Application Set Approximation in Optimal Input Design for Model Predictive Control

TL;DR

This paper introduces a computationally efficient method for approximating the set of models satisfying control specifications in optimal input design for MPC, enabling application to more complex plants.

Contribution

It presents a novel approach leveraging the structure of the optimal control problem to reduce computational effort in application set approximation.

Findings

The new method significantly reduces computation time.

It enables application-oriented input design for complex plants.

Numerical evaluation on a distillation control problem demonstrates effectiveness.

Abstract

This contribution considers one central aspect of experiment design in system identification. When a control design is based on an estimated model, the achievable performance is related to the quality of the estimate. The degradation in control performance due to errors in the estimated model is measured by an application cost function. In order to use an optimization based input design method, a convex approximation of the set of models that atisfies the control specification is required. The standard approach is to use a quadratic approximation of the application cost function, where the main computational effort is to find the corresponding Hessian matrix. Our main contribution is an alternative approach for this problem, which uses the structure of the underlying optimal control problem to considerably reduce the computations needed to find the application set. This technique allows the use of applications oriented input design for MPC on much more complex plants. The approach is numerically evaluated on a distillation control problem.