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Deep-Learning-Based Identification of LPV Models for Nonlinear Systems

Published 8 Apr 2022 in eess.SY, cs.SY, math.DS, and math.OC | (2204.04060v2)

Abstract: The Linear Parameter-Varying (LPV) framework provides a modeling and control design toolchain to address nonlinear (NL) system behavior via linear surrogate models. Despite major research effort on LPV data-driven modeling, a key shortcoming of the current identification theory is that often the scheduling variable is assumed to be a given measured signal in the data set. In case of identifying an LPV model of a NL system, the selection of the scheduling map, which describes the relation to the measurable scheduling signal, is put on the users' shoulder, with only limited supporting tools available. This choice however greatly affects the usability and complexity of the resulting LPV model. This paper presents a deep-learning-based approach to provide joint estimation of a scheduling map and an LPV state-space model of a NL system from input-output data, and has consistency guarantees under general innovation-type noise conditions. Its efficiency is demonstrated on a realistic identification problem.

Citations (9)

Summary

  • The paper introduces a deep learning framework that concurrently estimates the scheduling map and LPV state-space model for nonlinear system identification.
  • The LPV Sub-Space Encoder Network achieves robust performance under generalized noise conditions, ensuring reliability across varied datasets.
  • Simulation results validate the approach's efficiency and improved representational clarity compared to traditional LPV identification methods.

Deep-Learning-Based Identification of LPV Models for Nonlinear Systems

Introduction

The paper introduces a methodology for the identification of Linear Parameter-Varying (LPV) models that can represent nonlinear (NL) system behaviors using deep learning techniques. LPV models provide a structured framework for managing the complexity of NL systems by utilizing linear approximations that vary depending on certain parameters. A key challenge in LPV model identification is the determination of the scheduling map, which critically influences the model's effectiveness and complexity. Traditionally, this map is determined by measured signals, placing a considerable burden on users to make optimal choices without comprehensive support.

Problem Statement

The core objective addressed in the paper is developing an approach for identifying both the scheduling map and the LPV state-space model concurrently, using input-output data. The authors argue that existing methods largely assume the availability of a measurable scheduling variable, which limits their applicability and the autonomous ability of such systems to capture and adapt to complex nonlinear dynamics. This assumption necessitates user intervention with limited supporting tools, potentially impacting the model's applicability and the simplicity of its representation.

LPV Sub-Space Encoder Network

The proposed solution leverages deep learning techniques to yield a joint estimation of the scheduling map and the LPV model. Specifically, a neural network architecture called the LPV Sub-Space Encoder Network is utilized to process input-output data. This network structure is an extension of deep encoder networks historically used in the context of nonlinear system identification [beintema2021nonlinear]. The deep learning model provides consistency guarantees under generalized innovation-type noise conditions, ensuring robustness and reliability across varied datasets.

Simulation Results

Empirical analysis detailed within the paper involves applying the developed methodology to a realistic identification problem. The simulations demonstrate the efficiency and practicality of the approach, providing numerical evidence of effectiveness compared to previous methods. The results underscore the LPV Sub-Space Encoder Network's capability to produce identifiable and usable scheduling maps alongside the LPV model, optimizing representational clarity and predictive accuracy.

Conclusion

This paper contributes significantly to advancing LPV model identification by alleviating the need for external intervention during the scheduling map determination, thus streamlining the process. The integration of deep learning methods facilitates more autonomous and accurate modeling of nonlinear systems. The ongoing development in this research area holds potential implications for various applications in control systems where NL system behavior modeling is crucial. Future developments may focus on enhancing model complexities and adaptability, ensuring broader spectrum applications in diverse fields such as aerospace systems and autonomous vehicle control.

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