Adaptive Dynamic Mode Decomposition for Stable Reduced-Order Control
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Solution Overview
Problem
Existing data-driven control methods lack robustness in handling uncertainties in dynamical systems, leading to instability and prediction degradation due to truncation of higher modes and parametric uncertainties, particularly in nonlinear systems like HVAC and windfarms.
Innovation Solution
The development of robust adaptive dynamic mode decomposition (RA-DMD) models that incorporate a robust closure model framework, using dynamic mode decomposition to reduce partial differential equations to stable reduced-order models, and an adaptation layer for real-time tuning via data-driven extremum seeking controllers.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If dynamic mode decomposition is used to reduce PDE models to finite-dimensional ODEs, then computational efficiency is improved, but stability loss and prediction degradation occur due to truncation of higher modes and parametric uncertainties
Solution Approach 1:
The patent implements dynamic adaptation of the reduced-order model by continuously tuning parameters based on real-time system behavior. The adaptation layer modifies model parameters dynamically to compensate for truncation errors and parametric uncertainties, allowing the model to maintain stability across varying operating conditions while preserving computational efficiency.
Solution Approach 2:
The patent introduces a feedback mechanism where the reduced-order model predictions are compared with actual system measurements, and the discrepancy is used to update model parameters. This closed-loop approach corrects the instability caused by mode truncation and parametric uncertainties, ensuring the model remains reliable while maintaining the computational benefits of reduction.
2Device complexity
If data-driven models are constructed from operational data, then model design complexity is reduced, but robustness to uncertainties deteriorates due to uncaptained system uncertainties and noisy measurements
Solution Approach 1:
The patent creates a composite modeling approach that combines data-driven dynamic mode decomposition with physics-based reduced-order modeling frameworks. This hybrid structure leverages the simplicity of data-driven methods while incorporating physics-based constraints and uncertainty quantification techniques to enhance robustness against uncaptained uncertainties and measurement noise.
Solution Approach 2:
The patent preemptively addresses robustness issues by integrating uncertainty quantification and validation procedures during the model construction phase. By preparing the model with built-in robustness mechanisms before deployment, it compensates for the inherent vulnerability of data-driven methods to uncertainties and noisy measurements without increasing operational complexity.
Data Source
AI summary
A computer-implemented method is provided. The computer-implemented includes a data-driven model and a robust closure model stored in a memory by using a processor for controlling a system. The computer-implemented method includes steps of acquiring sensor signals from at least one sensor of the system via an interface, computing a state of the system based on the sensor signals, determining a gain of the robust closure model based on the state of the system, reproducing a state of the system based on the determined gain, estimating a physics-based model of the system by combining the data-driven model and the robust closure model, and generating control commands by mapping the state of the system using the estimated physics-based model.