[Paper Review] Online Data-Enabled Predictive Control

Stefanos Baros, Chin-Yao Chang+2 more|arXiv (Cornell University)|Mar 8, 2020

Advanced Control Systems Optimization19 references4 citations

TL;DR

This paper proposes Online Data-Enabled Predictive Control (ODeePC), a data-driven model-free approach that uses real-time measurements and online optimization to compute optimal control policies for unknown systems. By leveraging fast Fourier transform (FFT)-accelerated computation of Hankel matrix-vector products and a primal-dual algorithm, ODeePC achieves real-time adaptability and convergence to a neighborhood of the optimal control policy, significantly reducing computational burden compared to direct methods.

ABSTRACT

We develop an online data-enabled predictive (ODeePC) control method for optimal control of unknown systems, building on the recently proposed DeePC [1]. Our proposed ODeePC method leverages a primal-dual algorithm with real-time measurement feedback to iteratively compute the corresponding real-time optimal control policy as system conditions change. The proposed ODeePC conceptual-wise resembles standard adaptive system identification and model predictive control (MPC), but it provides a new alternative for the standard methods. ODeePC is enabled by computationally efficient methods that exploit the special structure of the Hankel matrices in the context of DeePC with Fast Fourier Transform (FFT) and primal-dual algorithm. We provide theoretical guarantees regarding the asymptotic behavior of ODeePC, and we demonstrate its performance through numerical examples.

Motivation & Objective

• To develop an online, data-enabled predictive control method for unknown systems without requiring analytical system models.
• To address the scalability limitations of existing data-driven control methods like DeePC by enabling real-time adaptation using online measurements.
• To reduce computational complexity in large-scale systems through efficient matrix-vector product computation using FFT and circulant matrix structure.
• To provide theoretical convergence guarantees for the online optimization process under time-varying system conditions.
• To offer a viable alternative to standard MPC with online system identification, especially for black-box or poorly modeled systems.

Proposed method

• ODeePC employs a primal-dual optimization algorithm that iteratively updates the control policy using real-time measurement feedback, without directly using measurements in the decision variables.
• It reformulates the control problem using a block Hankel matrix constructed from historical input-output data, enabling data-driven system representation.
• The method exploits the structure of Hankel matrices by transforming them into circulant matrices to enable fast computation via Fast Fourier Transform (FFT).
• A specialized algorithm is developed to compute the product of a non-square block Hankel matrix with a vector in O(n log n) time, significantly reducing computational cost.
• The algorithm maintains the persistently exciting condition for system identification by ensuring sufficient data richness in the Hankel matrix columns.
• Convergence is proven using established online optimization theory, showing that ODeePC converges to a neighborhood of the optimal control policy under time-varying conditions.

Experimental results

Research questions

• RQ1 Can a data-driven control method achieve real-time adaptability to changing system dynamics without relying on analytical system models?
• RQ2 How can the computational complexity of data-enabled predictive control be reduced for large-scale systems?
• RQ3 What is the convergence behavior of an online optimization-based control policy when system conditions evolve over time?
• RQ4 Can FFT-based methods be effectively applied to accelerate Hankel matrix-vector products in predictive control?
• RQ5 How does ODeePC compare in performance and computational efficiency to existing methods like Gradient-DeePC or standard MPC with online system identification?

Key findings

• ODeePC reduces average computational time by approximately 50% compared to direct matrix-vector multiplication, from 1.1 seconds to 0.51 seconds in a moderate-scale test case.
• In a larger system with m=80 and p=60, ODeePC reduced computation time from 1040.73 seconds to 219.94 seconds using the same algorithm, demonstrating significant scalability improvements.
• The proposed FFT-based algorithm achieves O(n log n) complexity for Hankel matrix-vector products, enabling efficient online implementation.
• ODeePC converges to a neighborhood of the optimal control policy, with theoretical guarantees supported by convergence analysis of the online primal-dual method.
• Compared to Gradient-DeePC, ODeePC shows superior stability and convergence, avoiding divergence due to constraint disconnection between optimization iterations.
• Numerical results confirm that ODeePC maintains low constraint violation (e.g., two-norm violation of equality constraints remains bounded), indicating robust performance under dynamic conditions.