Lifted Predictive Control for Nonlinear Digital Twin Dynamics
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing systems struggle to accurately characterize and control systems with complicated, nonlinear dynamics, particularly in electromechanical and predictive management systems, due to limitations in linear representations, leading to inefficiencies and potential catastrophic consequences from unmanaged state changes.
Innovation Solution
The implementation of lifted predictive controllers using digital twin models and neural networks to create a linear representation of nonlinear systems, allowing for efficient modeling and control through the use of Koopman Operators and Dynamic Mode Decomposition, enabling quick updates and adaptability.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If linear representations are used for modeling and control, then computational efficiency is improved, but the ability to characterize complicated nonlinear dynamics deteriorates
Solution Approach 1:
The patent applies dimensionality change by transforming the system representation from the original state space to a lifted space using Koopman operators. This transformation maps nonlinear dynamics in the original space to linear dynamics in the lifted space, allowing linear control methods to effectively characterize and control complicated nonlinear systems while maintaining computational efficiency.
2Device complexity
If existing linear control approaches are used, then system simplicity is maintained, but the ability to manage rapid state changes in high-dimensional spaces deteriorates
Solution Approach 1:
The patent transforms the control problem from the original high-dimensional state space to a lifted space where rapid state changes and complex dynamics can be captured more effectively. The Koopman operator framework enables linear methods to operate in this transformed space, maintaining system simplicity while improving the ability to manage rapid state changes in high-dimensional spaces.
3Productivity
If finite prediction horizons are used, then computational tractability is improved, but adaptability to unforeseen circumstances and chaotic principles deteriorates
Solution Approach 1:
The patent implements continuous monitoring and update mechanisms that allow the predictive model to adapt to new information and unforeseen circumstances. By incorporating feedback loops that enable model updates as new data becomes available, the system maintains computational tractability while improving adaptability to changing conditions and chaotic behavior.
Data Source
AI summary
Various of the disclosed embodiments provide systems and methods for creating, deploying, and monitoring “lifted” controller systems able to operate in challenging environments expressing complicated dynamics. These controller systems may employ operator-based approaches, such as the Koopman Operator, to represent the system's complicated dynamics. Such improved representations may facilitate a variety of benefits, such as longer prediction horizons, more effective system predictions, and improved controls. Exemplary controllers suitable for managing both electromechanical systems, such as vehicles, as well as controllers suitable for managing resource allocation systems, such as healthcare networks, are disclosed. Variations and miscellaneous improvements to the creation, operation, and management of the “lifted” controller systems are likewise provided.