Learning an Approximate Model Predictive Controller with Guarantees (1806.04167v1)

Abstract: A supervised learning framework is proposed to approximate a model predictive controller (MPC) with reduced computational complexity and guarantees on stability and constraint satisfaction. The framework can be used for a wide class of nonlinear systems. Any standard supervised learning technique (e.g. neural networks) can be employed to approximate the MPC from samples. In order to obtain closed-loop guarantees for the learned MPC, a robust MPC design is combined with statistical learning bounds. The MPC design ensures robustness to inaccurate inputs within given bounds, and Hoeffding's Inequality is used to validate that the learned MPC satisfies these bounds with high confidence. The result is a closed-loop statistical guarantee on stability and constraint satisfaction for the learned MPC. The proposed learning-based MPC framework is illustrated on a nonlinear benchmark problem, for which we learn a neural network controller with guarantees.

• The paper proposes a supervised learning framework that approximates traditional MPC for nonlinear systems.
• It leverages neural networks and Hoeffding's Inequality to statistically guarantee stability and constraint satisfaction.
• The method is validated on a continuous stirred tank reactor benchmark, reducing computational complexity while maintaining robust control.

Summary of "Learning an Approximate Model Predictive Controller with Guarantees"

The paper "Learning an Approximate Model Predictive Controller with Guarantees" by Hertneck et al. addresses the challenge of reducing the computational complexity typically associated with Model Predictive Control (MPC) for nonlinear systems, while ensuring stability and constraint satisfaction. The authors propose a framework that employs supervised learning techniques, particularly neural networks, to approximate the MPC using offline sampling data, resulting in an Approximate Model Predictive Controller (AMPC).

Key Contributions

The significant contributions of the paper include:

1. Robust MPC Design: The design of a robust MPC that is resilient to input disturbances within a specified bound is presented. This robust design ensures the stability and constraint satisfaction of the control system, even when the inputs are perturbed to some degree. The robustness is validated using statistical learning bounds, specifically Hoeffding's Inequality, allowing the framework to statistically guarantee that the learned AMPC will perform as intended within given confidence limits.
2. Learning-Based Approximation: The framework utilizes supervised learning techniques to approximate the MPC's behavior. This learning process involves sampling the RMPC offline over a grid of feasible states, followed by the approximation using neural networks. The paper discusses the theoretical underpinning of this approximation process and provides a validation method to ensure that the error between the learned controller and the original MPC remains within an acceptable range.
3. Validation via Statistical Learning: The authors employ Hoeffding’s Inequality as a statistical tool to provide guarantees regarding the stability and constraint satisfaction of the resulting AMPC. This approach is innovative in the field of MPC approximation as it lends a probabilistic guarantee to the control performance, addressing the potentially unlimited configuration space of inputs and ensuring real-world applicability.
4. Numerical Example: The proposed framework is showcased using a nonlinear control benchmark problem, the continuous stirred tank reactor, where the AMPC is learned and validated successfully, highlighting both the efficiency and effectiveness of the approach in reducing computation while maintaining robust control.

Implications and Future Directions

The implications of this research span both theoretical advancements in control theory and practical applications in AI-enabled control systems. The reduction in computational demand of MPC by employing neural networks for approximation allows for more cost-effective hardware deployment without a compromise on system performance—an attractive proposition for industries implementing nonlinear control in real-time systems.

Looking ahead, future research may explore the adaptation of this framework to higher-dimensional systems, where computational efficiency becomes even more critical. Additionally, integrating other advanced learning algorithms and expanding the validation methodologies to cover more generalizable use cases will be important to enhance robustness further.

In essence, this paper contributes valuable insights into the intersection of control theory and supervised learning, merging the two to achieve a more computationally feasible solution while retaining the reliability that control systems demand. This work reflects a promising direction in the continual evolution of MPC methodologies, particularly for complex nonlinear systems requiring real-time decision-making capability.