Robust adaptive model predictive control for guaranteed fast and accurate stabilization in the presence of model errors

Abstract

AbstractNumerous control applications, including robotic systems such as unmanned aerial vehicles or assistive robots, are expected to guarantee high performance despite being deployed in unknown and dynamic environments where they are subject to disturbances, unmodeled dynamics, and parametric uncertainties. The fast feedback of adaptive controllers makes them an effective approach for compensating for disturbances and unmodeled dynamics, but adaptive controllers seldom achieve high performance, nor do they guarantee state and input constraint satisfaction. In this article we propose a robust adaptive model predictive controller for guaranteed fast and accurate stabilization in the presence of model uncertainties. The proposed approach combines robust model predictive control (RMPC) with an underlying discrete‐time adaptive controller. We refer to this combined controller as an RMPC‐ controller. The adaptive controller forces the system to behave close to a linear reference model despite the presence of parametric uncertainties. However, the true dynamics of the adaptive controlled system may deviate from the linear reference model. In this work we prove that this deviation is bounded and use it as the modeling error of the linear reference model. We combine adaptive control with an RMPC that leverages the linear reference model and the modeling error. We prove stability and recursive feasibility of the proposed RMPC‐. Furthermore, we validate the feasibility, performance, and accuracy of the proposed RMPC‐ on a stabilization task in a numerical experiment. We demonstrate that the proposed RMPC‐ outperforms adaptive control, robust MPC, and other baseline controllers in all metrics.