Explicit MPC for Parameter Dependent Linear Systems

TL;DR

This paper develops two explicit MPC methods for linear systems with parameters, directly incorporating parameter dependencies into system matrices and proposing approximations to manage increased complexity.

Contribution

It introduces two novel explicit MPC formulations that handle parameter-dependent linear systems by directly embedding parameters into the system matrices.

Findings

Both methods are applied to example systems and their performances are compared.

The proposed approaches effectively manage the complexity introduced by parameter dependencies.

Abstract

This paper presents two explicit Model Predictive Control formulations for linear systems parameterized in terms of design variables. Such parameter dependent behavior commonly arises from operating point dependent linearization of nonlinear systems as well as from variations in mechanical, electrical, or thermal properties associated with material selection in the design of the process or system components. In contrast to explicit MPC approaches that treat design parameter variations and dependencies as disturbances, the proposed methods incorporate the parameters directly into the system matrices in an affine manner. However, explicitly incorporating these dependencies significantly increases the complexity of explicit MPC formulations due to resulting nonlinear terms involving decision variables and parameters. We address this complexity by proposing two approximation methods. Both methods are applied to two examples, and their performances are compared with respect to the exact eMPC implementation.