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Hessian matrix estimation in hybrid systems based on an embedded FFNN.
Seung-Mook Baek1, Jung-Wook Park
1School of Electrical and Electronic Engineering, Yonsei University, Seoul 120-749, Korea. sm_baek@yonsei.ac.kr
IEEE Transactions on Neural Networks
|March 19, 2010
Summary
This study introduces a novel Hessian matrix estimation method for nonsmooth nonlinear parameters in hybrid systems. The feedforward neural network (FFNN) approach enables precise tuning of engineering system limiters.
Area of Science:
- Control Systems Engineering
- Computational Mathematics
- Artificial Intelligence
Background:
- Hybrid systems, characterized by differential-algebraic-impulsive-switched (DAIS) dynamics, present significant challenges in parameter estimation.
- Accurate estimation of system dynamics and their sensitivities is crucial for effective control and optimization.
- Nonsmooth nonlinear parameters complicate traditional estimation techniques.
Purpose of the Study:
- To develop and describe a method for estimating the Hessian matrix of nonsmooth nonlinear parameters in DAIS hybrid systems.
- To apply the feedforward neural network (FFNN) for accurate trajectory sensitivity and Hessian estimation.
- To utilize the estimated Hessian for optimal tuning of saturation limiters in practical engineering applications.
Main Methods:
- Modeling hybrid systems using the differential-algebraic-impulsive-switched (DAIS) structure.
- Employing a feedforward neural network (FFNN) to identify the full system dynamics.
- Estimating second-order derivatives (Hessian matrix) of an objective function with respect to nonlinear parameters using FFNN-derived gradient information (trajectory sensitivities).
Main Results:
- Successful estimation of the Hessian matrix for nonsmooth nonlinear parameters within the hybrid system framework.
- Demonstration of FFNN's capability in accurately calculating trajectory sensitivities.
- Effective application of the estimated Hessian for optimal tuning of a saturation limiter.
Conclusions:
- The proposed FFNN-based Hessian estimation method is effective for complex hybrid systems.
- This approach provides a robust tool for parameter identification and system optimization in engineering.
- The technique enhances the performance of practical engineering systems through precise control tuning.
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