mlsanityData to 7 Oct 2026

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

arXiv 2109.05710 ↗First posted 13 Sep 2021cs.LG cs.SY eess.SYcited by 1

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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.

Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 24 of its 85 references that are in the map. First posted on arXiv 13 Sep 2021.

Builds on

24 of 85 references.

References · 24

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2015Continuous control with deep reinforcement learningcited by 3,279
  3. 2015Trust Region Policy Optimizationcited by 2,503
  4. 2021Convex optimizationcited by 2,479
  5. 2016Asynchronous Methods for Deep Reinforcement Learningcited by 2,218
  6. 2018Regularisation of Neural Networks by Enforcing Lipschitz Continuitycited by 311
  7. 2017Deep Reinforcement Learning framework for Autonomous Drivingcited by 224
  8. 2018Model-Ensemble Trust-Region Policy Optimizationcited by 214
  9. 2018Model-Based Reinforcement Learning via Meta-Policy Optimizationcited by 99
  10. 2020Explainability in Deep Reinforcement Learningcited by 96
  11. 2017Control of a Quadrotor with Reinforcement Learningcited by 75
  12. 2018Efficient representation and approximation of model predictive control laws via deep learningcited by 55
12 more
  1. 2018Structured Evolution with Compact Architectures for Scalable Policy Optimizationcited by 48
  2. 2020Stability Analysis using Quadratic Constraints for Systems with Neural Network Controllerscited by 42
  3. 2020Actor-Critic Reinforcement Learning for Control with Stability Guaranteecited by 39
  4. 2020Imitation Learning with Stability and Safety Guaranteescited by 34
  5. 2019Adaptive Power System Emergency Control using Deep Reinforcement Learningcited by 26
  6. 2017DSOS and SDSOS Optimization: More Tractable Alternatives to Sum of Squares and Semidefinite Optimizationcited by 19
  7. 2019Asynchronous Episodic Deep Deterministic Policy Gradient: Towards Continuous Control in Computationally Complex Environmentscited by 13
  8. 2019Safe and Near-Optimal Policy Learning for Model Predictive Control using Primal-Dual Neural Networkscited by 13
  9. 2019Disciplined Quasiconvex Programmingcited by 8
  10. 2020Learning Lyapunov Functions for Piecewise Affine Systems with Neural Network Controllerscited by 7
  11. 2020Safe Reinforcement Learning for Emergency LoadShedding of Power Systemscited by 4
  12. 2020On Training Effective Reinforcement Learning Agents for Real-time Power Grid Operation and Controlcited by 2

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Citing papers per year: 2023: 1.

1 paper.

  1. 2023NeFT: Negative Feedback Training to Improve Robustness of Compute-In-Memory DNN Acceleratorscited by 2