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Neural Lyapunov Control [article]

Ya-Chien Chang, Nima Roohi, Sicun Gao
2020 arXiv   pre-print
We propose new methods for learning control policies and neural network Lyapunov functions for nonlinear control problems, with provable guarantee of stability.  ...  The framework consists of a learner that attempts to find the control and Lyapunov functions, and a falsifier that finds counterexamples to quickly guide the learner towards solutions.  ...  Learning to Stabilize with Neural Lyapunov Functions We now describe how to learn both a control function and a neural Lyapunov function together, so that the Lyapunov conditions can be rigorously verified  ... 
arXiv:2005.00611v3 fatcat:sbbzcgo4ejff3lhg4u6mk7vrle

Neural Koopman Lyapunov Control [article]

Vrushabh Zinage, Efstathios Bakolas
2022 arXiv   pre-print
affine nonlinear system as well as a Control Lyapunov Function (CLF) for the Koopman based bilinear model using a learner and falsifier.  ...  Learning and synthesizing stabilizing controllers for unknown nonlinear control systems is a challenging problem for real-world and industrial applications.  ...  In [35, 36, 37, 38] Lyapunov control methods are proposed based on Lyapunov neural networks. [39] proposes formal synthesis methods for learning Lyapunov functions.  ... 
arXiv:2201.05098v2 fatcat:2occi2ozxjh3nbwqtmv2otrzae

Neural Lyapunov Differentiable Predictive Control [article]

Sayak Mukherjee, Ján Drgoňa, Aaron Tuor, Mahantesh Halappanavar, Draguna Vrabie
2022 arXiv   pre-print
The neural Lyapunov differentiable predictive control (NLDPC) learns the policy by constructing a computational graph encompassing the system dynamics, state and input constraints, and the necessary Lyapunov  ...  We present a learning-based predictive control methodology using the differentiable programming framework with probabilistic Lyapunov-based stability guarantees.  ...  Simultaneous Learning of Constrained Neural Control Policy and Lyapunov Function We now describe how to learn both a control policy and a neural Lyapunov function together, so that the Lyapunov conditions  ... 
arXiv:2205.10728v1 fatcat:s3xhqomskrajje7ogqv7cea3wy

Lyapunov-stable neural-network control [article]

Hongkai Dai and Benoit Landry and Lujie Yang and Marco Pavone and Russ Tedrake
2021 arXiv   pre-print
To address this gap, we propose a generic method to synthesize a Lyapunov-stable neural-network controller, together with a neural-network Lyapunov function to simultaneously certify its stability.  ...  We apply our approach to robots including an inverted pendulum, a 2D and a 3D quadrotor, and showcase that our neural-network controller outperforms a baseline LQR controller.  ...  neural-network controller, together with a neural-network Lyapunov function, for a given dynamical system whose forward dynamics is approximated by another neural network.  ... 
arXiv:2109.14152v1 fatcat:oufz4aq6efapnkze5m54suf7nu

Compressor Surge Control Using Lyapunov Neural Networks

Åse Neverlien, Signe Moe, Jan T. Gravdahl
2020 Modeling, Identification and Control  
The control design is based on Lyapunov control theory in combination with neural networks (NNs) and focuses on minimization of loss of energy in the compressor system.  ...  The approach allows for control design with guaranteed region of attraction when considering saturated controls.  ...  LYAPUNOV NEURAL NETWORK In this Section the controller design based on the principle of Lyapunov control theory combined with neural networks will be presented.  ... 
doi:10.4173/mic.2020.2.1 fatcat:dp5hj2cr5fdwbmahu4hjkhxb6m

Safe Nonlinear Control Using Robust Neural Lyapunov-Barrier Functions [article]

Charles Dawson, Zengyi Qin, Sicun Gao, Chuchu Fan
2021 arXiv   pre-print
We take inspiration from robust convex optimization and Lyapunov theory to define robust control Lyapunov barrier functions that generalize despite model uncertainty.  ...  Safety and stability are common requirements for robotic control systems; however, designing safe, stable controllers remains difficult for nonlinear and uncertain models.  ...  First, we provide a novel extension of control Lyapunov barrier functions to robust control, defining a robust control Lyapunov barrier function (robust CLBF).  ... 
arXiv:2109.06697v2 fatcat:3nfpe2ijqffmrfsptm233lhlhi

Neural Lyapunov Model Predictive Control: Learning Safe Global Controllers from Sub-optimal Examples [article]

Mayank Mittal, Marco Gallieri, Alessio Quaglino, Seyed Sina Mirrazavi Salehian, Jan Koutník
2021 arXiv   pre-print
The terminal cost is constructed as a Lyapunov function neural network with the aim of recovering or extending the stable region of the initial demonstrator using a short prediction horizon.  ...  With a growing interest in data-driven control techniques, Model Predictive Control (MPC) provides an opportunity to exploit the surplus of data reliably, particularly while taking safety and stability  ...  Baseline Controllers Our Neural Lyapunov MPC has a single-step horizon and uses the learned Lyapunov function as the terminal cost.  ... 
arXiv:2002.10451v2 fatcat:mpmbdjk6ozhsbkqptyl2zl55oq

Stabilizing Neural Control Using Self-Learned Almost Lyapunov Critics [article]

Ya-Chien Chang, Sicun Gao
2021 arXiv   pre-print
We develop new methods for learning neural control policies and neural Lyapunov critic functions in the model-free reinforcement learning (RL) setting.  ...  The methods enhance stability of neural controllers for various nonlinear systems including automobile and quadrotor control.  ...  CONCLUSION We proposed new methods for training stable neural control policies using Lyapunov critic functions.  ... 
arXiv:2107.04989v1 fatcat:aq6rpkuf65bk3k4gdci2uzoara

Learning Lyapunov Functions for Piecewise Affine Systems with Neural Network Controllers [article]

Shaoru Chen, Mahyar Fazlyab, Manfred Morari, George J. Pappas, Victor M. Preciado
2020 arXiv   pre-print
We propose a learning-based method for Lyapunov stability analysis of piecewise affine dynamical systems in feedback with piecewise affine neural network controllers.  ...  We show that when the set of Lyapunov functions is full-dimensional in the parameter space, the overall procedure finds a Lyapunov function in a finite number of iterations.  ...  Neural network controllers with projection In Section 4, we studied the closed-loop stability of the PWA system (5) with a neural network controller u = π(x).  ... 
arXiv:2008.06546v2 fatcat:exyzy35ovrag5ff63y2a4tz6gq

Neural Lyapunov Control of Unknown Nonlinear Systems with Stability Guarantees [article]

Ruikun Zhou, Thanin Quartz, Hans De Sterck, Jun Liu
2022 arXiv   pre-print
The second neural network aims to identify a valid Lyapunov function and a provably stabilizing nonlinear controller.  ...  This paper proposes a learning framework to simultaneously stabilize an unknown nonlinear system with a neural controller and learn a neural Lyapunov function to certify a region of attraction (ROA) for  ...  provide theoretical analysis on the existence of a neural Lyapunov function that verifies the Lyapunov conditions, except on an arbitrarily small neighborhood of the origin, provided that the  ... 
arXiv:2206.01913v1 fatcat:5sqouqum65ephh5m4cfhre64e4

Analysis and Design of Quadratic Neural Networks for Regression, Classification, and Lyapunov Control of Dynamical Systems [article]

Luis Rodrigues, Sidney Givigi
2022 arXiv   pre-print
and control of dynamical systems.  ...  Several examples will show the effectiveness of quadratic neural networks in applications.  ...  ACKNOWLEDGEMENTS The authors would like to thank Burak Bartan and Mert Pilanci from Stanford University for the answers to all our questions about their work on quadratic neural networks presented in reference  ... 
arXiv:2207.13120v1 fatcat:3bky7dqrinh2dcyt64h6kccfrm

A pure neural network controller for double‐pendulum crane anti‐sway control: Based on Lyapunov stability theory

Qingrong Chen, Wenming Cheng, Lingchong Gao, Johannes Fottner
2019 Asian journal of control  
The Lyapunov method is utilized to design the weights update law of neural network, and the robustness of the proposed controller is proved by the Lyapunov stability theory.  ...  The results of numerical simulations show that the proposed neural network controller has excellent performance of trolley position tracking and payload anti-sway controlling.  ...  | CONCLUSION In this paper, based on the Lyapunov stability theory, we proposed a pure neural network controller, whose weights are updated online, and it is used to anti-sway control for crane systems  ... 
doi:10.1002/asjc.2226 fatcat:yrmirefizbeylhlqs7xultgxom

Lyapunov-Based Dynamic Neural Network for Adaptive Control of Complex Systems

Farouk Zouari, Kamel Ben Saad, Mohamed Benrejeb
2012 Journal of Software Engineering and Applications  
A Lyapunov-Base training algorithm is proposed and used to adjust on-line the network weights so that the neural model output follows the desired one.  ...  In this paper, an adaptive neuro-control structure for complex dynamic system is proposed.  ...  JSEA Lyapunov-Based Dynamic Neural Network for Adaptive Control of Complex Systems  ... 
doi:10.4236/jsea.2012.54028 fatcat:adsuloxfgzgwfpus5c3lokqbx4

Sampled-data synchronization control for chaotic neural networks with mixed delays: A discontinuous Lyapunov functional approach

Quan Hai
2021 IEEE Access  
CONCLUSION In this paper, the synchronization control problem has been investigated for chaotic neural networks with mixed delays by sampled-data control.  ...  Utilizing output feedback H ∞ control to consider synchronization problem of chaotic neural networks [11] , [12] , design the asynchronization scheme by the control strategy in finite-time [34] , [  ...  Moreover, the sample-date controller gain matrix is given by K = X −1 Y . IV.  ... 
doi:10.1109/access.2021.3057918 fatcat:uvg5xwhpgnfyxgo3xby6hhxb5u

Indirect Adaptive Control for Synchronous Generator: Comparison of MLP/RBF Neural Networks Approach With Lyapunov Stability Analysis

J.-W. Park, R.G. Harley, G.K. Venayagamoorthy
2004 IEEE Transactions on Neural Networks  
Index Terms-Indirect adaptive control, Lyapunov transient stability analysis, multilayer perceptron neural network (MLPN), on-line training, radial basis function neural network (RBFN), synchronous generator  ...  The different damping and transient performances of two neurocontrollers are compared with those of conventional linear controllers, and analyzed based on the Lyapunov direct method.  ...  Indirect Adaptive Control for Synchronous Generator: Comparison of MLP/RBF Neural Networks Approach With Lyapunov Stability Analysis I. INTRODUCTION  ... 
doi:10.1109/tnn.2004.824260 pmid:15384538 fatcat:caxy5si7ord5fkgfiyvddcshiy
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