Data‐enabled predictive control for quadcopters

Abstract

We study the application of a data‐enabled predictive control (DeePC) algorithm for position control of real‐world nano‐quadcopters. The DeePC algorithm is a finite‐horizon, optimal control method that uses input/output measurements from the system to predict future trajectories without the need for system identification or state estimation. The algorithm predicts future trajectories of the quadcopter by linearly combining previously measured trajectories (motion primitives). We illustrate the necessity of a regularized variant of the DeePC algorithm to handle the nonlinear nature of the real‐world quadcopter dynamics with noisy measurements. Simulation‐based analysis is used to gain insights into the effects of regularization, and experimental results validate that these insights carry over to the real‐world quadcopter. Moreover, we demonstrate the reliability of the DeePC algorithm by collecting a new set of input/output measurements for every real‐world experiment performed. The performance of the DeePC algorithm is compared to Model Predictive Control based on a first‐principles model of the quadcopter. The results are demonstrated with a video of successful trajectory tracking of the real‐world quadcopter.

Linear tracking MPC for nonlinear systems Part II: The data-driven case

“…Remark 1. Inspired by [11], the regularization of α(t) is not w.r.t. zero but depends on α sr since we want to track the generally non-zero equilibrium (u sr , y sr ) and due to the affine system dynamics (cf.…”

“…Different contributions have analyzed such schemes in the presence of noise with regard to open-loop robustness [5], [6], [7], [8] or closed-loop stability/robustness both with [9] and without [10] terminal ingredients. Although different successful applications to complex nonlinear systems have been reported in the literature, see, e.g., [11], [12], providing theoretical guarantees of data-driven MPC for nonlinear systems remains a widely open research problem. The literature contains various extensions and variations of [2] for specific classes of nonlinear systems such as Hammerstein and Wiener systems [13], Volterra systems [14], polynomial systems [15], [16], systems with rational dynamics [17], flat systems [18], and linear parameter-varying systems [19].…”

Quadratic Regularization of Data-Enabled Predictive Control: Theory and Application to Power Converter Experiments

“…Rather than a parametric model, in the spirit of the Fundamental Lemma, the DeePC algorithm relies only on input/output data measured from the unknown system to predict future trajectories and compute safe and optimal control inputs for the system. The DeePC algorithm has been successfully applied in many scenarios, including power systems (Huang et al, 2019a,b), motor drives (Carlet et al, 2020), and quadcopters (Elokda et al, 2019). It has been frequently observed that regularization terms are very important to ensure good performance when the system is subjected to disturbances.…”

Robust stability analysis of a simple data-driven model predictive control approach

“…For instance, recent work in [27] shows that the open-loop optimal control problem for data-driven MPC as considered in this paper is a convex relaxation of the corresponding problem in the indirect approach. Additionally, direct data-driven MPC and the indirect approach have been compared for practical applications, e.g., in [28]. An in-depth theoretical comparison of closed-loop properties for the two approaches is an interesting direction for future research.…”