Empirical Study of Dynamic Regret in Online Model Predictive Control for Linear Time-Varying Systems

TL;DR

The paper empirically validates dynamic regret guarantees for online MPC in Linear Time-Varying systems, bridging theory (Lin et al. 2022) and practice. By simulating an LQR/LTV setup with controllable prediction errors and horizons, it analyzes how per-step error and total regret scale, including a neural-network predictor for problem data. Key findings show sublinear dynamic regret under disturbance-only prediction errors for sufficiently long horizons, with more restrictive conditions when all problem data are perturbed; per-step errors decay with horizon in noiseless cases and plateau under noise, sometimes causing divergence. The work advances practical MPC design by informing horizon selection and predictor choices and motivates adaptive strategies and broader empirical validation beyond linear settings.

Abstract

Model Predictive Control (MPC) is a widely used technique for managing timevarying systems, supported by extensive theoretical analysis. While theoretical studies employing dynamic regret frameworks have established robust performance guarantees, their empirical validation remains sparse. This paper investigates the practical applicability of MPC by empirically evaluating the assumptions and theoretical results proposed by Lin et al. [2022]. Specifically, we analyze the performance of online MPC under varying prediction errors and prediction horizons in Linear Time-Varying (LTV) systems. Our study examines the relationship between dynamic regret, prediction errors, and prediction horizons, providing insights into the trade-offs involved. By bridging theory and practice, this work advances the understanding and application of MPC in real-world scenarios.

Figures (9)

• Figure 1: Empirical dynamic regret when prediction errors only affect the disturbance. For each subplot, the x-axis represents episode length $T$, ranging from 20 to 200.
• Figure 2: Empirical dynamic regret when prediction errors are present in all problem data of the optimization. For each subplot, the x-axis represents episode length $T$, ranging from 20 to 200.
• Figure 3: Per-step error (log scale) for cases with prediction errors on disturbance only (left) and on all problem data (right). For noise strength $0$, there are no prediction errors, and the results are identical for both cases.
• Figure 4: Mean empirical dynamic regret over 5 runs for prediction errors on disturbance only.
• Figure 5: Mean empirical dynamic regret over 5 runs for prediction errors on all problem data.