Computationally Efficient Approximation of Data-Enabled Predictive Control

Core Concepts

The core message of this paper is to propose a computationally efficient approximation of Data-Enabled Predictive Control (DeePC) by introducing the notion of a scoring function and approximating it with a learned, reduced-order differentiable convex program.

Abstract

This paper presents a computationally efficient approximation of Data-Enabled Predictive Control (DeePC), a data-driven control approach that bypasses the need for system identification. The key idea is to reformulate the DeePC optimization problem as the minimization of the sum of a control cost function and a scoring function. The scoring function evaluates the fitness of a predicted input-output (I/O) sequence to the system dynamics based on the collected data. To accelerate the evaluation of the scoring function, the authors propose to approximate it with a learned, reduced-order differentiable convex program. The parameters of this approximate scoring function are learned offline, decoupling the scale of the online control problem from the amount of data used. The authors demonstrate through numerical simulations on a quadruple tank system that the proposed learning-based approximation can significantly reduce the computational time required for DeePC, while maintaining comparable control performance. The main contributions are: Reformulating DeePC in terms of a control cost and a scoring function. Proposing a learning-based approximation of the scoring function using a differentiable convex program. Showing through simulations that the learned approximation can achieve a 5x reduction in computational time compared to the original DeePC.

Stats

The quadruple tank system is subject to process noise w(t) ~ N(0, 0.01I4) and measurement noise v(t) ~ N(0, 0.1I2). The control cost matrices are Q = 35 · I2 and R = 10−4I2. The control input and output constraints are U = Y = [−2, 2]. The setpoint is r(t) = [0.65, 0.77]T. The prediction horizon is N = 20, and the initial sequence length is Tini = 10.

Quotes

"An advantage of our approach is its computational merit in decoupling the scale of the control problem from the amount of data used." "Once the form of the approximate scoring function is determined, one can train its parameters offline with a large dataset, without affecting the number of variables or constraints in the control problem to be solved online."

Key Insights Distilled From

Learning-Based Efficient Approximation of Data-enabled Predictive Control

by Yihan Zhou,Y... at arxiv.org 04-26-2024

https://arxiv.org/pdf/2404.16727.pdf

Deeper Inquiries

How can the proposed learning-based approximation be extended to handle nonlinear systems or time-varying dynamics

To extend the proposed learning-based approximation to handle nonlinear systems or time-varying dynamics, we can incorporate techniques such as neural networks or kernel methods to capture the nonlinearities in the system dynamics. By using deep learning models, we can learn complex mappings between inputs and outputs, enabling the approximation of the scoring function for nonlinear systems. Additionally, recurrent neural networks or attention mechanisms can be employed to account for time-varying dynamics by capturing temporal dependencies in the data. By training these models on a diverse dataset that includes nonlinear or time-varying behaviors, the learned approximate controller can adapt to a wider range of system dynamics.

What are the theoretical guarantees on the performance of the learned approximate controller compared to the original DeePC

Theoretical guarantees on the performance of the learned approximate controller compared to the original DeePC can be established through analysis of the approximation error and convergence properties. By leveraging tools from optimization theory and control theory, we can derive bounds on the difference between the true scoring function and the learned approximation. Additionally, stability analysis can be conducted to ensure that the learned controller maintains stability properties similar to DeePC. By proving convergence results and performance guarantees, we can establish the effectiveness and reliability of the learned approximate controller in practical applications.

Can the proposed framework be applied to other data-driven control methods beyond DeePC, and what are the potential benefits and challenges

The proposed framework can be applied to other data-driven control methods beyond DeePC by adapting the learning-based approximation to the specific characteristics of the control algorithm. For instance, the approach can be extended to model predictive control (MPC) or reinforcement learning-based controllers by formulating the control objective and scoring function accordingly. The benefits of applying this framework to other methods include improved computational efficiency, reduced data requirements, and enhanced control performance. However, challenges may arise in translating the learning-based approximation to different control paradigms, as the structure of the control problem and the nature of the data may vary. Addressing these challenges would involve customizing the learning approach to suit the specific requirements of the target control method.