Summary of Certified Robust Invariant Polytope Training in Neural Controlled Odes, by Akash Harapanahalli et al.
Certified Robust Invariant Polytope Training in Neural Controlled ODEs
by Akash Harapanahalli, Samuel Coogan
First submitted to arxiv on: 2 Aug 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Systems and Control (eess.SY); Optimization and Control (math.OC)
GrooveSquid.com Paper Summaries
GrooveSquid.com’s goal is to make artificial intelligence research accessible by summarizing AI papers in simpler terms. Each summary below covers the same AI paper, written at different levels of difficulty. The medium difficulty and low difficulty versions are original summaries written by GrooveSquid.com, while the high difficulty version is the paper’s original abstract. Feel free to learn from the version that suits you best!
| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary The proposed framework trains controllers using feedforward neural networks, which are parameterized as state feedback controllers for nonlinear control systems. The trained controllers ensure robust forward invariant polytopes, guaranteeing that any initialized trajectory remains within the polytope despite disturbances. This is achieved by lifting the original neural controlled system to a higher-dimensional space, where interval analysis and neural network verifiers construct lifted embedding systems that capture the invariant subspace. By treating the controller and lifted system parameters as variables, an algorithm trains controllers with certified forward invariant polytopes in closed-loop control systems. The approach scales well with system dimension and outperforms state-of-the-art Lyapunov-based sampling methods in runtime. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper develops a new way to train controllers for complex systems using neural networks. It helps make sure that the systems behave correctly even when there are disturbances or unexpected things happen. The method uses special techniques called interval analysis and neural network verifiers to create a kind of blueprint of the system’s behavior. This allows it to design controllers that can handle big systems with many states, which is important for real-world applications. |
Keywords
» Artificial intelligence » Embedding » Neural network
