Tube-Based Model Predictive Control Based on Constrained Zonotopes

This paper introduces a tube-based Model Predictive Control (MPC) formulation for high-order uncertain Linear Parameter-Varying (LPV) systems, utilizing efficient set representations. Initially, a feedback gain is designed based on a new set of LMIs in order to compensate the mismatch between the uncertain LPV system and a nominal model. Thereafter, aiming to reduce the computational cost, we propose an offline computation of the reachable set based on zonotopes and considering the feedback gain previously computed. In addition, from the feedback gain, the reachable set, and considering the admissible state and control sets as constrained zonotopes, we ensures the existence of the nominal control and state sets to be used within the nominal MPC. Lastly, a novel MPC formulation based on constrained zonotopes is developed to enhance the computational cost of the entire methodology. Accordingly, the optimal control problem is redesigned as a function of the constrained zonotope structure. We evaluate the performance of our proposed approach controlling a tiltrotor unmanned aerial vehicle (UAV) carrying a suspended load, a high-order system with twenty-four states, and fast dynamic behavior. A hardware-in-the-loop (HIL) framework is used to carry out the experiments, where control algorithms are implemented on an embedded computer, and the dynamics of the tiltrotor UAV with suspended load are emulated using the high-fidelity ProVANT Simulator.