Explicit MPC for Parameter Dependent Linear Systems
This work addresses a domain-specific problem in control systems engineering, offering incremental improvements for handling parameter dependencies in explicit MPC.
The paper tackles the complexity of explicit Model Predictive Control for linear systems with design-dependent parameters by proposing two approximation methods that incorporate parameters directly into system matrices, and demonstrates their performance through application to two examples compared to exact implementations.
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.