Safety verification for distributed parameter systems using barrier functionals

Mohamadreza Ahmadi (1) , Giorgio Valmorbida (2) , Antonis Papachristodoulou (3)

1 University of Texas at Austin [Austin]
2 L2S - Laboratoire des signaux et systèmes
3 Department of Engineering Science

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.

Mots clés: Safety Verification; Barrier Certificates; Sum-of-Squares Programming; Distributed Parameter Systems

Domaines: Automatique / Robotique

Mohamadreza Ahmadi, Giorgio Valmorbida, Antonis Papachristodoulou. Safety verification for distributed parameter systems using barrier functionals. Systems and Control Letters, 2017, 108, pp.33 - 39. ⟨10.1016/j.sysconle.2017.08.002⟩. ⟨hal-01721707⟩