Process Performance Verification Using Viability Theory

The development of efficient methods for process performance verification has drawn a lot of attention in the research community. Viability theory is a mathematical tool to identify the trajectories of a dynamical system which remains in a constraint set. In this paper, viability theory is investigated for this purpose in the case of nonlinear processes that can be represented in Linear Parameter Varying (LPV) form. In particular, verification algorithms based on the use of invariance and viability kernels and capture basin are proposed. The difficulty with the application of this theory is the computation of these sets. A Lagrangian method has been used to approximate these sets. Because of simplicity and efficient computations, zonotopes are adopted for set representation. Two new sets called Safe Work Area (SWA) and Required Performance (RP) are defined and an algorithm is proposed to use these concepts for the verification purpose. Finally, two application examples based on well-known case studies, a two-tank system and PH neutralization plant, are provided to show the effectiveness of the proposed method.