Methodology for robust multi-parametric control in linear continuous-time systems - Sun, Muxin; Villanueva, Mario E.; Pistikopoulos, Efstratios N.; Chachuat, Benoît (Journal of process control, 2019)
•Robust multi-parametric NCO-tracking controllers do not entail a discretization of the continuous-time dynamics.•The robust-counterpart multi-parametric dynamic optimization (mp-DO) problem retains the same complexity as nominal mp-DO.•Data classifiers based on deep learning can accurately describe the critical regions in (nominal or robust) mp-DO.•The methodology is demonstrated for a fluid catalytic cracking (FCC) unit and a chemical reactor cascade. This paper presents an extension of the recent multi-parametric (mp-)NCO-tracking methodology by Sun et al. [Comput. Chem. Eng. 92 (2016) 64–77] for the design of robust multi-parametric controllers for constrained continuous-time linear systems in the presence of uncertainty. We propose a robust-counterpart formulation and solution of multi-parametric dynamic optimization (mp-DO), whereby the constraints are backed-off based on a worst-case propagation of the uncertainty using either interval analysis or ellipsoidal calculus and an ancillary linear state feedback. We address the case of additive uncertainty, and we discuss approaches to dealing with multiplicative uncertainty that retain tractability of the mp-NCO-tracking design problem, subject to extra conservativeness. In order to assist with the implementation of these controllers, we also investigate the use of data classifiers based on deep learning for approximating the critical regions in continuous-time mp-DO problems, and subsequently searching for a critical region during on-line execution. We illustrate these developments with the case studies of a fluid catalytic cracking (FCC) unit and a chemical reactor cascade.