Two-component controller design to safeguard data-driven predictive control

TL;DR

This work proposes a two-component controller that integrates data-driven predictive control (via DeePC or EDMD-based MPC) with a model-free funnel safeguarding loop to achieve reference tracking under output constraints for systems of relative degree two. The data-driven component learns surrogate dynamics online from streaming data, while the safeguarding outer loop guarantees constraint satisfaction and can actively steer exploration to improve data coverage, e.g., reducing the fill distance in the Koopman embedding. The approach provides theoretical safeguarding guarantees and leverages error bounds for kernel-EDMD to justify data-driven predictions, demonstrated on a nonlinear oscillator through stabilization and set-point transitions. Practically, this framework enables safe, online, data-enabled control with bounded tracking errors and adaptable data acquisition, suitable for applications where offline training is impractical or risky.

Abstract

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 has 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.

Figures (9)

• Figure 1: Schematic illustration of tracking error, funnel boundary as well as safe and safety-critical areas gottschalk2024reinforcement.
• Figure 2: Structure of the two-component controller. The data-driven learning-based Predictive Controller in the gray box is safeguarded by the Funnel Controller. To limit activity of the latter, the input $u_{\rm FC}$ is multiplied by the activation function $a_\tau$. For brevity, the reference $y_{\rm ref}$ is not shown explicitly but it is provided to both controller components.
• Figure 3: Flowchart illustrating the procedure to generate a data-driven surrogate model with prescribed accuracy using \ref{['eq:FunnelControl']}
• Figure 4: Stabilizing the origin. Visualization of the output $y(t) = x_1(t)$ and the error boundary $\sigma(t)$ given by \ref{['eq:example:error-boundary']}.
• Figure 5: Stabilizing the origin. Visualization of the activation function $a_\tau(t,e_2(t))$ (left) and the input $u(t) = \mu(t) + a_\tau(t,e_2(t)) \, u_{\rm FC}(t)$ (right).

Theorems & Definitions (8)

• Remark 1
• Theorem 1: Safeguarding property
• Lemma 1: willems2005note
• Remark 2
• Remark 3
• Definition 1: Fill distance $h_\mathcal{X}$
• Theorem 2: Theorem 5.2 of kohne2024infty
• Theorem 3: Theorem 2 of BoldScha25