Offline Robust Model Predictive Control Using Linear Matrix Inequality-based Optimization

Abstract

This paper proposes a new approach to handle offline robust model predictive control (RMPC) using linear matrix inequality-based (LMI-based) optimization. To address system parameter uncertainties, we consider uncertain parameters within a polytope. A set of LMIs is then utilized to determine an optimal controller gain based on the polytope. The main contribution of this paper is establishing the upper bound of the cost function as a quadratic function of the state variable. It opens the opportunity to obtain the optimal controller gain in an offline environment, significantly reducing the computation burden. With this approach, robust stability of a closed-loop system can be achieved with a broad range of model uncertainties. Furthermore, the input and output constraints are enforced to ensure the system's operation in a specific range. To validate the efficacy of the proposed approach, our simulation results are provided and compared with the existing method.