Abstract
The chapter deals with the design of event-triggering mechanisms (ETM) for discrete-time linear systems stabilized by neural network controllers. The proposed event-triggering mechanism is based on the use of local sector conditions related to the activation functions, to reduce the computational cost associated with the neural network evaluation. Such a mechanism avoids redundant computations by updating only a portion of the layers instead of evaluating periodically the complete neural network. Sufficient matrix inequality conditions are provided to design the parameters of the event-triggering mechanism and compute an inner-approximation of the region of attraction for the feedback system. The theoretical conditions are obtained by using a quadratic Lyapunov function and an adequate abstraction of the activation functions via generalised sector condition to decide whether the outputs of the layers should be transmitted through the network or not. Convex optimisation procedures can be associated to the theoretical conditions in order to maximise the approximation of the region of attraction or to minimise the number of updates. The advantages and the drawbacks of our approach are illustrated in an example borrowed from the literature, namely the nonlinear inverted pendulum system stabilized by a trained neural network.
This work has been supported by ANR under the project HANDY number 18-CE40-0010.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
De Souza, C., Girard, A., Tarbouriech, S.: Event-triggered neural network control using quadratic constraints for perturbed systems. Automatica (2023). To appear
de Souza, C., Tarbouriech, S., Girard, A.: Event-triggered neural network control for lti systems. IEEE Control Syst. Lett. 7, 1381–1386 (2023)
de Souza, C., Tarbouriech, S., Leite, V.J.S., Castelan, E.B.: Co-design of an event-triggered dynamic output feedback controller for discrete-time LPV systems with constraints. J. Franklin Inst. (2020). Submitted
Fazlyab, M., Morari, M., Pappas, G.J.: Safety verification and robustness analysis of neural networks via quadratic constraints and semidefinite programming. IEEE Trans. Autom, Control (2020)
Fazlyab, M., Robey, A., Hassani, H., Morari, M., Pappas, G.: Efficient and accurate estimation of lipschitz constants for deep neural networks. Adv. Neural Inf. Process. Syst. 32 (2019)
Gao, Y., Guo, X., Yao, R., Zhou, W., Cattani, C.: Stability analysis of neural network controller based on event triggering. J. Franklin Inst. 357(14), 9960–9975 (2020)
Girard, A.: Dynamic triggering mechanisms for event-triggered control. IEEE Trans. Autom. Control 60(7), 1992–1997 (2014)
Heemels, W.P.M.H., Donkers, M.C.F., Teel, A.R.: Periodic event-triggered control for linear systems. IEEE Trans. Autom. Control 58(4), 847–861 (2012)
Hertneck, M., Köhler, J., Trimpe, S., Allgöwer, F.: Learning an approximate model predictive controller with guarantees. IEEE Control Syst. Lett. 2(3), 543–548 (2018)
Hu, T., Lin, Z.: Control Systems with Actuator Saturation: Analysis and Design. Birkhäuser, Boston (2001)
Hu, T., Teel, A.R., Zaccarian, L.: Stability and performance for saturated systems via quadratic and nonquadratic Lyapunov functions. IEEE Trans. Autom. Control 51(11), 1770–1786 (2006)
Jin, M., Lavaei, J.: Stability-certified reinforcement learning: a control-theoretic perspective. IEEE Access 8, 229086–229100 (2020)
Karg, B., Lucia, S.: Efficient representation and approximation of model predictive control laws via deep learning. IEEE Trans. Cybern. 50(9), 3866–3878 (2020)
Kim, K.-K.K., Patrón, E.R., Braatz, R.D.: Standard representation and unified stability analysis for dynamic artificial neural network models. Neural Netw. 98, 251–262 (2018)
Pauli, P., Koch, A., Berberich, J., Kohler, P., Allgöwer, F.: Training robust neural networks using lipschitz bounds. IEEE Control Syst. Lett. 6, 121–126 (2021)
Pauli, P., Köhler, J., Berberich, J., Koch, A., Allgöwer, F.: Offset-free setpoint tracking using neural network controllers. In: Learning for Dynamics and Control, pp. 992–003. PMLR (2021)
Revay, M., Wang, R., Manchester, I.R.: Lipschitz bounded equilibrium networks. arXiv preprint arXiv:2010.01732 (2020)
Sahoo, A., Xu, H., Jagannathan, S.: Neural network-based event-triggered state feedback control of nonlinear continuous-time systems. IEEE Trans. Neural Netw. Learn. Syst. 27(3), 497–509 (2015)
Schmitendorf, W.E., Barmish, B.R.: Null controllability of linear systems with constrained controls. SIAM J. Contr. Opt. 18(4), 327–345 (1980)
Tabuada, P.: Event-triggered real-time scheduling of stabilizing control tasks. IEEE Trans. Autom. Control 52(9), 1680–1685 (2007)
Tanaka, K.: An approach to stability criteria of neural-network control systems. IEEE Trans. Neural Netw. 7(3), 629–642 (1996)
Tarbouriech, S., Garcia, G., Gomes da Silva Jr. J.M., Queinnec, I.: Stability and Stabilization of Linear Systems with Saturating Actuators. Springer (2011)
Vamvoudakis, K.G.: Event-triggered optimal adaptive control algorithm for continuous-time nonlinear systems. IEEE/CAA J. Autom. Sin. 1(3), 282–293 (2014)
Xiang, W., Musau, P., Wild, A.A., Lopez, D.M., Hamilton, N., Yang, X., Rosenfeld, J., Johnson, T.T.: Verification for machine learning, autonomy, and neural networks survey. arXiv preprint arXiv:1810.01989 (2018)
Yin, H., Seiler, P., Arcak, M.: Stability analysis using quadratic constraints for systems with neural network controllers. IEEE Trans. Autom, Control (2021)
Yin, H., Seiler, P., Jin, M., Arcak, M.: Imitation learning with stability and safety guarantees. IEEE Control Syst. Lett. 6, 409–414 (2021)
Zaccarian, L., Teel, A.R.: Modern Anti-windup Synthesis: Control Augmentation for Actuator Saturation, vol. 36. Princeton University Press (2011)
Zhang, X., Bujarbaruah, M., Borrelli, F.: Safe and near-optimal policy learning for model predictive control using primal-dual neural networks. In: American Control Conference, pp. 354–359. IEEE (2019)
Zhong, X., Ni, Z., He, H., Xu, X., Zhao, D.: Event-triggered reinforcement learning approach for unknown nonlinear continuous-time system. In: International Joint Conference on Neural Networks (IJCNN), pp. 3677–3684. IEEE (2014)
Acknowledgements
This work was supported by the “Agence Nationale de la Recherche” (ANR) under Grant HANDY ANR-18-CE40-0010.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2024 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Tarbouriech, S., De Souza, C., Girard, A. (2024). Layers Update of Neural Network Control via Event-Triggering Mechanism. In: Postoyan, R., Frasca, P., Panteley, E., Zaccarian, L. (eds) Hybrid and Networked Dynamical Systems. Lecture Notes in Control and Information Sciences, vol 493. Springer, Cham. https://doi.org/10.1007/978-3-031-49555-7_11
Download citation
DOI: https://doi.org/10.1007/978-3-031-49555-7_11
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-49554-0
Online ISBN: 978-3-031-49555-7
eBook Packages: EngineeringEngineering (R0)