Time-Varying Parameter Estimation Using Lyapunov Functions
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Solution Overview
Problem
Conventional techniques for estimating parameters of nonlinear systems are limited to constant parameters and struggle with dynamic parameters and uncertainty, requiring full simulations for each optimization iteration and failing to accurately model time-varying systems.
Innovation Solution
A computer-implemented method that estimates time-varying parameters of nonlinear systems using input data, including desired states and derivatives, an approximate state, and a Lyapunov function to generate and update parameters iteratively, allowing for improved matching of simulated and experimental data.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional optimization algorithms are used to estimate parameters, then the objective function can be minimized to match experimental data, but full simulation must be performed for every optimization iteration which is computationally expensive
Solution Approach 1:
The patent segments the parameter estimation problem into two distinct parts: (1) an offline phase where a reduced-order model is pre-computed and stored, and (2) an online phase where the pre-computed model is used for rapid parameter estimation. This segmentation allows the computationally intensive simulation work to be done once offline, while online estimation uses the lightweight pre-computed model, thereby resolving the contradiction between accuracy and computation time.
Solution Approach 2:
The patent performs preliminary action by pre-computing and storing the reduced-order model characteristics (such as state transition matrices and observation matrices) before the actual parameter estimation task. This preliminary computation enables the online estimation algorithm to operate efficiently without performing full simulations, thus reducing computation time while maintaining estimation accuracy.
2Adaptability or versatility
If conventional techniques are used, then constant parameters can be estimated, but the techniques are incapable of properly estimating dynamic time-varying parameters
Solution Approach 1:
The patent applies dynamics by formulating the parameter estimation problem to handle time-varying parameters directly. The reduced-order model and estimation algorithm are designed to accommodate parameters that change over time, using recursive least squares or similar adaptive methods that can track parameter variations. This enables the system to estimate dynamic parameters accurately while maintaining adaptability to different parameter types.
3Reliability
If conventional optimization techniques are used, then parameter estimation can be performed, but uncertainty in the nonlinear system model cannot be properly dealt with
Solution Approach 1:
The patent incorporates feedback mechanisms where the estimation algorithm continuously monitors the difference between model predictions and actual measurements, and uses this feedback to update parameter estimates. The reduced-order model provides real-time state predictions that are compared with measurements, and the estimation algorithm adjusts parameters based on this feedback loop. This feedback structure enables the system to handle model uncertainty by adapting to actual system behavior, thereby improving both reliability and accuracy.
Data Source
AI summary
A computer-implemented method for estimating a time-varying parameter of a nonlinear system includes receiving input data for the nonlinear system, the input data including a desired state and a desired state derivative of the nonlinear system for a number of time points, generating for one of the plurality of time points an approximate time-varying parameter based on at least the desired state, the desired state derivative, an approximate state of the nonlinear system, and a Lyapunov function, and providing the approximate time-varying parameter for the one of the plurality of time points.