Koopman–Polynomial-chaos funnel synthesis for safe control of uncertain CSTRs
Publikationstyp
Journal Article
Date Issued
2026-08-16
Sprache
English
Journal
Volume
166
Article Number
103828
Citation
Journal of Process Control 166: 103828 (2026)
Publisher DOI
Scopus ID
Publisher
Elsevier
This paper presents a robust funnel synthesis framework for uncertain continuous stirred tank reactors (CSTRs), aimed at providing a certificate for safe operation around a nominal reactor trajectory. First, Koopman lifting is used to construct a control-oriented linear representation of the reactor dynamics in a finite-dimensional observable space. The lifting is chosen to include the dominant Arrhenius reaction coordinate, while the remaining finite dictionary modelling error is explicitly bounded. Second, sparse polynomial chaos expansion (sparse-PCE) is used to describe how uncertainty in the kinetic parameters affects the identified lifted model. This gives structured matrix uncertainty bounds without relying only on Monte Carlo sampling for bound construction. Third, these uncertainty bounds are incorporated into a robust funnel synthesis problem that computes a time-varying invariant tube and a feedback law for safe trajectory tracking. A CSTR case study is used to demonstrate the complete workflow, including Koopman model identification, sparse uncertainty propagation, funnel synthesis, and nonlinear closed-loop validation. The results show that the sparse polynomial chaos representation captures the dominant parametric dependence of the lifted model using only a small active basis. In the reported reduced projected implementation, all sampled admissible nonlinear Monte Carlo trajectories remain inside the projected funnel under bounded kinetic uncertainty and disturbances, subject to the stated Koopman residual and sparse-PCE residual assumptions. The results indicate that Koopman-based lifted modelling, when combined with sparse uncertainty quantification and robust funnel synthesis, provides a promising route towards safe and uncertainty-aware control of nonlinear process systems.
Subjects
Continuous stirred tank reactor
Differential linear matrix inequalities (DLMI)
Funnel synthesis
Koopman operator
Robust control
Sparse polynomial chaos expansion
DDC Class
620: Engineering