Bridging the Gaps: Learning Verifiable Model-Free Quadratic Programming Controllers Inspired by Model Predictive Control

Core Concepts

This paper proposes a new class of parameterized controllers that resemble a Quadratic Programming (QP) solver of a linear Model Predictive Control (MPC) problem, with the parameters of the controller being trained via Deep Reinforcement Learning (DRL) rather than derived from system models. This approach addresses the limitations of common controllers with Multi-Layer Perceptron (MLP) or other general neural network architecture used in DRL, in terms of verifiability and performance guarantees, while empirically matching MPC and MLP controllers in terms of control performance and exhibiting superior robustness and computational efficiency.

Abstract

The paper introduces a new class of parameterized controllers that draw inspiration from Model Predictive Control (MPC). The key idea is to design the controller to resemble a Quadratic Programming (QP) solver of a linear MPC problem, but with the parameters of the controller being trained via Deep Reinforcement Learning (DRL) rather than derived from system models. The proposed approach addresses the limitations of common DRL controllers with Multi-Layer Perceptron (MLP) or other general neural network architectures, in terms of verifiability and performance guarantees. The learned controllers possess verifiable properties like persistent feasibility and asymptotic stability akin to MPC. Numerical examples illustrate that the proposed controller empirically matches MPC and MLP controllers in terms of control performance, and has superior robustness against modeling uncertainty and noise. Furthermore, the proposed controller is significantly more computationally efficient compared to MPC and requires fewer parameters to learn than MLP controllers. Real-world experiments on a vehicle drift maneuvering task demonstrate the potential of these controllers for robotics and other demanding control tasks, despite the high nonlinearity of the system. The paper also provides theoretical analysis to establish performance guarantees of the learned QP controller, including sufficient conditions for persistent feasibility and asymptotic stability of the closed-loop system.

Stats

The paper does not contain any explicit numerical data or statistics. The key results are presented through qualitative comparisons and empirical evaluations on benchmark systems and a real-world robotic task.

Quotes

"Leveraging the fact that linear MPC solves a Quadratic Programming (QP) problem at each time step, we consider a parameterized class of controllers with QP structure similar to MPC." "In contrast to most DRL-trained controllers, which often lack rigorous theoretical guarantees, our MPC-inspired controller is proven to enjoy verifiable properties like persistent feasibility and asymptotic stability." "Lastly, though we only provide theoretical guarantees for controlling a linear system, the generalizability of the proposed constroller is empirically demonstrated via vehicle drift maneuvering, a challenging nonlinear robotics control task, indicating potential applications of our controller to real-world nonlinear robotic systems."

Key Insights Distilled From

MPC-Inspired Reinforcement Learning for Verifiable Model-Free Control

by Yiwen Lu,Zis... at arxiv.org 04-10-2024

https://arxiv.org/pdf/2312.05332.pdf

Deeper Inquiries

How can the proposed MPC-inspired controller be extended to handle more complex nonlinear systems beyond the linear case considered in the theoretical analysis?

The proposed MPC-inspired controller can be extended to handle more complex nonlinear systems by incorporating nonlinear dynamics into the QP formulation. One approach is to use nonlinear function approximators, such as neural networks, to model the system dynamics within the QP solver. By replacing the linear system matrices with neural network approximations, the controller can adapt to the nonlinearities present in the system. This extension allows the controller to learn complex system behaviors and control strategies that go beyond the capabilities of linear models. Additionally, the QP solver iterations can be modified to accommodate the nonlinear dynamics by incorporating techniques like implicit differentiation or higher-order optimization methods. These modifications enable the controller to handle the nonlinearity of the system more effectively and improve its performance in controlling complex nonlinear systems.

What are the potential limitations or drawbacks of the QP-based controller structure compared to more general neural network architectures, and how can these be addressed?

One potential limitation of the QP-based controller structure is its restricted flexibility compared to more general neural network architectures. The QP formulation imposes constraints on the controller's structure, limiting its ability to capture complex and nonlinear relationships between states and control inputs. This can lead to suboptimal performance in scenarios where the system dynamics are highly nonlinear or unknown. To address this limitation, one approach is to introduce additional flexibility into the QP-based controller by incorporating neural network components. By combining the QP structure with neural networks, the controller can benefit from the interpretability and stability of the QP formulation while leveraging the expressive power of neural networks to handle complex nonlinearities. This hybrid approach allows for a more adaptable and robust controller that can effectively control a wider range of systems.

Given the connections between the proposed controller and MPC, how can the insights from this work be leveraged to develop novel MPC formulations or algorithms that better integrate learning-based components?

The insights from the proposed controller can be leveraged to develop novel MPC formulations or algorithms that better integrate learning-based components by incorporating the following strategies: Hybrid MPC-Learning Approaches: Develop MPC algorithms that combine traditional model-based control with learning-based components. This hybrid approach can leverage the stability and performance guarantees of MPC while incorporating learning to adapt to uncertainties and improve control performance. Data-Driven MPC: Utilize data-driven techniques, such as reinforcement learning or imitation learning, to enhance the predictive models used in MPC. By training the predictive models on real-world data, the MPC controller can better capture the system dynamics and make more informed control decisions. Online Learning in MPC: Integrate online learning mechanisms into MPC algorithms to adapt the controller in real-time based on feedback from the system. This adaptive MPC approach can improve the controller's robustness and adaptability to changing system conditions. By incorporating these insights, novel MPC formulations can be developed that leverage the strengths of both model-based control and learning-based approaches to achieve superior control performance in complex and uncertain environments.