Adaptive Parameter Estimation under Finite Excitation: A Novel Method Combining Newton Algorithm and Time-Varying Factor

Core Concepts

A novel method combining the Newton algorithm and time-varying factor achieves exponential convergence under finite excitation for parameter estimation in nonlinear systems.

Abstract

In the field of adaptive parameter estimation, persistent excitation is crucial for exponential convergence, but practical applications may not always guarantee it. Recent research focuses on finite excitation as an alternative condition. The proposed method transforms the nominal system to a linear parameterized form using pre-filtering. Mathematical derivation outlines an estimation error accumulated cost function with detailed stability and robustness analysis. Comparative simulations demonstrate the superiority of this new method over existing ones.
Adaptive parameter estimation has wide applications in aerospace, chemical processes, and automotive systems. Various solutions have been proposed to address issues related to boundedness of estimation errors without requiring persistent excitation. The paper introduces a novel estimator that ensures exponential convergence even under relaxed excitation conditions.
The study compares different estimators like Gradient-Based Estimator (GBE), Least-Squares Estimator (LSE), Robust Adaptive Estimator (RAE), and the proposed Newton-Based Estimator (NBE). It discusses their convergence properties under both finite and persistent excitation conditions.
The NBE method guarantees boundedness of learning gains even under finite excitation conditions, ensuring robust convergence of estimated parameters. Theoretical proofs establish the effectiveness of NBE in achieving compact set convergence for estimation errors.

Stats

Persistent excitation is crucial for exponential convergence in adaptive parameter estimation.
The proposed method combines the Newton algorithm and time-varying factor for exponential convergence under finite excitation.
Comparative simulations illustrate the superiority of the new method over existing approaches.
Various solutions have been developed to ensure boundedness of estimation errors without persistent excitation.
The NBE method guarantees boundedness of learning gains even under finite excitation conditions.

Quotes

Key Insights Distilled From

Adaptive Parameter Estimation under Finite Excitation

by Siyu Chen,Ji... at arxiv.org 03-19-2024

https://arxiv.org/pdf/2305.12730.pdf

Deeper Inquiries

How does the introduction of time-varying factors impact the stability and robustness of parameter estimation methods

The introduction of time-varying factors, such as forgetting factors and weight coefficients, plays a crucial role in enhancing the stability and robustness of parameter estimation methods. By adjusting these factors over time, the estimator can adapt to changing conditions or uncertainties in the system dynamics. This adaptability helps prevent issues like unbounded growth of learning gains or estimation errors, which can lead to instability or divergence in traditional approaches. The time-varying nature allows for more flexibility in controlling the convergence rate and ensuring boundedness under varying excitation conditions.

What are potential real-world applications where finite excitation-based methods could outperform traditional approaches

Finite excitation-based methods offer advantages over traditional approaches in various real-world applications where persistent excitation may not be guaranteed or practical. For instance, in adaptive control systems for aerospace vehicles, finite excitation conditions could help avoid unnecessary energy consumption or stress on aircraft components caused by continuous high-frequency inputs required for persistent excitation. Additionally, industries with processes that experience intermittent disturbances or changes could benefit from finite excitation-based methods to achieve accurate parameter estimations without relying on constant excitations.

How can these findings be applied to other fields beyond engineering to improve iterative algorithms or estimations

The findings from applying finite excitation-based methods to improve iterative algorithms and estimations can be extended beyond engineering disciplines into other fields like finance, healthcare, and artificial intelligence. In finance, these techniques could enhance risk management models by providing more robust estimates of market parameters under varying market conditions. In healthcare analytics, they could optimize patient treatment plans by adapting to changing patient data trends over time. Furthermore, in AI applications like reinforcement learning algorithms, incorporating time-varying factors based on environmental stimuli could improve decision-making processes and policy optimization strategies.