Summary of Lyapunov-stable Neural Control For State and Output Feedback: a Novel Formulation, by Lujie Yang et al.
Lyapunov-stable Neural Control for State and Output Feedback: A Novel Formulation
by Lujie Yang, Hongkai Dai, Zhouxing Shi, Cho-Jui Hsieh, Russ Tedrake, Huan Zhang
First submitted to arxiv on: 11 Apr 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Artificial Intelligence (cs.AI); Robotics (cs.RO); Systems and Control (eess.SY); Optimization and Control (math.OC)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary This paper presents a novel framework for learning neural network (NN) controllers with Lyapunov certificates, enabling formal stability guarantees over the region-of-attraction (ROA). The approach leverages fast empirical falsification and strategic regularizations to define a larger verifiable ROA than existing methods. It also refines conventional Lyapunov derivative constraints to focus on certifiable ROAs. The framework is efficient, flexible, and scalable, accelerating full training and verification procedures on GPUs without relying on expensive solvers for sums-of-squares (SOS), mixed-integer programming (MIP), or satisfiability modulo theories (SMT). As a result, the authors demonstrate Lyapunov-stable output feedback control with synthesized NN-based controllers and NN-based observers, providing formal stability guarantees for the first time in literature. The paper proposes a novel formulation that defines a larger verifiable ROA than shown in the literature, using branch-and-bound with scalable linear bound propagation-based NN verification techniques. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This research creates a new way to learn neural network controllers that can be proven to work well for complex systems like robots. It’s usually hard to show mathematically that these controllers will behave well, but this paper presents a method that makes it possible. The approach uses clever tricks and fast computer algorithms to make the calculations faster and more efficient. This means that engineers can use this method to design better robot controllers and ensure they work safely and correctly. |
Keywords
* Artificial intelligence * Neural network
