Instrumental Variables based DREM for Online Asymptotic Identification of Perturbed Linear Systems

Core Concepts

The proposed online estimation law ensures exact asymptotic identification of unknown parameters of linear systems in the presence of unknown but bounded perturbations, and has relaxed convergence conditions compared to existing approaches.

Abstract

The content presents a novel online continuous-time parameter estimator for linear systems affected by unknown but bounded perturbations. The key highlights are:

The estimator is designed by augmenting the Dynamic Regressor Extension and Mixing (DREM) procedure with an Instrumental Variables (IV) based extension scheme and filtering with averaging.

This approach ensures that the perturbation in the new regression equations asymptotically vanishes, even if the original disturbance and system regressor are dependent.

The gradient-based estimator designed on the scalar regression equations obtained through DREM guarantees online unbiased asymptotic identification of the system parameters under weak independence and excitation assumptions.

Compared to existing approaches, the proposed estimator ensures exact asymptotic parameter convergence (P1) with exponential rate in the perturbation-free case (P2), and has relaxed convergence conditions (P3).

The theoretical results are supported by adequate numerical simulations, which demonstrate the superior performance of the proposed estimator over standard approaches.

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Key Insights Distilled From

Instrumental Variables based DREM for Online Asymptotic Identification of Perturbed Linear Systems

by Anton Glushc... at arxiv.org 04-08-2024

https://arxiv.org/pdf/2312.15631.pdf

Deeper Inquiries

How can the rate of convergence of the proposed estimator be further improved to enhance its alertness to changes in the plant parameters

To improve the rate of convergence of the proposed estimator and enhance its alertness to changes in plant parameters, several strategies can be implemented.

Adaptive Learning Rates: Implement adaptive learning rates that adjust based on the rate of change in the system parameters. This can help the estimator react more quickly to parameter variations.

Advanced Filtering Techniques: Utilize advanced filtering techniques such as Kalman filters or particle filters to improve the estimation accuracy and speed of convergence.

Model Predictive Control: Incorporate model predictive control techniques to predict future parameter changes and adjust the estimation process accordingly.

Online Parameter Tuning: Implement online parameter tuning algorithms that continuously optimize the estimator's parameters based on the system's behavior.

Nonlinear Estimation Methods: Explore nonlinear estimation methods such as extended Kalman filters or unscented Kalman filters to handle complex system dynamics and improve convergence rates.

How can the proposed estimation law be applied to solve indirect adaptive control and adaptive observer design problems

The proposed estimation law can be applied to solve indirect adaptive control and adaptive observer design problems by following these steps:

Indirect Adaptive Control:

Design an adaptive control law that uses the estimated parameters from the proposed estimator to adjust the controller parameters indirectly.
Implement a feedback loop that continuously updates the controller based on the estimated parameters to achieve desired system performance.

Adaptive Observer Design:

Use the estimated parameters from the proposed estimator to design an adaptive observer that can accurately estimate unmeasurable states of the system.
Incorporate the adaptive observer into the control system to improve state estimation and overall system performance.

Closed-Loop System Identification:

Apply the proposed estimation law in a closed-loop system to identify unknown parameters and disturbances in real-time.
Use the estimated parameters to adapt the controller and observer for improved system performance.

What specific classes of control and disturbance signals can ensure the satisfaction of both the independence requirement and the condition for relaxed convergence in the proposed approach

Specific classes of control and disturbance signals that can ensure the satisfaction of both the independence requirement and the condition for relaxed convergence in the proposed approach include:

Multiharmonic Signals:

Signals with multiple non-common frequencies can ensure independence between the regressor and perturbations, meeting the condition for relaxed convergence.

Stationary Signals:

Stationary signals with varying frequencies can help satisfy the independence requirement and ensure convergence of the estimator under the proposed approach.

Piecewise-Constant Signals:

Signals that change abruptly at certain time points can provide the necessary richness for the estimator to adapt to parameter variations and disturbances.

Sinusoidal Signals with Varying Amplitudes:

Sinusoidal signals with varying amplitudes and frequencies can create a diverse input space for the estimator, improving its robustness and convergence properties.