Robust Data-Based Model Predictive Control for Nonlinear Constrained Systems

Learning-Based Model Predictive Control: Toward Safe Learning in Control

“…The methods generally suffer from the nonsmooth function estimate f (illustrated in Figure 1), which makes numerical optimization in an MPC scheme challenging. Ideas for smoothing the predictions have been proposed that use either a convex combination resulting from a number of data points surrounding the query point (68,69) or a weighted sum of basis functions (70), both of which improve the computational properties while maintaining favorable theoretical guarantees.…”

A Computationally Efficient Robust Model Predictive Control Framework for Uncertain Nonlinear Systems

“…using Gaussian Processes (GPs) [15], [16], (local) weighted Bayesian linear regression (wBLR) [18] and kinky inference [17], to name a few. Such approaches use different (potentially less restrictive) a priori assumptions [15], [16], [17] and also perform well in some experiments [15], [16], [18]. However, currently the corresponding robust MPC literature that can provide theoretical guarantees using such models seems rather immature compared to classical RAMPC approaches, see [33] for a more general discussion.…”

“…This has motivated an increasing amount of research focused on online model adaptation/learning in MPC, spanning the last two This work was supported by the German Research Foundation under Grants GRK 2198/1, AL 316/12-2, and MU 3929/1-2, and by the International Max Planck Research School for Intelligent Systems (IMPRS-IS). 1 decades [2], [3], [4], with current research focused on robust adaptive formulations [5], [6], [7], [8], [9], [10], [11], [12], dual/learning formulations [13], [14] and machine learning based approaches [15], [16], [17], [18]. However, all of these approaches suffer from at least one of the following shortcomings: a) limitation to restrictive system classes, such as linear systems [5], [6], [7], [8] or feedback linearizable systems [9], b) failure to provide theoretical guarantees regarding recursive feasibility, closed-loop stability and constraint satisfaction [14], [15], [16], [18], c) significant increase in the computational complexity [11,Chap.…”

Constrained robust model predictive control embedded with a new data‐driven technique

“…However, treating model uncertainty as a priori constant worst‐case bound, the approach assures robust constraints satisfaction by using a tightening method, which only fits for small error and uses learning technique to update a nominal prediction, which has great conservativeness. This also accounts for [24] where the machine learning method is used to infer worst‐case constant error bound and robust constraints satisfaction is assured by assuming the tightening set is non‐empty. Considering the state‐dependency property of modelling error and updating state‐dependent uncertainty over prediction horizon, the authors of [25] required the variation rate of uncertainty with respect to states needs to be a priori, which is often inaccessible in complex systems.…”