(705h) Economic Linear Optimal Control with Model Uncertainty

Authors: 
Chmielewski, D. J., Illinois Institute of Technology
Zhang, J., Illinois Institute of Technology
This work investigates how to address box-type uncertainties in Economic Linear Optimal Control (ELOC). We propose two approaches, Robust ELOC for when the uncertainty is completely unknown and Linear Parameter-Varying (LPV) ELOC for when uncertainty can be measured in real time. In Robust ELOC, two types of problem formulations are put forward, Robust ELOC with nominal steady-state model and Robust ELOC with uncertain steady-state model, both of which are developed using a single parameter-independent quadratic Lyapunov function. For Linear Parameter-Varying ELOC, two types of problem formulations are also presented: ELOC+LPV using a single parameter-independent quadratic Lypunov function and ELOC+LPV using a parameter-dependent Lyapunov function. In all cases, the infinite number of conditions that need to be satisfied are reduced to a finite set of constraints. The resulting problem formulations of the first type of Robust ELOC and the both types of ELOC+LPV problems have similar structure to the ELOC and can be solved globally by employing the generalized Benders decomposition [1], while the second type of Robust ELOC is in a form of max-min optimization and can be solved locally using
fmincon.

1. Zhang, J. B.P. Omell, and D.J. Chmielewski, "On the Tuning of Predictive Controllers: Application of Generalized Benders Decomposition to the ELOC Problem," Comp. Chem. Eng., 82, pp 105-114 (2015).