{"payload":{"feedbackUrl":"https://github.com/orgs/community/discussions/53140","repo":{"id":726546116,"defaultBranch":"main","name":"DeepLyapunovFunction","ownerLogin":"DeepDynaSim","currentUserCanPush":false,"isFork":false,"isEmpty":false,"createdAt":"2023-12-02T17:40:16.000Z","ownerAvatar":"https://avatars.githubusercontent.com/u/35817872?v=4","public":true,"private":false,"isOrgOwned":false},"refInfo":{"name":"","listCacheKey":"v0:1701551348.0","currentOid":""},"activityList":{"items":[{"before":"45660819bd6f05ad6e51d652ac0aa88a41142734","after":"a400dc8421ef14129c835d21627c06f00a2185fc","ref":"refs/heads/main","pushedAt":"2023-12-07T09:37:20.000Z","pushType":"push","commitsCount":1,"pusher":{"login":"DeepDynaSim","name":"Caglar Uyulan","path":"/DeepDynaSim","primaryAvatarUrl":"https://avatars.githubusercontent.com/u/35817872?s=80&v=4"},"commit":{"message":"Add files via upload\n\nThe preprinted version is available: https://www.researchsquare.com/article/rs-3698604/v1","shortMessageHtmlLink":"Add files via upload"}},{"before":"d79ece8a399fd52675d597f5bd6bde25bb546185","after":"45660819bd6f05ad6e51d652ac0aa88a41142734","ref":"refs/heads/main","pushedAt":"2023-12-07T09:36:05.000Z","pushType":"push","commitsCount":1,"pusher":{"login":"DeepDynaSim","name":"Caglar Uyulan","path":"/DeepDynaSim","primaryAvatarUrl":"https://avatars.githubusercontent.com/u/35817872?s=80&v=4"},"commit":{"message":"Delete Efficient Computation of Lyapunov Functions Using Deep Neural Networks for the Assesment of Stability in Controller Design.pdf","shortMessageHtmlLink":"Delete Efficient Computation of Lyapunov Functions Using Deep Neural …"}},{"before":"7276a884a8a6e98961dd00dbf9959047be4d36e2","after":"d79ece8a399fd52675d597f5bd6bde25bb546185","ref":"refs/heads/main","pushedAt":"2023-12-02T21:09:08.000Z","pushType":"push","commitsCount":1,"pusher":{"login":"DeepDynaSim","name":"Caglar Uyulan","path":"/DeepDynaSim","primaryAvatarUrl":"https://avatars.githubusercontent.com/u/35817872?s=80&v=4"},"commit":{"message":"Add files via upload\n\nThe preprinted version of the paper.","shortMessageHtmlLink":"Add files via upload"}},{"before":"d4333fb06a6ca2e34fe123e335967688ba19dace","after":"7276a884a8a6e98961dd00dbf9959047be4d36e2","ref":"refs/heads/main","pushedAt":"2023-12-02T20:37:28.000Z","pushType":"push","commitsCount":1,"pusher":{"login":"DeepDynaSim","name":"Caglar Uyulan","path":"/DeepDynaSim","primaryAvatarUrl":"https://avatars.githubusercontent.com/u/35817872?s=80&v=4"},"commit":{"message":"Update README.md","shortMessageHtmlLink":"Update README.md"}},{"before":"8cf4bd6945b6c63e4680171b797b515ffcb873fe","after":"d4333fb06a6ca2e34fe123e335967688ba19dace","ref":"refs/heads/main","pushedAt":"2023-12-02T17:59:23.000Z","pushType":"push","commitsCount":1,"pusher":{"login":"DeepDynaSim","name":"Caglar Uyulan","path":"/DeepDynaSim","primaryAvatarUrl":"https://avatars.githubusercontent.com/u/35817872?s=80&v=4"},"commit":{"message":"Update README.md","shortMessageHtmlLink":"Update README.md"}},{"before":"9c0bf6cd95f187f6b51235da4a602dcba35aac86","after":"8cf4bd6945b6c63e4680171b797b515ffcb873fe","ref":"refs/heads/main","pushedAt":"2023-12-02T17:56:35.000Z","pushType":"push","commitsCount":1,"pusher":{"login":"DeepDynaSim","name":"Caglar Uyulan","path":"/DeepDynaSim","primaryAvatarUrl":"https://avatars.githubusercontent.com/u/35817872?s=80&v=4"},"commit":{"message":"Update README.md","shortMessageHtmlLink":"Update README.md"}},{"before":"8088cba9ea919e379c2a6320cb45f0524e3f5472","after":"9c0bf6cd95f187f6b51235da4a602dcba35aac86","ref":"refs/heads/main","pushedAt":"2023-12-02T17:54:43.000Z","pushType":"push","commitsCount":1,"pusher":{"login":"DeepDynaSim","name":"Caglar Uyulan","path":"/DeepDynaSim","primaryAvatarUrl":"https://avatars.githubusercontent.com/u/35817872?s=80&v=4"},"commit":{"message":"Create README.md","shortMessageHtmlLink":"Create README.md"}},{"before":"482748276a571d152cb96caa6b6c66b4e2292843","after":"8088cba9ea919e379c2a6320cb45f0524e3f5472","ref":"refs/heads/main","pushedAt":"2023-12-02T17:51:12.000Z","pushType":"push","commitsCount":1,"pusher":{"login":"DeepDynaSim","name":"Caglar Uyulan","path":"/DeepDynaSim","primaryAvatarUrl":"https://avatars.githubusercontent.com/u/35817872?s=80&v=4"},"commit":{"message":"Add files via upload\n\nDefine Neural Network Architecture for Each Subsystem:\r\nThe code starts by setting up the neural network architecture for each subsystem. In this example, two neural networks are created to represent two subsystems.\r\ninputSize specifies the dimension of the input layer, corresponding to the state dimension of the subsystem.\r\nhiddenLayers defines the sizes of the hidden layers. Here, two hidden layers with 20 and 15 neurons, respectively, are used.\r\noutputSize is set to 1, as the output of each network is a scalar value representing the Lyapunov function value.\r\nfeedforwardnet is used to create feedforward neural networks for each subsystem, and configure sets up the networks with the specified input and output sizes.\r\nGenerate Training Data:\r\nThis section involves generating training data for the neural networks. This data should ideally come from simulations of the subsystems.\r\nPlaceholder data is created for illustration, using random values. dataSubsystem1 and dataSubsystem2 represent random states of each subsystem.\r\nlyapunovValues1 and lyapunovValues2 are placeholders for the Lyapunov function values corresponding to each state of the subsystems.\r\nTraining Neural Networks:\r\nThe neural networks are trained using the generated data. train function is used for this purpose.\r\nThe networks net1 and net2 are trained with their respective data (dataSubsystem1 with lyapunovValues1 and dataSubsystem2 with lyapunovValues2).\r\nCompose Global Lyapunov Function:\r\nAfter training the individual networks, a global Lyapunov function is composed using the outputs of these networks.\r\nThis composition is an example and should be adapted to the specific system under study.\r\ncomposeLyapunovFunction is an anonymous function that combines the outputs of net1 and net2 to compute the global Lyapunov function value.\r\nStability Analysis Using Global Lyapunov Function:\r\nThe final section of the code uses the composed global Lyapunov function to analyze the stability of the overall system.\r\nsystemState is a placeholder for the actual system state.\r\nglobalLyapunovValue calculates the value of the global Lyapunov function for the given state.\r\nA simple stability check is performed, where the system is considered stable if the Lyapunov function value is below a certain threshold (in this example, less than 1).\r\nThis code is a generic and simplified illustration. In practice, each step would require more detailed implementation, especially the generation of training data, the architecture of the neural networks, and the criteria used for stability analysis.","shortMessageHtmlLink":"Add files via upload"}},{"before":"08509fb379d130acd4c6ee3d92fd5c922ba9d3d6","after":"482748276a571d152cb96caa6b6c66b4e2292843","ref":"refs/heads/main","pushedAt":"2023-12-02T17:45:18.000Z","pushType":"push","commitsCount":1,"pusher":{"login":"DeepDynaSim","name":"Caglar Uyulan","path":"/DeepDynaSim","primaryAvatarUrl":"https://avatars.githubusercontent.com/u/35817872?s=80&v=4"},"commit":{"message":"Add files via upload\n\nThis code is designed to approximate a Lyapunov function for a given dynamical system using a deep neural network and to compute the orbital derivative of this function. The code consists of several key components:\r\n\r\nSystem Dynamics Function (system_dynamics): This function defines the dynamics of the system under study. It takes the state vector as input and returns its time derivative, representing how the system evolves over time.\r\n\r\nNeural Network Model: The code assumes the existence of a pre-trained TensorFlow model that approximates the Lyapunov function for the specified system. This model is a result of a deep learning process where the network learns to approximate the complex behavior of the Lyapunov function.\r\n\r\nOrbital Derivative Function (orbital_derivative): This function calculates the derivative of the Lyapunov function along the system's trajectories. It uses TensorFlow's automatic differentiation feature to compute this derivative, which is crucial for analyzing the stability of the system.\r\n\r\nVisualization Function (plot_lyapunov_and_derivative): This function generates a 2D plot of both the approximated Lyapunov function and its orbital derivative. It is particularly useful for visualizing these functions in a lower-dimensional slice of the state space, aiding in the interpretation and analysis of the system's stability properties.","shortMessageHtmlLink":"Add files via upload"}},{"before":"f5cb94bcf3b6a91482a8f747d7908812ff1deb24","after":"08509fb379d130acd4c6ee3d92fd5c922ba9d3d6","ref":"refs/heads/main","pushedAt":"2023-12-02T17:44:49.000Z","pushType":"push","commitsCount":1,"pusher":{"login":"DeepDynaSim","name":"Caglar Uyulan","path":"/DeepDynaSim","primaryAvatarUrl":"https://avatars.githubusercontent.com/u/35817872?s=80&v=4"},"commit":{"message":"Add files via upload\n\nThis code is designed to approximate a Lyapunov function for a given dynamical system using a deep neural network and to compute the orbital derivative of this function. The code consists of several key components:\r\n\r\nSystem Dynamics Function (system_dynamics): This function defines the dynamics of the system under study. It takes the state vector as input and returns its time derivative, representing how the system evolves over time.\r\n\r\nNeural Network Model: The code assumes the existence of a pre-trained TensorFlow model that approximates the Lyapunov function for the specified system. This model is a result of a deep learning process where the network learns to approximate the complex behavior of the Lyapunov function.\r\n\r\nOrbital Derivative Function (orbital_derivative): This function calculates the derivative of the Lyapunov function along the system's trajectories. It uses TensorFlow's automatic differentiation feature to compute this derivative, which is crucial for analyzing the stability of the system.\r\n\r\nVisualization Function (plot_lyapunov_and_derivative): This function generates a 2D plot of both the approximated Lyapunov function and its orbital derivative. It is particularly useful for visualizing these functions in a lower-dimensional slice of the state space, aiding in the interpretation and analysis of the system's stability properties.","shortMessageHtmlLink":"Add files via upload"}},{"before":null,"after":"f5cb94bcf3b6a91482a8f747d7908812ff1deb24","ref":"refs/heads/main","pushedAt":"2023-12-02T17:40:17.000Z","pushType":"branch_creation","commitsCount":0,"pusher":{"login":"DeepDynaSim","name":"Caglar Uyulan","path":"/DeepDynaSim","primaryAvatarUrl":"https://avatars.githubusercontent.com/u/35817872?s=80&v=4"},"commit":{"message":"Initial commit","shortMessageHtmlLink":"Initial commit"}}],"hasNextPage":false,"hasPreviousPage":false,"activityType":"all","actor":null,"timePeriod":"all","sort":"DESC","perPage":30,"cursor":"djE6ks8AAAADw8ffzgA","startCursor":null,"endCursor":null}},"title":"Activity · DeepDynaSim/DeepLyapunovFunction"}