Robust optimization of periodically operated nonlinear uncertain processes

TL;DR

This paper introduces a robust optimization method for periodically operated nonlinear systems with uncertain parameters, ensuring stability and economic performance through bifurcation-based constraints.

Contribution

It develops a general approach to incorporate stability constraints into nonlinear programming for uncertain, oscillating processes, demonstrated on chemical reaction systems.

Findings

Stability constraints can be integrated into nonlinear programming.

Optimized chemical systems maintain stability under uncertainty.

Method ensures economic performance with guaranteed stability.

Abstract

We present a method for determining optimal modes of operation for autonomously oscillating systems with uncertain parameters. In a typical application of the method, a nonlinear dynamical system is optimized with respect to an economic objective function with nonlinear programming methods, and stability is guaranteed for all points in a robustness region around the optimal point. The stability constraints are implemented by imposing a lower bound on the distance between the optimal point and all stability boundaries in its vicinity, where stability boundaries are described with notions from bifurcation theory. We derive the required constraints for a general class of periodically operated processes and show how these bounds can be integrated into standard nonlinear programming methods. We present results of the optimization of two chemical reaction systems for illustration.