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Meta-Learning-Based Adaptive Stability Certificates for Dynamical Systems (2312.15340v1)
Published 23 Dec 2023 in eess.SY, cs.LG, and cs.SY
Abstract: This paper addresses the problem of Neural Network (NN) based adaptive stability certification in a dynamical system. The state-of-the-art methods, such as Neural Lyapunov Functions (NLFs), use NN-based formulations to assess the stability of a non-linear dynamical system and compute a Region of Attraction (ROA) in the state space. However, under parametric uncertainty, if the values of system parameters vary over time, the NLF methods fail to adapt to such changes and may lead to conservative stability assessment performance. We circumvent this issue by integrating Model Agnostic Meta-learning (MAML) with NLFs and propose meta-NLFs. In this process, we train a meta-function that adapts to any parametric shifts and updates into an NLF for the system with new test-time parameter values. We demonstrate the stability assessment performance of meta-NLFs on some standard benchmark autonomous dynamical systems.
- Task2vec: Task embedding for meta-learning. In Proceedings of the IEEE/CVF international conference on computer vision, 6430–6439.
- Learning a synaptic learning rule. Citeseer.
- Safe model-based reinforcement learning with stability guarantees. Advances in neural information processing systems, 30.
- Learning stability certificates from data. In Conference on Robot Learning, 1341–1350. PMLR.
- Neural lyapunov control. Advances in neural information processing systems, 32.
- On quadratic Lyapunov functions. IEEE Transactions on Automatic Control, 48(5): 885–890.
- Chiang, H.-D. 1989. Study of the existence of energy functions for power systems with losses. IEEE Transactions on Circuits and Systems, 36(11): 1423–1429.
- Reinforcement learning for safety-critical control under model uncertainty, using control lyapunov functions and control barrier functions. arXiv preprint arXiv:2004.07584.
- Lyapunov-stable neural-network control. arXiv preprint arXiv:2109.14152.
- Safe Control with Learned Certificates: A Survey of Neural Lyapunov, Barrier, and Contraction methods. arXiv preprint arXiv:2202.11762.
- Model-agnostic meta-learning for fast adaptation of deep networks. In International conference on machine learning, 1126–1135. PMLR.
- Positive polynomials in control, volume 312. Springer Science & Business Media.
- Learning to learn using gradient descent. In International conference on artificial neural networks, 87–94. Springer.
- Natural language to structured query generation via meta-learning. arXiv preprint arXiv:1803.02400.
- A neural lyapunov approach to transient stability assessment of power electronics-interfaced networked microgrids. IEEE Transactions on Smart Grid, 13(1): 106–118.
- Receding horizon control of the Caltech ducted fan: A control Lyapunov function approach. In Proceedings of the 1999 IEEE International Conference on Control Applications (Cat. No. 99CH36328), volume 1, 51–56. IEEE.
- Some controls applications of sum of squares programming. In IEEE Conference on Decision and Control (CDC), 4676–4681.
- Distributed Learning of Neural Lyapunov Functions for Large-Scale Networked Dissipative Systems. arXiv preprint arXiv:2207.07731.
- Telex: Passive stl learning using only positive examples. In International Conference on Runtime Verification, 208–224. Springer.
- Neural certificates for safe control policies. arXiv preprint arXiv:2006.08465.
- Simulation-guided Lyapunov analysis for hybrid dynamical systems. In Proceedings of the 17th international conference on Hybrid systems: computation and control, 133–142.
- Khalil, H. K. 2015. Nonlinear control, volume 406. Pearson New York.
- Learning control Lyapunov function to ensure stability of dynamical system-based robot reaching motions. Robotics and Autonomous Systems, 62(6): 752–765.
- Learning stable deep dynamics models. Advances in neural information processing systems, 32.
- Neural lyapunov redesign. arXiv preprint arXiv:2006.03947.
- Learning to adapt in dynamic, real-world environments through meta-reinforcement learning. arXiv preprint arXiv:1803.11347.
- Parrilo, P. A. 2000. Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization. California Institute of Technology.
- Robust controller synthesis of switched systems using counterexample guided framework. In 2016 international conference on embedded software (EMSOFT), 1–10. IEEE.
- The lyapunov neural network: Adaptive stability certification for safe learning of dynamical systems. In Conference on Robot Learning, 466–476. PMLR.
- Shifting inductive bias with success-story algorithm, adaptive Levin search, and incremental self-improvement. Machine Learning, 28(1): 105–130.
- Meta-adaptive nonlinear control: Theory and algorithms. Advances in Neural Information Processing Systems, 34: 10013–10025.
- Episodic learning with control lyapunov functions for uncertain robotic systems. In 2019 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 6878–6884. IEEE.
- Learning to learn: Introduction and overview. In Learning to learn, 3–17. Springer.
- Local stability analysis using simulations and sum-of-squares programming. Automatica, 44(10): 2669–2675.
- Robust region-of-attraction estimation. IEEE Transactions on Automatic Control, 55(1): 137–142.
- An uncertainty-based control Lyapunov approach for control-affine systems modeled by Gaussian process. IEEE Control Systems Letters, 2(3): 483–488.
- Meta-learning with backpropagation. In IJCNN’01. International Joint Conference on Neural Networks. Proceedings (Cat. No. 01CH37222), volume 3. IEEE.
- Analysis and optimization of droop controller for microgrid system based on small-signal dynamic model. IEEE Transactions on Smart Grid, 7(2): 695–705.