Modeling and Optimization Strategies for Discretized Differential-Algebraic Systems

Robert Parker, Carnegie Mellon University
Shutterstock Fluid Dynamic Graphic

Nonlinear local optimization is an important tool for engineering research. In particular, nonlinear programs with discretized differential-algebraic (DAE) systems as equality constraints can be used to make optimal operating decisions with solve times that have potential to be used in real-time applications. However, these optimization problems are often difficult to construct, analyze, and converge.

This seminar presents three recent projects that aim to alleviate these difficulties in the context of a chemical looping combustion reactor modeled with IDAES and Pyomo DAE. We first automatically identify differential and algebraic subsystems of the discretized model and identify causes of structural and numerical singularity using algorithms from graph theory. We then analyze the stability of our PDE discretization using newly introduced utilities in Pyomo. Finally, we present an implicit function formulation for optimization of the discretized model that converges more reliably, solving 50% more problem instances without an increase in solve time.