Affiliation:
1. 9149 Universität Stuttgart , Institut für Systemtheorie und Regelungstechnik , Stuttgart , Germany
Abstract
Abstract
Neural networks are widely applied in control applications, yet providing safety guarantees for neural networks is challenging due to their highly nonlinear nature. We provide a comprehensive introduction to the analysis of recurrent neural networks (RNNs) using robust control and dissipativity theory. Specifically, we consider
H
2
{\mathcal{H}_{2}}
-performance and the
ℓ
2
{\ell _{2}}
-gain to quantify the robustness of dynamic RNNs with respect to input perturbations. First, we analyze the robustness of RNNs using the proposed robustness certificates and then, we present linear matrix inequality constraints to be used in training of RNNs to enforce robustness. Finally, we illustrate in a numerical example that the proposed approach enhances the robustness of RNNs.
Funder
Deutsche Forschungsgemeinschaft
Subject
Electrical and Electronic Engineering,Computer Science Applications,Control and Systems Engineering
Reference23 articles.
1. Delgado, A., C. Kambhampati and K. Warwick. 1995. Dynamic recurrent neural network for system identification and control. IEE Proceedings-Control Theory and Applications 142(4): 307–314.
2. Gu, F., H. Yin, L.E. Ghaoui, M. Arcak, P. Seiler and M. Jin. 2021. Recurrent neural network controllers synthesis with stability guarantees for partially observed systems. arXiv preprint arXiv:2109.03861.
3. Nikolakopoulou, A., M.S. Hong and R.D. Braatz. 2020. Feedback control of dynamic artificial neural networks using linear matrix inequalities. In: 2020 59th IEEE Conference on Decision and Control (CDC). IEEE, pp. 2210–2215.
4. Fazlyab, M., M. Morari and G.J. Pappas. 2020. Safety verification and robustness analysis of neural networks via quadratic constraints and semidefinite programming. IEEE Transactions on Automatic Control.
5. Yin, H., P. Seiler and M. Arcak. 2021. Stability analysis using quadratic constraints for systems with neural network controllers. IEEE Transactions on Automatic Control.
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献
1. Neural network training under semidefinite constraints;2022 IEEE 61st Conference on Decision and Control (CDC);2022-12-06