Introducing Implicit Tube Model Predictive Control to MPT+: Efficient Design for Large-Scale Systems

As society advances, increasingly complex systems pose new challenges for control engineers. To address these challenges, researchers continually develop state-of-the-art control techniques. This creates a demand for software tools that integrate these advanced methods and allow users to utilize them with ease. In this paper, we aim to enhance the MPT+ toolbox, an extension of the widely used Multi-Parametric Toolbox (MPT), with a novel implicit tube Model Predictive Control (MPC) approach. This approach avoids geometric set operations and enables robust MPC designs for large-scale problems. It will be shown that MPT+ allows users to apply this control strategy within a few lines in a user-friendly manner. Moreover, via a case study, we demonstrate that the implicit tube MPC approach enables us to design robust controllers for more complex systems, which were previously computationally intractable with the commonly used rigid tube MPC methods.