |