Barrier Functionals for Output Functional Estimation of PDEs
  We propose a method for computing bounds on output functionals of a class of time-dependent PDEs. To this end, we introduce barrier functionals for PDE systems. By defining appropriate unsafe sets and optimization problems, we formulate an output functional bound estimation approach based on barrier functionals. In the case of polynomial data, sum of squares (SOS) programming is used to construct the barrier functionals and thus to compute bounds on the output functionals via semidefinite programs (SDPs). An example is given to illustrate the results. 
Mohamadreza Ahmadi, Giorgio Valmorbida, Antonis Papachristodoulou
math.OC