# Hybrid Systems Neural Control with Region-of-Attraction Planner

arXiv: https://arxiv.org/abs/2303.10327 · HTML: https://mlsanity.com/paper/2303.10327/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 73 references that are in the map.
- First posted on arXiv 18 Mar 2023.

## Builds on (most cited first, 22 of 22)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Continuous control with deep reinforcement learning](https://mlsanity.com/paper/1509.02971/) (2015)
- [When to Trust Your Model: Model-Based Policy Optimization](https://mlsanity.com/paper/1906.08253/) (2019)
- [Safe Control with Learned Certificates: A Survey of Neural Lyapunov, Barrier, and Contraction methods](https://mlsanity.com/paper/2202.11762/) (2022)
- [Neural Lyapunov Control](https://mlsanity.com/paper/2005.00611/) (2020)
- [Safe Nonlinear Control Using Robust Neural Lyapunov-Barrier Functions](https://mlsanity.com/paper/2109.06697/) (2021)
- [The Lyapunov Neural Network: Adaptive Stability Certification for Safe Learning of Dynamical Systems](https://mlsanity.com/paper/1808.00924/) (2018)
- [Learning Safe Multi-Agent Control with Decentralized Neural Barrier Certificates](https://mlsanity.com/paper/2101.05436/) (2021)
- [Learning Certified Control using Contraction Metric](https://mlsanity.com/paper/2011.12569/) (2020)
- [Continuous-Discrete Reinforcement Learning for Hybrid Control in Robotics](https://mlsanity.com/paper/2001.00449/) (2020)
- [MBRL-Lib: A Modular Library for Model-based Reinforcement Learning](https://mlsanity.com/paper/2104.10159/) (2021)
- [Neural Bridge Sampling for Evaluating Safety-Critical Autonomous Systems](https://mlsanity.com/paper/2008.10581/) (2020)
- [Learning Lyapunov Functions for Hybrid Systems](https://mlsanity.com/paper/2012.12015/) (2020)
- [Warm Start of Mixed-Integer Programs for Model Predictive Control of Hybrid Systems](https://mlsanity.com/paper/1910.08251/) (2019)
- [Reactive and Safe Road User Simulations using Neural Barrier Certificates](https://mlsanity.com/paper/2109.06689/) (2021)
- [Computation of Regions of Attraction for Hybrid Limit Cycles Using Reachability: An Application to Walking Robots](https://mlsanity.com/paper/2201.08538/) (2022)
- [Learning Stable Nonparametric Dynamical Systems with Gaussian Process Regression](https://mlsanity.com/paper/2006.07868/) (2020)
- [Poincar'e-Bendixson Theorem for Hybrid Systems](https://mlsanity.com/paper/1801.09014/) (2018)
- [Switching between Limit Cycles in a Model of Running Using Exponentially Stabilizing Discrete Control Lyapunov Function](https://mlsanity.com/paper/1807.02696/) (2018)
- [Region of Attraction for Power Systems using Gaussian Process and Converse Lyapunov Function -- Part I: Theoretical Framework and Off-line Study](https://mlsanity.com/paper/1906.03590/) (2019)

## Built on by (most cited first, 1 of 1)

- [Gait Switching and Enhanced Stabilization of Walking Robots with Deep Learning-based Reachability: A Case Study on Two-link Walker](https://mlsanity.com/paper/2409.16301/) (2024)

## Abstract (arXiv)

Hybrid systems are prevalent in robotics. However, ensuring the stability of hybrid systems is challenging due to sophisticated continuous and discrete dynamics. A system with all its system modes stable can still be unstable. Hence special treatments are required at mode switchings to stabilize the system. In this work, we propose a hierarchical, neural network (NN)-based method to control general hybrid systems. For each system mode, we first learn an NN Lyapunov function and an NN controller to ensure the states within the region of attraction (RoA) can be stabilized. Then an RoA NN estimator is learned across different modes. Upon mode switching, we propose a differentiable planner to ensure the states after switching can land in next mode's RoA, hence stabilizing the hybrid system. We provide novel theoretical stability guarantees and conduct experiments in car tracking control, pogobot navigation, and bipedal walker locomotion. Our method only requires 0.25X of the training time as needed by other learning-based methods. With low running time (10-50X faster than model predictive control (MPC)), our controller achieves a higher stability/success rate over other baselines such as MPC, reinforcement learning (RL), common Lyapunov methods (CLF), linear quadratic regulator (LQR), quadratic programming (QP) and Hamilton-Jacobian-based methods (HJB). The project page is on https://mit-realm.github.io/hybrid-clf.