# Robust Stability of Neural Network-controlled Nonlinear Systems with Parametric Variability

arXiv: https://arxiv.org/abs/2109.05710 · HTML: https://mlsanity.com/paper/2109.05710/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 85 references that are in the map.
- First posted on arXiv 13 Sep 2021.

## Builds on (most cited first, 24 of 24)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Continuous control with deep reinforcement learning](https://mlsanity.com/paper/1509.02971/) (2015)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Asynchronous Methods for Deep Reinforcement Learning](https://mlsanity.com/paper/1602.01783/) (2016)
- [Regularisation of Neural Networks by Enforcing Lipschitz Continuity](https://mlsanity.com/paper/1804.04368/) (2018)
- [Deep Reinforcement Learning framework for Autonomous Driving](https://mlsanity.com/paper/1704.02532/) (2017)
- [Model-Ensemble Trust-Region Policy Optimization](https://mlsanity.com/paper/1802.10592/) (2018)
- [Model-Based Reinforcement Learning via Meta-Policy Optimization](https://mlsanity.com/paper/1809.05214/) (2018)
- [Explainability in Deep Reinforcement Learning](https://mlsanity.com/paper/2008.06693/) (2020)
- [Control of a Quadrotor with Reinforcement Learning](https://mlsanity.com/paper/1707.05110/) (2017)
- [Efficient representation and approximation of model predictive control laws via deep learning](https://mlsanity.com/paper/1806.10644/) (2018)
- [Structured Evolution with Compact Architectures for Scalable Policy Optimization](https://mlsanity.com/paper/1804.02395/) (2018)
- [Actor-Critic Reinforcement Learning for Control with Stability Guarantee](https://mlsanity.com/paper/2004.14288/) (2020)
- [Stability Analysis using Quadratic Constraints for Systems with Neural Network Controllers](https://mlsanity.com/paper/2006.07579/) (2020)
- [Imitation Learning with Stability and Safety Guarantees](https://mlsanity.com/paper/2012.09293/) (2020)
- [Adaptive Power System Emergency Control using Deep Reinforcement Learning](https://mlsanity.com/paper/1903.03712/) (2019)
- [DSOS and SDSOS Optimization: More Tractable Alternatives to Sum of Squares and Semidefinite Optimization](https://mlsanity.com/paper/1706.02586/) (2017)
- [Asynchronous Episodic Deep Deterministic Policy Gradient: Towards Continuous Control in Computationally Complex Environments](https://mlsanity.com/paper/1903.00827/) (2019)
- [Safe and Near-Optimal Policy Learning for Model Predictive Control using Primal-Dual Neural Networks](https://mlsanity.com/paper/1906.08257/) (2019)
- [Disciplined Quasiconvex Programming](https://mlsanity.com/paper/1905.00562/) (2019)
- [Safe Reinforcement Learning for Emergency LoadShedding of Power Systems](https://mlsanity.com/paper/2011.09664/) (2020)
- [Learning Lyapunov Functions for Piecewise Affine Systems with Neural Network Controllers](https://mlsanity.com/paper/2008.06546/) (2020)
- [On Training Effective Reinforcement Learning Agents for Real-time Power Grid Operation and Control](https://mlsanity.com/paper/2012.06458/) (2020)

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

- [NeFT: Negative Feedback Training to Improve Robustness of Compute-In-Memory DNN Accelerators](https://mlsanity.com/paper/2305.14561/) (2023)

## Abstract (arXiv)

Stability certification and identifying a safe and stabilizing initial set are two important concerns in ensuring operational safety, stability, and robustness of dynamical systems. With the advent of machine-learning tools, these issues need to be addressed for the systems with machine-learned components in the feedback loop. To develop a general theory for stability and stabilizability of a neural network (NN)-controlled nonlinear system subject to bounded parametric variation, a Lyapunov-based stability certificate is proposed and is further used to devise a maximal Lipschitz bound for the NN controller, and also a corresponding maximal region-of-attraction (RoA) inside a given safe operating domain. To compute such a robustly stabilizing NN controller that also maximizes the system's long-run utility, a stability-guaranteed training (SGT) algorithm is proposed. The effectiveness of the proposed framework is validated through an illustrative example.