Volume 73, Issue 6 - Special Issue: Data-Driven and Learning-Based Control – Perspectives and Prospects; Guest Editors: Timm Faulwasser, Annika Eichler and Julian Berberich

Data-driven predictive control (DPC), using linear combinations of recorded trajectory data, has recently emerged as a popular alternative to traditional model predictive control (MPC). Without an explicitly enforced prediction model, the effects of commonly used regularization terms – and the resulting predictions – can be opaque. This opacity may lead to practical challenges, such as reliance on empirical tuning of regularization parameters based on closed-loop performance, and potentially misleading heuristic interpretations of norm-based regularizations. However, by examining the structure of the underlying optimal control problem (OCP), more precise and insightful interpretations of regularization effects can be derived. In this paper, we demonstrate how to analyze the predictive behavior of DPC through implicit predictors and the trajectory-specific effects of quadratic regularization. We further extend these results to cover typical DPC modifications, including DPC for affine systems, offset regularizations, slack variables, and terminal constraints. Additionally, we provide a simple but general result on (recursive) feasibility in DPC. This work aims to enhance the explainability and reliability of DPC by providing a deeper understanding of these regularization mechanisms.

We design a two-component controller to achieve reference tracking with output constraints – exemplified on systems of relative degree two. One component is a data-driven or learning-based predictive controller, which uses data samples to learn a model and predict the future behavior of the system. We exemplify this component concisely by data-enabled predictive control (DeePC) and by model predictive control based on extended dynamic mode decomposition (EDMD). The second component is a model-free high-gain feedback controller, which ensures satisfaction of the output constraints if that cannot be guaranteed by the predictive controller. This may be the case, for example, if too little data have been collected for learning or no (sufficient) guarantees on the approximation accuracy derived. In particular, the reactive/adaptive feedback controller can be used to support the learning process by leading safely through the state space to collect suitable data, e.g., to ensure a sufficiently-small fill distance. Numerical examples are provided to illustrate the combination of EDMD-based model predictive control and a safeguarding feedback for the set-point transitions including the transition between the set points within prescribed bounds.

This article investigates the core mechanisms of indirect data-driven control for unknown systems, focusing on the application of policy iteration (PI) within the context of the linear quadratic regulator (LQR) optimal control problem. Specifically, we consider a setting where data is collected sequentially from a linear system subject to exogenous process noise, and is then used to refine estimates of the optimal control policy. We integrate recursive least squares (RLS) for online model estimation within a certainty-equivalent framework, and employ PI to iteratively update the control policy. In this work, we investigate first the convergence behavior of RLS under two different models of adversarial noise, namely point-wise and energy bounded noise, and then we provide a closed-loop analysis of the combined model identification and control design process. This iterative scheme is formulated as an algorithmic dynamical system consisting of the feedback interconnection between two algorithms expressed as discrete-time systems. This system-theoretic viewpoint on indirect data-driven control allows us to establish convergence guarantees to the optimal controller in the face of uncertainty caused by noisy data. Simulations illustrate the theoretical results.

In this paper, we provide a tutorial overview and an extension of a recently developed framework for data-driven control of unknown nonlinear systems with rigorous closed-loop guarantees. The proposed approach relies on the Koopman operator representation of the nonlinear system, for which a bilinear surrogate model is estimated based on data. In contrast to existing Koopman-based estimation procedures, we state guaranteed bounds on the approximation error using the stability- and certificate-oriented extended dynamic mode decomposition (SafEDMD) framework. The resulting surrogate model and the uncertainty bounds allow us to design controllers via robust control theory and sum-of-squares optimization, guaranteeing desirable properties for the closed-loop system. We present results on stabilization both in discrete and continuous time, and we derive a method for controller design with performance objectives. The benefits of the presented framework over established approaches are demonstrated with a numerical example.

For many engineering problems involving control systems, finding a good working point for steady-state operation is crucial. Therefore, this paper presents an application of steady-state optimization with feedback on particle accelerators, specifically the European X-ray free-electron laser. In simulation studies, we demonstrate that feedback optimization is able to reach a near-optimal steady-state operation in the presence of uncertainties, even without relying on a priori known model information but purely data-driven through input-output measurements. Additionally, we discuss the importance of including second-order information in the optimization to ensure a satisfactory convergence speed and propose an approximated Hessian representation for problems without second-order knowledge on the plant.

The model-based control of building energy systems (BES) is a hard task, since the system identification is very labor-intensive. This results in inexact models, which are subject to parameter uncertainties. Additionally, disturbances like solar radiation have a great impact on the system dynamics. In this paper we used stochastic model predictive control (SMPC) to account for parameter and disturbance uncertainties. The disturbances are modeled as time-dependent Gaussian Processes (GP), which are known as Latent-Force Models (LFM). The proposed approach is evaluated for two different BES using experimentally obtained data. The results show that the LFM-SMPC results in the lowest discomfort with a reasonable higher energy consumption compared to a constant disturbance prediction.

A controller for the air temperature and relative humidity of a greenhouse is presented that relies only on the efficient exploitation of natural ventilation. Due to the difficulty of modeling greenhouse climate from first principles, Neural Predictive Control (NPC) is chosen, which combines the advantages of learning with Model Predictive Control (MPC) under constraints. Feedforward Neural Networks (NNs) are used to obtain a predictive model and a simulation model for the complex nonlinear dynamics of the temperature and humidity inside a greenhouse. The NNs are trained and validated with an 81-day dataset recorded in a Mediterranean greenhouse. The MPC approach applies operational constraints to compute the optimal vent opening. It minimizes temperature and humidity tracking errors, limits control increments to reduce motor wear, and enforces soft bounds on greenhouse temperature and humidity. Hard constraints include vent saturation and a wind speed limit for safety. The NPC strategy was evaluated in simulation with real weather, featuring both sunny and windy conditions. The results show small validation errors of the NNs. The tracking error in the control approach in situations without saturated input is below 3 K and in 81 % of the time the humidity is within the bounds. The presented data-driven control approach is attractive for controller design as data availability in greenhouses is expected to increase in the coming years.