Analysis and design of dynamical system controllers using neural differential equations
Inventors
Divakaran, Ajay • Roy, Anirban • Jha, Susmit
Assignees
Publication Number
US-12236330-B2
Publication Date
2025-02-25
Expiration Date
2041-05-26
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Abstract
In general, the disclosure describes techniques for characterizing a dynamical system and a neural ordinary differential equation (NODE)-based controller for the dynamical system. An example analysis system is configured to: obtain a set of parameters of a NODE model used to implement the NODE-based controller, the NODE model trained to control the dynamical system; determine, based on the set of parameters, a system property of a combined system comprising the dynamical system and the NODE-based controller, the system property comprising one or more of an accuracy, safety, reliability, reachability, or controllability of the combined system; and output the system property to modify one or more of the dynamical system or the NODE-based controller to meet a required specification for the combined system.
Core Innovation
The invention provides techniques for characterizing a dynamical system and a neural ordinary differential equation (NODE)-based controller for that system. An analysis system obtains a set of parameters from a NODE model, which has been trained to control a physical process modeled as a dynamical system. With these parameters, the system determines a property of the combined system (including both the dynamical process and the NODE-based controller), where the property may be accuracy, safety, reliability, reachability, or controllability.
The problem addressed is the difficulty in analyzing or characterizing dynamical systems that are controlled using neural network-based controllers. Existing approaches often rely on deep neural networks which are hard to interpret and require brute force approximation, making it challenging to extract transfer functions, analyze system properties, or ensure compliance with operational specifications.
This disclosure offers a systematic method to obtain analytically tractable representations of NODE-based controllers by processing their learned parameters. An analysis system leverages these tractable models to calculate system properties of the overall closed-loop system, enabling modifications to the dynamical process and/or the controller to bring the system within required specifications. This approach can be iteratively applied to improve controller design or system operation parameters.
Claims Coverage
The patent has three independent claims, each detailing an analysis system, a system with a NODE-based controller and analysis, and a method for characterizing and modifying NODE-controlled dynamical systems.
Analysis system for characterizing a NODE-based controller and dynamical system
An analysis system comprising memory and one or more processors is configured to: - Obtain a set of parameters from a NODE model used to implement a controller, where the NODE model is trained to control a dynamical system. - Determine, based on these parameters, a system property of the combined system (dynamical system and NODE-based controller), the property being one or more of: accuracy, safety, reliability, reachability, or controllability. - Output the determined system property to modify one or more of the dynamical system or NODE-based controller to meet required specifications for the combined system.
System with NODE-based controller, analysis, and property-based modification
A system comprising: - A NODE-based controller for a dynamical system, with processing circuitry and a trained NODE model possessing a set of parameters. - An analysis system with processing circuitry configured to: - Process the set of parameters to compute a system property of the combined system (dynamical system and NODE controller), where the property is accuracy, safety, reliability, reachability, or controllability. - Modify one or more of the dynamical system or NODE-based controller to meet the required specification for the dynamical system.
Method for characterizing and modifying NODE-controlled dynamical systems
A method comprising: - Obtaining, by an analysis system, a set of parameters from a NODE model used to implement a NODE-based controller, the NODE model trained to control a dynamical system. - Determining, based on these parameters, a system property of a combined system (dynamical system and NODE-based controller), the property being one or more of: accuracy, safety, reliability, reachability, or controllability. - Outputting the system property to modify one or more of the dynamical system or NODE-based controller to meet a required specification for the combined system.
The inventive features center on: automated analysis of NODE-based controllers through parameter extraction, computation of specific system properties, and the feedback-driven modification of either the controller or dynamical process to align with desired specifications. This is achieved for systems where controllers are modeled by NODE architectures.
Stated Advantages
Provides analytically tractable neural network controllers, allowing for easier extraction and analysis of transfer functions compared to traditional deep neural networks.
Enables systematic analysis of system properties (such as accuracy, safety, reliability, reachability, or controllability) for the combined system of controller and dynamical process.
Improves scalability due to the parametric efficiency of NODE models versus traditional neural networks.
Offers more adaptive complexity and avoids restrictive assumptions like linear modeling present in prior approaches.
Documented Applications
Modeling and controlling real-world physical processes such as robots, robotic environments, computing systems, flight systems, reinforcement learning systems, navigation systems, anatomical processes, autonomous driving systems, and industrial processes.
Applications to autonomous vehicles, firewalls or intrusion and detection systems, building management systems, factory monitoring and control systems, and flight control systems.
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