innsikt - Control Systems - # Neural Lyapunov Control

Actor-Critic Physics-informed Neural Lyapunov Control Framework for Nonlinear Systems

Q: How can this framework be extended to incorporate robustness against model uncertainty

To extend this framework to incorporate robustness against model uncertainty, one approach could be to introduce a regularization term in the loss function that penalizes deviations from expected behavior due to uncertainties. This regularization term can account for variations in system dynamics or disturbances that are not explicitly modeled. By incorporating uncertainty-aware components into the loss function, such as probabilistic models or ensemble methods, the neural network controller and Lyapunov function can adapt and generalize better in uncertain environments. Additionally, techniques like Bayesian deep learning or dropout layers can help capture model uncertainty and improve the robustness of the learned control policies.

Q: What are potential implications of using physics-informed loss functions in other control system applications

The use of physics-informed loss functions in other control system applications can have significant implications for enhancing stability guarantees and performance optimization. By leveraging domain-specific knowledge encoded in physical laws or principles through these loss functions, controllers can be designed with improved accuracy and efficiency. For instance, in robotics applications where precise motion planning is crucial, integrating physics-based constraints into the learning process can lead to more reliable control strategies that adhere to fundamental laws governing motion dynamics. Moreover, by incorporating physics-informed priors during training, it becomes possible to achieve better generalization across different operating conditions and scenarios.

Q: How might this approach impact advancements in reinforcement learning beyond control systems

This approach has the potential to catalyze advancements in reinforcement learning beyond traditional control systems by offering a principled way to combine data-driven techniques with domain expertise. The integration of physics-informed neural networks allows for more interpretable models that align with underlying physical principles while maintaining flexibility for complex nonlinear systems. In fields like autonomous vehicles, healthcare robotics, or finance where safety-critical decisions are made based on learned policies, employing such frameworks could enhance reliability and trustworthiness by ensuring adherence to known rules while adapting intelligently based on data-driven insights. Furthermore, this methodology opens up avenues for developing formal verification tools that certify reinforcement learning agents' behaviors according to specified safety requirements.

Grunnleggende konsepter

Training a neural network controller and Lyapunov function to maximize the region of attraction while respecting actuation constraints.

Sammendrag

The article introduces an actor-critic framework for training a neural network controller and Lyapunov function to enhance the region of attraction. It leverages Zubov's Partial Differential Equation to precisely define the true domain of attraction. The method alternates between learning the Zubov function and improving the control policy. By minimizing the PDE residual, significant improvements in the size of the resulting region of attraction are observed in numerical experiments. The approach aims to address stability concerns in applying neural network policies to physical systems by providing provable guarantees through Lyapunov functions.

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arxiv.org

Statistikk

Numerical experiments show 2-4 times larger verified DoA compared to other methods.
Hyperparameters include dimensions for Wθ and πγ, α values, and c thresholds for different systems.

Sitater

"Learning-based methods can be applied to more general nonlinear systems beyond linear and polynomial systems."
"Our approach significantly enlarges the DoA compared to state-of-the-art methods."
"The proposed method outperforms competitive approaches in enlarging the domain of attraction."

Viktige innsikter hentet fra

Actor-Critic Physics-informed Neural Lyapunov Control

by Jiarui Wang,... klokken arxiv.org 03-14-2024

https://arxiv.org/pdf/2403.08448.pdf

Actor-Critic Physics-informed Neural Lyapunov Control

Dypere Spørsmål

How can this framework be extended to incorporate robustness against model uncertainty

To extend this framework to incorporate robustness against model uncertainty, one approach could be to introduce a regularization term in the loss function that penalizes deviations from expected behavior due to uncertainties. This regularization term can account for variations in system dynamics or disturbances that are not explicitly modeled. By incorporating uncertainty-aware components into the loss function, such as probabilistic models or ensemble methods, the neural network controller and Lyapunov function can adapt and generalize better in uncertain environments. Additionally, techniques like Bayesian deep learning or dropout layers can help capture model uncertainty and improve the robustness of the learned control policies.

What are potential implications of using physics-informed loss functions in other control system applications

The use of physics-informed loss functions in other control system applications can have significant implications for enhancing stability guarantees and performance optimization. By leveraging domain-specific knowledge encoded in physical laws or principles through these loss functions, controllers can be designed with improved accuracy and efficiency. For instance, in robotics applications where precise motion planning is crucial, integrating physics-based constraints into the learning process can lead to more reliable control strategies that adhere to fundamental laws governing motion dynamics. Moreover, by incorporating physics-informed priors during training, it becomes possible to achieve better generalization across different operating conditions and scenarios.

How might this approach impact advancements in reinforcement learning beyond control systems

This approach has the potential to catalyze advancements in reinforcement learning beyond traditional control systems by offering a principled way to combine data-driven techniques with domain expertise. The integration of physics-informed neural networks allows for more interpretable models that align with underlying physical principles while maintaining flexibility for complex nonlinear systems. In fields like autonomous vehicles, healthcare robotics, or finance where safety-critical decisions are made based on learned policies, employing such frameworks could enhance reliability and trustworthiness by ensuring adherence to known rules while adapting intelligently based on data-driven insights. Furthermore, this methodology opens up avenues for developing formal verification tools that certify reinforcement learning agents' behaviors according to specified safety requirements.