Parameter Estimation-Based States Reconstruction of Uncertain Linear Systems with Overparameterization and Unknown Additive Perturbations

Основні поняття

A novel adaptive observer is proposed for reconstructing physical states in uncertain linear systems, ensuring convergence to zero under specific conditions.

Анотація

The article discusses a novel approach for state reconstruction in uncertain linear systems with overparameterization and unknown additive perturbations. The proposed adaptive observer aims to reconstruct the physical state of the original system, ensuring exponential convergence of the reconstruction error to zero under certain conditions. By using a parametrization method for uncertain linear systems with unknown additive perturbations, along with dynamic regressor extension and mixing procedures, the authors provide detailed stability analysis and simulation results to validate their theoretical findings. The study extends previous work by addressing systems with disturbances generated by exosystems with fully uncertain parameters.

The introduction highlights the importance of simultaneous reconstruction of unmeasured system states and unknown parameters using adaptive observers. Two main design principles are discussed based on existing studies by R. Carroll and K. S. Narendra.

The article presents techniques based on system transformation to an observer canonical form for parameter estimation in linear time-invariant systems. It also introduces a novel adaptive algebraic observer for uncertain linear time-varying systems with unknown additive perturbations.

Overall, the study focuses on developing an adaptive observer that can accurately reconstruct physical states in uncertain linear systems, providing a significant advancement in state estimation methodologies.

Статистика

Financial support provided by Grants Council of the President of Russian Federation (MD-1787.2022.4).

Цитати

"The proposed solution uses a recently published parametrization of uncertain linear systems with unknown additive perturbations."
"Main idea is to obtain LRE w.r.t TI = T −1 with clever/tedious parametrization."

Ключові висновки, отримані з

Parameter Estimation-Based States Reconstruction of Uncertain Linear Systems with Overparameterization and Unknown Additive Perturbations

by Anton Glushc... о arxiv.org 03-14-2024

https://arxiv.org/pdf/2308.10289.pdf

Глибші Запити

How can this adaptive observer be applied to real-world engineering systems

The adaptive observer proposed in the study can be applied to real-world engineering systems by providing a robust method for state reconstruction in uncertain linear time-invariant systems with overparameterization and unknown additive perturbations. This approach allows for the estimation of system states even when certain parameters are not directly measurable, making it suitable for various control applications where accurate state information is crucial. By utilizing adaptive laws and parameter estimators, this observer can enhance system performance, improve stability, and enable better decision-making based on reliable state reconstructions.

What are potential limitations or challenges when implementing this approach in practical scenarios

While the adaptive observer offers significant benefits for state reconstruction in complex systems, there are potential limitations and challenges when implementing this approach in practical scenarios. One challenge could be related to the computational complexity of the algorithms involved, especially as system dimensions increase or when dealing with real-time applications that require fast response times. Additionally, ensuring convergence of parameter estimates and avoiding issues like singularities or numerical instabilities may require careful tuning of parameters and validation through extensive simulations or experiments. Another limitation could arise from assumptions made about system dynamics or disturbances which may not always hold true in real-world settings, leading to discrepancies between theoretical models and actual observations.

How does this research contribute to advancements in control theory beyond traditional methods

This research contributes to advancements in control theory beyond traditional methods by offering a novel solution for state reconstruction in uncertain linear systems with overparameterization and unknown perturbations. The proposed adaptive observer addresses key challenges such as reconstructing physical states instead of virtual ones, ensuring exponential convergence under specific conditions, and handling uncertainties introduced by external disturbances generated by exosystems with fully uncertain constant parameters. By combining techniques from parametrized uncertainty modeling, dynamic regressor extension procedures, and physical states reconstruction methods developed by the authors, this research provides a comprehensive framework for addressing complex control problems in practical engineering systems. The integration of advanced mathematical tools with practical considerations enhances the applicability of control theory in diverse industrial sectors where precise state estimation is essential for optimal system performance.