Continuous stirred tank reactors (CSTRs) are strongly nonlinear systems, and uncertainty in their kinetic parameters together with external disturbances makes it difficult to guarantee that the reactor stays close to its intended operating path. This paper presents a robust funnel synthesis framework for uncertain CSTRs, aimed at providing a certificate for safe operation around a nominal reactor trajectory.
The framework combines three steps. First, Koopman lifting is used to construct a linear representation of the reactor dynamics that is suited for control, in an observable space of finite dimension. The lifting is chosen to include the dominant Arrhenius reaction coordinate, while the remaining modelling error of the finite dictionary is explicitly bounded. Second, a sparse polynomial chaos expansion describes how uncertainty in the kinetic parameters affects the identified lifted model, which gives structured matrix uncertainty bounds without relying only on Monte Carlo sampling. Third, these bounds are incorporated into a robust funnel synthesis problem that computes an invariant tube varying in ti me and a feedback law for safe trajectory tracking.
A CSTR case study demonstrates the complete workflow, from Koopman model identification and sparse uncertainty propagation to funnel synthesis and nonlinear validation in closed loop. The sparse polynomial chaos representation captures the dominant parametric dependence of the lifted model using only a small active basis. In the 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 assumptions on the residuals of the Koopman model and of the polynomial chaos expansion.
The results indicate that Koopman based lifted modelling, combined with sparse uncertainty quantification and robust funnel synthesis, provides a promising route towards safe control of nonlinear process systems that takes uncertainty into account.
The study was carried out at the Institute of Control Systems at Hamburg University of Technology within the Collaborative Research Centre CRC 1615 (SMART Reactors).
Srimanta Santra (2026). Koopman-Polynomial-chaos funnel synthesis for safe control of uncertain CSTRs. Journal of Process Control 166, 103828.
