Robust Simulation and Design Using Parametric Interval Methods

A method is presented for guaranteeing robust steady-state operation of chemical processes using a model-based approach, taking into account uncertainty in the model parameters and disturbances in the process inputs. Intractable bilevel optimization formulations have been proposed for this problem in the past. A new approach is presented in which the equality constraints (process model equations) are solved numerically for the process variables as implicit functions of the uncertainty parameters and controls. The problem is then formulated as a semi-infinite program (SIP) constrained only by the performance specifications as semi-infinite inequality constraints. A rigorous algorithm for solving such SIPs is proposed, making no assumptions on convexity, which makes use of the novel developments of parametric interval Newton methods for bounding implicit functions and McCormick relaxations of algorithms. Upper and lower bounding techniques are applied within the Branch & Bound framework. Finite -optimal convergence to the global solution of the SIP is guaranteed with the existence of a Slater point arbitrarily close to a maximizer.