A Barrier Certificate Approach to the Verification of the Safe Operation of a Chemical Reactor

Abstract

In industrial practice, extensive simulations are performed in order to analyse the safety and the correct operation of controlled chemical processes. One aspect of verifying the safe operation is to prove that the states of the system stay within a safe region for a certain set of inputs or disturbances which is the main theme of this paper. Recently, a rigorous method for this type of verification problem has been proposed which makes use of Barrier Certificates for verifying whether an undesired set of states can be reached. If the system dynamics can be described in polynomial form, the safety of the system can be proven algorithmically. The determination of a barrier certificate is a sum-of-squares (SOS) problem which can further be transformed into a non-convex Bilinear Matrix Inequality (BMI) problem. This paper deals with proving the safety of a Continuously Stirred Tank Reactor (CSTR), a non-linear system, using barrier certificates. Uncertainties are represented by a bounded disturbance acting on the system. Safety is explicitly proven for a convex set of initial conditions and a non-convex unbounded unsafe set. Two situations are considered, the uncontrolled plant and the closed-loop system with a state-feedback controller. For the solution of the BMI problem, three different numerical approaches are compared. It turned out that solving the non-convex BMI problem directly is more efficient than solving it using the convex iterative approach.