A Discrete-Time Suboptimal Robust MPC Framework for Systems with Inverse-Proportional Dynamics

This study presents the development and implementation of a robust model predictive control (MPC) strategy for dynamically inverse-proportional systems. Such systems arise frequently in practical settings, particularly in applications involving electronic sensors, among other domains. However, the existing literature lacks a comprehensive and systematic design framework for robust MPC specifically tailored to this class of systems. To address this gap, we realize an inverse-proportional system by employing a Van der Pol oscillator in conjunction with a low-pass filter stage. For the purpose of robust MPC design, a dynamically inverse-proportional system is modeled as a linear perturbed system characterized by a negative gain in the input channel. This formulation is considered within the discrete-time control framework, where a suboptimal control problem is effectively formulated. Furthermore, the explicit realization of an inverse-proportional system enables a rigorous assessment of controller performance in this setting. The effectiveness of the proposed control scheme is supported through a reproducible numerical experiment, which serves as validation of the approach.