Learning an Approximate Model Predictive Controller with Guarantees

A supervised learning framework is proposed to approximate a model predictive controller (MPC) with reduced computational complexity and guarantees on stability and constraint satisfaction. The framework can be used for a wide class of nonlinear systems. Any standard supervised learning technique (e.g. neural networks) can be employed to approximate the MPC from samples. In order to obtain closed-loop guarantees for the learned MPC, a robust MPC design is combined with statistical learning bounds. The MPC design ensures robustness to inaccurate inputs within given bounds, and Hoeffding's Inequality is used to validate that the learned MPC satisfies these bounds with high confidence. The result is a closed-loop statistical guarantee on stability and constraint satisfaction for the learned MPC. The proposed learning-based MPC framework is illustrated on a nonlinear benchmark problem, for which we learn a neural network controller with guarantees.Comment: 6 pages, 3 figures, to appear in IEEE Control Systems Letter

Stability and performance in MPC using a finite-tail cost

In this paper, we provide a stability and performance analysis of model predictive control (MPC) schemes based on finite-tail costs. We study the MPC formulation originally proposed by Magni et al. (2001) wherein the standard terminal penalty is replaced by a finite-horizon cost of some stabilizing control law. In order to analyse the closed loop, we leverage the more recent technical machinery developed for MPC without terminal ingredients. For a specified set of initial conditions, we obtain sufficient conditions for stability and a performance bound in dependence of the prediction horizon and the extended horizon used for the terminal penalty. The main practical benefit of the considered finite-tail cost MPC formulation is the simpler offline design in combination with typically significantly less restrictive bounds on the prediction horizon to ensure stability. We demonstrate the benefits of the considered MPC formulation using the classical example of a four tank system

Detecting instruction effects. Deciding between covariance analytical and change-score approach

The article focuses on estimating effects in nonrandomized studies with two outcome measurement occasions and one predictor variable. Given such a design, the analysis approach can be to include the measurement at the previous time point as a predictor in the regression model (ANCOVA), or to predict the change-score of the outcome variable (CHANGE). Researchers demonstrated that both approaches can result in different conclusions regarding the reported effect. Current recommendations on when to apply which approach are, in part, contradictory. In addition, they lack direct reference to the educational and instructional research contexts, since they do not consider latent variable models in which variables are measured without measurement error. This contribution assists researchers in making decisions regarding their analysis model. Using an underlying hypothetical data-generating model, we identify for which kind of data-generating scenario (i.e., under which assumptions) the defined true effect equals the estimated regression coefficients of the ANCOVA and the CHANGE approach. We give empirical examples from instructional research and discuss which approach is more appropriate, respectively. (DIPF/Orig.

Robust adaptive MPC using control contraction metrics

We present a robust adaptive model predictive control (MPC) framework for nonlinear continuous-time systems with bounded parametric uncertainty and additive disturbance. We utilize general control contraction metrics (CCMs) to parameterize a homothetic tube around a nominal prediction that contains all uncertain trajectories. Furthermore, we incorporate model adaptation using set-membership estimation. As a result, the proposed MPC formulation is applicable to a large class of nonlinear systems, reduces conservatism during online operation, and guarantees robust constraint satisfaction and convergence to a neighborhood of the desired setpoint. One of the main technical contributions is the derivation of corresponding tube dynamics based on CCMs that account for the state and input dependent nature of the model mismatch. Furthermore, we online optimize over the nominal parameter, which enables general set-membership updates for the parametric uncertainty in the MPC. Benefits of the proposed homothetic tube MPC and online adaptation are demonstrated using a numerical example involving a planar quadrotor.Comment: This is the accepted version of the paper in Automatica, 202

Analysis and design of model predictive control frameworks for dynamic operation -- An overview

This article provides an overview of model predictive control (MPC) frameworks for dynamic operation of nonlinear constrained systems. Dynamic operation is often an integral part of the control objective, ranging from tracking of reference signals to the general economic operation of a plant under online changing time-varying operating conditions. We focus on the particular challenges that arise when dealing with such more general control goals and present methods that have emerged in the literature to address these issues. The goal of this article is to present an overview of the state-of-the-art techniques, providing a diverse toolkit to apply and further develop MPC formulations that can handle the challenges intrinsic to dynamic operation. We also critically assess the applicability of the different research directions, discussing limitations and opportunities for further researc